Monty Hall Simulations

太过爱你忘了你带给我的痛 2022-08-20 07:15 96阅读 0赞

#### The Monty Hall Problem ####

There’ve been many simulations of the [Monty Hall-problem][] done in R. But since I’m trying to learn R, I wanted to try to simulate the paradox over many different trails and plot them all using *ggplot2.*The problem was originally posed as follows (from wikipedia):

“Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1 \[but the door is not opened\], and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?”

#### Writing the R code ####

Most of you already now what strategy is best. But to try it out I wrote the following code:

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     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># load libraries</code> 
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      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">library</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(ggplot2)</code> 
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      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">library</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(reshape2)</code> 
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       &nbsp; 
     </div> 
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      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">N &lt;- 10000 </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># Number of guesses per trail</code> 
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      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">T &lt;- 100 </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># trails</code> 
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       &nbsp; 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># Function to create a list with N-number</code> 
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      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># winning doors who are randomly chosen from 1,2,3</code> 
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      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">winning.door.func &lt;- </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">function</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">() { </code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">winning.door &lt;- </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">sample</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(1:3, N, replace=</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-weight:bold!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,102,153)!important; background:none!important">TRUE</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">)</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">}</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
       &nbsp; 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># Create a matrix with the winning.door.func()</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># replicated T-number of times.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">winning.door.matrix &lt;- </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">replicate</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(T, </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">winning.door.func</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">())</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">switch.door.matrix &lt;- 2 + (winning.door.matrix != 2)</code> 
     </div> 
    </div> </td> 
  </tr> 
 </tbody> 
</table>

To keep it simple, we **always** chose door number 1 as our first choice. The simulation would run the same, regardless of which door we choose. Since we always start with door 1, we can calculate which door we must switch to by 2 + (winning.door.matrix != 2). We can never choose to switch to either door 2 or 3 in the same game. Because if door 2 is the winner, door 3 will be opened by the host and if door 3 is the winner, door 2 will be opened by the host. Therefore, if we switch to 2 and 2 is the winner the condition in this calculation will be FALSE, hence 2 will be added to switch.door.matrix. And, likewise, if door 2 is not the winner, the condition will be TRUE and 3 will be added toswitch.door.matrix. If the winning door is 1 the host will open either door 2 or 3. And we will add 2 to our matrix, because the condition is not met. Since we record switches in this way, we can calculate winnings by switch.door.matrix == winning.door.matrix.

<table style="border-collapse:collapse; border-spacing:0px; width:668px; margin:0px!important; border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; table-layout:auto!important; background:none!important"> 
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   <td style="border:0px!important; padding:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; color:rgb(175,175,175)!important; background:none!important"> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      1 
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      2 
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      3 
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      4 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      5 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      6 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      7 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      8 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      9 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      10 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      11 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      12 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      13 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      14 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      15 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      16 
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      17 
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      23 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
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      25 
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      29 
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      30 
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      31 
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      32 
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      33 
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      34 
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      35 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      36 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      37 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      38 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      39 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      40 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      41 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      42 
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    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      43 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      44 
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      45 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      46 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      47 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      48 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      49 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      50 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      51 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      52 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      53 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      54 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      55 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      56 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      57 
    </div> 
    <div style="border-width:0px 3px 0px 0px!important; border-right-style:solid!important; border-right-color:rgb(108,226,108)!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 0.5em 0px 1em!important; position:static!important; right:auto!important; text-align:right!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
      58 
    </div> </td> 
   <td style="width:628.667px; border:0px!important; padding:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; background:none!important"> 
    <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:relative!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; background:none!important"> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important">## Option 1: STAY with first choice.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important">#create a matrix with number of winnings for each guess and trail.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">stay.winnings &lt;- switch.door.matrix</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># change value to 1 on each winnings.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">stay.winnings[winning.door.matrix == 1] &lt;- 1</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># change value to 0 on each loss.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">stay.winnings[winning.door.matrix != 1] &lt;- 0</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># make each trail cumulative for nicer plots.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">for </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(i </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-weight:bold!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,102,153)!important; background:none!important">in</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important"> 1:T) { </code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">stay.winnings[,i] &lt;- </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">cumsum</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(stay.winnings[,i])</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">}</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
       &nbsp; 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important">## Option 2: Always switch</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">switch.winnings &lt;- switch.door.matrix</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># change value to 1 if we switch to the winning door.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">switch.winnings[winning.door.matrix == switch.door.matrix] &lt;- 1</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># change value to 0 if we switch to a losing door.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">switch.winnings[winning.door.matrix != switch.door.matrix] &lt;- 0</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># make each trail cumulative for nicer plots.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">for </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(i </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-weight:bold!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,102,153)!important; background:none!important">in</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important"> 1:T) { </code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">switch.winnings[,i] &lt;- </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">cumsum</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(switch.winnings[,i])</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">}</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
       &nbsp; 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># Create a data.frames from the switch.door.matrix</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">switch.data &lt;- </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">as.data.frame</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(switch.winnings)</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># Add a column named "category" cointaining row index.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">switch.data$category &lt;- </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">row.names</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(switch.data)</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># "Melt" the data.frame from wide to long-format.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># The reason for doing this is so we can plot</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># each trail in the same plot, using trail as "group".</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">switch.data.molten &lt;- </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">melt</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(switch.data)</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
       &nbsp; 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># Melt stay data.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">stay.data &lt;- </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">as.data.frame</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(stay.winnings)</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">stay.data$category &lt;- </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">row.names</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(stay.winnings)</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">stay.data.molten &lt;- </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">melt</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(stay.data)</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
       &nbsp; 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># Plot using ggplot2.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># start with stay.data</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">ggplot</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(stay.data.molten, </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">aes</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(1:N,value, group=variable, color=</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">"Stay"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">)) +</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">ylab</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">"Winnings (cumulative)"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">) + </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># y-label</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">xlab</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">"Guesses"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">) + </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># x-label</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># draw stay.data as a lines</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">geom_line</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(alpha = </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">I</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(3/10)) +</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># add another layer to draw switch.data as a lines.</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">geom_line</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(data=switch.data.molten, </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">aes</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(,value, group=variable,</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">color=</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">"Switch"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">),</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">alpha = </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">I</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(3/10)) +</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># create a manual legend</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">scale_color_manual</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">"Choices"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">, values = </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">c</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">"Switch"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important"> = </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">"blue"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">,</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">"Stay"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important"> = </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">"red"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">)) +</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important"># Title over the plot</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">opts</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(title = </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">paste</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(T, </code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">"Monty Hall-simulations \n each containing"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">, N,</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">"guesses"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">))</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important">
       &nbsp; 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(0,130,0)!important; background:none!important">#Calculate mean probablities</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">mean</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">colMeans</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(switch.data[N,1:T]))/N</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">mean</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">colMeans</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(stay.data[N,1:T]))/N</code> 
     </div> 
     <div style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px 1em!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-size:1em!important; direction:ltr!important; white-space:pre!important"> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">ggsave</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(filename=</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:rgb(255,20,147)!important; background:none!important">paste</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">(</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">"monty_hall_"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">,T,</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">"x"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">,N,</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; color:blue!important; background:none!important">".jpg"</code> 
      <code style="border:0px!important; bottom:auto!important; float:none!important; height:auto!important; left:auto!important; line-height:1.1em!important; margin:0px!important; outline:0px!important; overflow:visible!important; padding:0px!important; position:static!important; right:auto!important; top:auto!important; vertical-align:baseline!important; width:auto!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; direction:ltr!important; display:inline!important; background:none!important">), dpi=300)</code> 
     </div> 
    </div> </td> 
  </tr> 
 </tbody> 
</table>

# Results #

I ran the codes using different values for trails (T) and guesses (N). I started with 100 trails x 10 guesses and ended with 100 trails x 10 000, and it clearly demonstrates that we need quite a lot of guesses before the lines converge towards the expected value. The 100 x 10 000 simulation gave a mean probability of winning if you chose not to change door = 0.333701 and 0.666299 if you always switched door. But already at the 100 x 100 plot we can see that it’s always better to switch door.

[Monty Hall 100 x 10][]  
[Monty Hall 100 x 50][]  
[Monty Hall 100 x 100][]  
[Monty Hall 100 x 500][]  
[Monty Hall 100 x 5000][]  
[Monty Hall 100 x 10000][]

#### Resources used ####

For this R session I used the following books:  
Matloff, N. (2011).  *The Art of R Programming*. San Francisco: No Starch Pess.  
Wickham, H. (2009).  *ggplot2: elegant graphics for data analysis*. New York: Springer.

[Monty Hall-problem]: http://en.wikipedia.org/wiki/Monty_hall_problem
[Monty Hall 100 x 10]: http://rpsychologist.com/wp-content/uploads/2012/03/monty_hall_100x10.jpg
[Monty Hall 100 x 50]: http://rpsychologist.com/wp-content/uploads/2012/03/monty_hall_100x50.jpg
[Monty Hall 100 x 100]: http://rpsychologist.com/wp-content/uploads/2012/03/monty_hall_100x100.jpg
[Monty Hall 100 x 500]: http://rpsychologist.com/wp-content/uploads/2012/03/monty_hall_100x500.jpg
[Monty Hall 100 x 5000]: http://rpsychologist.com/wp-content/uploads/2012/03/monty_hall_100x5000.jpg
[Monty Hall 100 x 10000]: http://rpsychologist.com/wp-content/uploads/2012/03/monty_hall_100x10000.jpg