<story><title>Monty Hall Problem</title><url>https://en.wikipedia.org/wiki/Monty_Hall_problem</url></story><parent_chain><item><author>hinkley</author><text>You want to have an ugly argument with other developers, bring up the Monty Hall problem. People who are wrong will &lt;i&gt;not&lt;/i&gt; let it go.&lt;p&gt;We had it beaten into us not to use truth tables to solve problems in college, because it doesn&amp;#x27;t scale. But the Monty Hall problem has a finite set of states you can easily write on a piece of paper. And then you&amp;#x27;ll see that it jumps from 2&amp;#x2F;6 successes to 3&amp;#x2F;6.&lt;p&gt;I tried to replicate that table under duress once (see initial comment) and I couldn&amp;#x27;t get it sorted. I should try it again and write it down this time.&lt;p&gt;Edit: Why do work when you can find someone else who already has:&lt;p&gt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;www.statisticshowto.datasciencecentral.com&amp;#x2F;probability-and-statistics&amp;#x2F;monty-hall-problem&amp;#x2F;&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.statisticshowto.datasciencecentral.com&amp;#x2F;probabili...&lt;/a&gt;&lt;p&gt;and particular to my statement, this table:&lt;p&gt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;www.statisticshowto.datasciencecentral.com&amp;#x2F;wp-content&amp;#x2F;uploads&amp;#x2F;2014&amp;#x2F;12&amp;#x2F;monty-hall-problem2.png&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.statisticshowto.datasciencecentral.com&amp;#x2F;wp-conten...&lt;/a&gt;&lt;p&gt;When switching the number of lose scenarios is lower than a naive expectation of outcomes.</text></item><item><author>drfuchs</author><text>I found the easiest way to convince non-mathematical types is by suggesting we do the million-door version: “Ok, pick a door between 1 and 1,000,000. We’ll call that door N.  Now, I’ll open 999,998 bad doors.  So, now only door N and door 223,205 are still closed, and one of them has the good prize.  Want to keep door N, or swap?”</text></item></parent_chain><comment><author>shadowgovt</author><text>Reasoning through Monty Hall was my freshmen year introduction to the power of computing simulation.&lt;p&gt;I couldn&amp;#x27;t get my mind to accept the explanation. So I coded it and ran the simulation 100,000 times.&lt;p&gt;I got about 50,000 instances where switching won the prize. Biases confirmed.&lt;p&gt;... until I found the bug in my code where Monty was allowed to open the door containing the car as the one showed to the player.&lt;p&gt;Fixed the bug, and switching won the prize in about 66,666 instances.</text></comment>
<story><title>Monty Hall Problem</title><url>https://en.wikipedia.org/wiki/Monty_Hall_problem</url></story><parent_chain><item><author>hinkley</author><text>You want to have an ugly argument with other developers, bring up the Monty Hall problem. People who are wrong will &lt;i&gt;not&lt;/i&gt; let it go.&lt;p&gt;We had it beaten into us not to use truth tables to solve problems in college, because it doesn&amp;#x27;t scale. But the Monty Hall problem has a finite set of states you can easily write on a piece of paper. And then you&amp;#x27;ll see that it jumps from 2&amp;#x2F;6 successes to 3&amp;#x2F;6.&lt;p&gt;I tried to replicate that table under duress once (see initial comment) and I couldn&amp;#x27;t get it sorted. I should try it again and write it down this time.&lt;p&gt;Edit: Why do work when you can find someone else who already has:&lt;p&gt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;www.statisticshowto.datasciencecentral.com&amp;#x2F;probability-and-statistics&amp;#x2F;monty-hall-problem&amp;#x2F;&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.statisticshowto.datasciencecentral.com&amp;#x2F;probabili...&lt;/a&gt;&lt;p&gt;and particular to my statement, this table:&lt;p&gt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;www.statisticshowto.datasciencecentral.com&amp;#x2F;wp-content&amp;#x2F;uploads&amp;#x2F;2014&amp;#x2F;12&amp;#x2F;monty-hall-problem2.png&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.statisticshowto.datasciencecentral.com&amp;#x2F;wp-conten...&lt;/a&gt;&lt;p&gt;When switching the number of lose scenarios is lower than a naive expectation of outcomes.</text></item><item><author>drfuchs</author><text>I found the easiest way to convince non-mathematical types is by suggesting we do the million-door version: “Ok, pick a door between 1 and 1,000,000. We’ll call that door N.  Now, I’ll open 999,998 bad doors.  So, now only door N and door 223,205 are still closed, and one of them has the good prize.  Want to keep door N, or swap?”</text></item></parent_chain><comment><author>anon1m0us</author><text>&amp;gt; And then you&amp;#x27;ll see that it jumps from 2&amp;#x2F;6 successes to 3&amp;#x2F;6.&lt;p&gt;It jumps to 4&amp;#x2F;6! Even better.</text></comment>