<story><title>The Time Everyone “Corrected” the World’s Smartest Woman (2015)</title><url>https://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/</url></story><parent_chain><item><author>javajosh</author><text>So this is at least in part about the &amp;quot;Monty Hall Problem&amp;quot; and why it&amp;#x27;s solution not intuitive. The article missed an important angle: when the host opens a door, he&amp;#x27;s giving you &lt;i&gt;more information&lt;/i&gt;, which explains why it&amp;#x27;s better to switch. If you&amp;#x27;re the host, you need to know which door the car is behind to do your job 2&amp;#x2F;3 of the time, to avoid revealing it.&lt;p&gt;It&amp;#x27;s this quality of unexpected information exchange that I find most fascinating about this particular puzzle!</text></item></parent_chain><comment><author>haberman</author><text>When you choose the first door, you are partitioning the &amp;quot;board&amp;quot; into two parts: the door you chose, and &amp;quot;everything else&amp;quot;.&lt;p&gt;By opening a door, Monty lets you cover 100% of the &amp;quot;everything else&amp;quot; partition using only one guess.&lt;p&gt;So now you get to choose between partition 1, which covers 1&amp;#x2F;3 of the board, and partition 2, which covers 2&amp;#x2F;3 of the board.</text></comment>
<story><title>The Time Everyone “Corrected” the World’s Smartest Woman (2015)</title><url>https://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/</url></story><parent_chain><item><author>javajosh</author><text>So this is at least in part about the &amp;quot;Monty Hall Problem&amp;quot; and why it&amp;#x27;s solution not intuitive. The article missed an important angle: when the host opens a door, he&amp;#x27;s giving you &lt;i&gt;more information&lt;/i&gt;, which explains why it&amp;#x27;s better to switch. If you&amp;#x27;re the host, you need to know which door the car is behind to do your job 2&amp;#x2F;3 of the time, to avoid revealing it.&lt;p&gt;It&amp;#x27;s this quality of unexpected information exchange that I find most fascinating about this particular puzzle!</text></item></parent_chain><comment><author>dllthomas</author><text>Interestingly, if the host picks randomly (and if he reveals the car, you... start over, or you get the car, or you get nothing, or ... it doesn&amp;#x27;t matter because it happens not to have happened in the time we&amp;#x27;re considering) then you are faced with a 50&amp;#x2F;50 chance.</text></comment>