<story><title>Marilyn vos Savant and the Monty Hall Problem (2015)</title><url>https://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/</url></story><parent_chain><item><author>NoboruWataya</author><text>Wow, I knew about the problem and was vaguely aware that it had generated some controversy amongst statisticians but I had no idea about the insanely arrogant and obnoxious (not to mention wrong) abuse Marilyn had received from the &amp;quot;intellectual elite&amp;quot;.&lt;p&gt;I have little sympathy for the &amp;quot;ambiguous question&amp;quot; defence. Not only is Marilyn&amp;#x27;s interpretation grammatically valid, it just wouldn&amp;#x27;t make sense in the context of the game show for the presenter (who knows where the goats are) to ever open a door to reveal the car and give you the option to switch. The game would be reduced to &amp;quot;does Monty feel like gifting you a car or a goat today&amp;quot;.&lt;p&gt;Furthermore, Marilyn&amp;#x27;s own explanation of her answer makes it very clear that &lt;i&gt;she&lt;/i&gt; interpreted the question as meaning that the presenter will only ever open goat doors. And all the attacks seem to focus on her grasp of the math rather than her interpretation of the problem question.&lt;p&gt;To be clear, I think it&amp;#x27;s perfectly reasonable for a person to interpret the problem the other way without thinking too much about it, and casually throw out an incorrect answer. But I would expect an academic to devote at least another 30 seconds of thought to the problem before publicly excoriating a woman known for her high intelligence.</text></item></parent_chain><comment><author>HarHarVeryFunny</author><text>I think the problem statement is clear, and is independent of how the TV show actually operated.&lt;p&gt;The problem posed is that you have three closed doors, behind one of which is a car, and behind the other two are goats. You get to pick one of the closed doors, and will win whatever is behind it (you want the car).&lt;p&gt;One of the doors you did not pick is now opened, revealing a goat. You therefore now know the car is either behind the door you picked or behind the other closed door.&lt;p&gt;In this setup, the question is: if offered the chance to switch your selection from the door you initially picked to the other closed door, should you switch? Does it make a difference?&lt;p&gt;Mariyln Vos Savant said switch. The peanut gallery (some statisticians who should have known better) said it makes no difference - with two doors left you&amp;#x27;ve got a 50&amp;#x2F;50 chance of winning the car whether you switch or not.&lt;p&gt;First off, you can run multiple simulations of the game (with random positions of the goats and car), and prove for yourself that always switching is a better strategy, so it&amp;#x27;s sad that anyone would insist that it&amp;#x27;s not, even if that &lt;i&gt;seems&lt;/i&gt; logical.&lt;p&gt;The simplest way to explain why switching is the correct strategy is this:&lt;p&gt;When you make your initial selection, you have:&lt;p&gt;a) A 1&amp;#x2F;3 chance of selecting the car, and&lt;p&gt;b) A 2&amp;#x2F;3 chance of selecting one of the two goats&lt;p&gt;So, 1&amp;#x2F;3 of the time you selected the car and will therefore lose if you switch, and 2&amp;#x2F;3 of the time you selected a goat and will therefore win if you switch. Switching will therefore be a winning strategy 2&amp;#x2F;3 of the time.</text></comment>
<story><title>Marilyn vos Savant and the Monty Hall Problem (2015)</title><url>https://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/</url></story><parent_chain><item><author>NoboruWataya</author><text>Wow, I knew about the problem and was vaguely aware that it had generated some controversy amongst statisticians but I had no idea about the insanely arrogant and obnoxious (not to mention wrong) abuse Marilyn had received from the &amp;quot;intellectual elite&amp;quot;.&lt;p&gt;I have little sympathy for the &amp;quot;ambiguous question&amp;quot; defence. Not only is Marilyn&amp;#x27;s interpretation grammatically valid, it just wouldn&amp;#x27;t make sense in the context of the game show for the presenter (who knows where the goats are) to ever open a door to reveal the car and give you the option to switch. The game would be reduced to &amp;quot;does Monty feel like gifting you a car or a goat today&amp;quot;.&lt;p&gt;Furthermore, Marilyn&amp;#x27;s own explanation of her answer makes it very clear that &lt;i&gt;she&lt;/i&gt; interpreted the question as meaning that the presenter will only ever open goat doors. And all the attacks seem to focus on her grasp of the math rather than her interpretation of the problem question.&lt;p&gt;To be clear, I think it&amp;#x27;s perfectly reasonable for a person to interpret the problem the other way without thinking too much about it, and casually throw out an incorrect answer. But I would expect an academic to devote at least another 30 seconds of thought to the problem before publicly excoriating a woman known for her high intelligence.</text></item></parent_chain><comment><author>lucas_membrane</author><text>&amp;gt;&amp;gt; The game would be reduced to &amp;quot;does Monty feel like gifting you a car or a goat today&amp;quot;.&lt;p&gt;But, in fact, that is the way the real show worked.  He was more likely to give you a car when he hadn&amp;#x27;t given away any cars for a while.  And Marilyn&amp;#x27;s description of the problem included no information about whether or not Monty 
offered to swap doors rarely, frequently, or always,  or about the previously observed outcomes depending on whether or not the contestant took the bait.  And she surely did not say that Monty was a robot and had no interest in what happened on his show.&lt;p&gt;The way the game actually worked is like  how poker and life work until proven otherwise.  Every high-stakes game has a sucker, and if you do not know who is the sucker, it is you.  Read the story in which a NY Times reporter interviewed Monty about the controversy and you will learn how it really worked.</text></comment>