Gambler’s Fallacy and the Regression to the Mean
So the author presents the Monty Hall problem this way (very explicitly saying that the host knows where the prize is an will not reveal it):<p>&gt; You are given a choice of three doors, behind one is a prize. You can choose one door. The host of this game, who knows where the prize is, then opens one door without a prize (again – they know where the prize is and deliberately choose one of the unchosen doors without a prize), and then ask if you want to change your choice to the other unopened door. If you change your choice your odds of winning go up from 1&#x2F;3 to 2&#x2F;3.<p>which to me makes intuitive sense. Every other time I&#x27;ve encountered this it&#x27;s usually presented in a very ambiguous way, where it isn&#x27;t clear if the host has any information about what&#x27;s behind the doors. If the host is choosing a door randomly and it doesn&#x27;t happen to contain the prize, your odds don&#x27;t improve if you switch your answer.<p>...I guess I just want to say that I think the Monty Hall problem is dumb. It&#x27;s not some mind blowing truth of probabilities that human brains can&#x27;t grasp; it&#x27;s just a poorly worded problem that causes you to make incorrect assumptions.<p>You could argue that if you don&#x27;t know whether or not the host has any knowledge about where the prize is you might as well switch, because if they do you&#x27;ve improved your odds and if they don&#x27;t you haven&#x27;t made things worse. But still, the &quot;problem&quot; itself doesn&#x27;t seem that interesting.