Re:Gambler’s Fallacy and the Regression to the Mean
by tzs on Saturday January 08, 2022 @12:08AM
(#29848804)
That statement of the Monty Hall problem is still not quite correct. It needs to also include that you are told beforehand that the host will be opening a door and giving you a chance to switch.
If the host is not bound to make the offer, they could do something like only make the offer if you have picked the right door. Switching would then always lose.
People would learn that is the case, and no one would switch which would not be as interesting for the audience. To avoid this the host could give the option to switch half the time when the player picks an empty door and all the time when they pick the prize door. On average under this approach the player wins 1/3 of the time regardless of their choice.
If the host is not bound to make the offer, they could do something like only make the offer if you have picked the right door. Switching would then always lose.
People would learn that is the case, and no one would switch which would not be as interesting for the audience. To avoid this the host could give the option to switch half the time when the player picks an empty door and all the time when they pick the prize door. On average under this approach the player wins 1/3 of the time regardless of their choice.