Strange variant of Monte Hall problem I managed to confuse myself with: You are presented with the three doors but do not know if you will have a chance to switch later. You know the host can decide to open one of the losing doors and give you the opportunity to switch or not, and does not wish to give away the prize.
If the player chooses the correct door first he is incentivized to open one and give you the option to switch, but since the player is informed of the rules that may convince the player not to switch. If the player chooses an incorrect door first he disincentivized to give you the option to switch, but since the player is informed of the rules that may convince the player not to switch. After the host informs you if do you or do not have the option to switch, you are given a piece of paper and asked to predict what is behind the door. If your prediction is correct you get what is behind the door. If your prediction is wrong && [a door was opened] you get what is behind the other one, If prediction is wrong && [no door was opened] you get what is behind one of the remaining doors at random.
Is there an optimal strategy: For the host? For the player? My working memory is now shot and I can’t say I’m confident the puzzle is logically coherent, but it was fun to make.
The player can force a strategy where they win 2⁄3 of the time (guess a door and never switch). The player never needs to accept worse
The host can force a strategy where the player loses 1⁄3 of the time (never let the player switch). The host never needs to accept worse.
Therefore, the equilibrium has 2⁄3 win for the player. The player can block this number from going lower and the host can block this number from going higher.
Strange variant of Monte Hall problem I managed to confuse myself with:
You are presented with the three doors but do not know if you will have a chance to switch later. You know the host can decide to open one of the losing doors and give you the opportunity to switch or not, and does not wish to give away the prize.
If the player chooses the correct door first he is incentivized to open one and give you the option to switch, but since the player is informed of the rules that may convince the player not to switch.
If the player chooses an incorrect door first he disincentivized to give you the option to switch, but since the player is informed of the rules that may convince the player not to switch.
After the host informs you if do you or do not have the option to switch, you are given a piece of paper and asked to predict what is behind the door. If your prediction is correct you get what is behind the door. If your prediction is wrong && [a door was opened] you get what is behind the other one, If prediction is wrong && [no door was opened] you get what is behind one of the remaining doors at random.
Is there an optimal strategy: For the host? For the player?
My working memory is now shot and I can’t say I’m confident the puzzle is logically coherent, but it was fun to make.
The player can force a strategy where they win 2⁄3 of the time (guess a door and never switch). The player never needs to accept worse
The host can force a strategy where the player loses 1⁄3 of the time (never let the player switch). The host never needs to accept worse.
Therefore, the equilibrium has 2⁄3 win for the player. The player can block this number from going lower and the host can block this number from going higher.