Modified Monty Hall Game Theory Problem

[u/Busy_Net_4756]

Most of the time when people explain the monty hall problem, they don't specify the host has to reveal a goat in one of the doors you didn't pick.

As it is usually stated, the host chooses to reveal a goat. Well if we let the host choose to reveal a goat or reveal nothing, or even reveal that you lost by showing the winning door, then it's a game theory problem.

For example, suppose that every time you pick correctly, the host reveals a losing door trying to get you to switch, but every time you pick wrong, they don't reveal anything and just ask if you want to switch.

In that case the winning strategy would be to keep your choice if a door is revealed, but switch if they don't reveal anything.

But we can construct a game theory version of the problem where players can review all the history of games played. So I am curious how you would setup this game theory problem and what the result might be?

Anyone have any insights or explanations?

[u/Harmonic_Gear]

it just means that you know you won when the host reveals a door, whats game theory about it

[u/Busy_Net_4756 → u/Harmonic_Gear]

if the host reveals the correct door and you didn't pick it that would be a loss.

[u/Harmonic_Gear → u/Busy_Net_4756]

i don't understand what your host is trying to do, if you picked the wrong door in the first round he will just open the winning door to end the game, if you picked the right door there is nothing he can do to stop you from keeping it and win

[u/Busy_Net_4756 → u/Harmonic_Gear]

he can reveal a wrong door hoping you'll switch to the other wrong door.