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 Monty Hall variant (Posted on 2018-09-30)
There are three closed doors. One has a new car, one has the keys to the car and one has a goat. These prizes are randomly assigned.

There are two players: the first player has to find the car, the second player has to find the keys to the car. If both players succeed they win the car.

The first player enters the room and may open any two of the three doors, one after the other. If successful, the doors are closed again and the second player enters the room. The second player may also open two of the three doors, but cannot communicate with the first player.

Surprisingly there is a strategy where the probability of winning is better than (2/3)2. Find it.

 No Solution Yet Submitted by Jer No Rating

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 re: question | Comment 5 of 6 |
(In reply to question by Steven Lord)

Your first questions are irrelevant since the chance of winning becomes zero.

3) It says the doors are closed again before P2 enters.

4)  They can definitely communicate beforehand.  They need to set up a good strategy for how to guess.  Each knows the other's plan but once it begins there is no further communication.

 Posted by Jer on 2018-09-30 20:54:51

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