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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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 Solution (spoiler) Comment 6 of 6 |

The optimal strategy is as follows:

• Player 1 first opens door 1. If the car is behind the door, he is successful. If the keys were behind the door, he next opens door 2; if instead the goat was behind the door, he next opens door 3.
• Player 2 first opens door 2. If the keys are behind the door, he is successful. If the goat was behind the door, he next opens door 3; whereas if the car was behind the door, he next opens door 1.

Tabulation of the possible outcomes shows that the winning probability is 2/3 which is optimal since the first player cannot have a higher winning probability than that.

 Posted by broll on 2018-09-30 21:32:27

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