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Lets play the following game: Guess a number from 0 to 100 with the goal of making your guess as close as possible to two-thirds

Lets play the following game: Guess a number from 0 to 100 with the goal of making your guess as close as possible to two-thirds of the average guess of those participating in the contest. Now lets assume, everyone in the game is completely rational. What number will everyone choose? Why? Explain.

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