An Asymptotic Solution of Dresher's Guessing Game

In his 1961 monograph on Game Theory, Melvin Dresher considered a high-low guessing game on N numbers. The game was solved for N≤11 by Selmer Johnson but solutions for higher values of N have never been reported in the literature. In this paper we derive an asymptotic formula for the value of the game as N→∞ and we present an algorithm that allows us to numerically solve the game for N≤256.

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