THE HORSE GAME

Abstract

N independent and identically distributed observations of some random variable with a continuous distribution F are sequentially presented to two players, White and Black. Each player is required to select exactly one observation without recall to rejected observations. As long as both players have not made a selection, White is always given the first option to accept or reject an observation. Both players are given the same information and are aware of the selection made by the other player. The player selecting the largest number wins the game. This problem is considered for the two cases, when either F is known or unknown. The probability of each player winning and the distribution of the location in the sample where selections are made is obtained. Also asymptotic results are derived. The problem is couched in terms of a horse bet.

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