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In some games, which are a combination of both chance and skill, this skill may be employed not only in playing but also in the strategy used in betting. Betting strategies only affect the expected gain when it is possible to break down the game into a set of sub-games, where each sub-game is characterized by some control variable. The purpose of this note is to obtain an upper bound for the increase in expected gain in such a compound game when only a limited range of bets is possible. The general theory is illustrated by numerical results for the game of blackjack.
Journal of the Royal Statistical Society. Series A (General) © 1969 Royal Statistical Society