A model for real poker with an upper bound of assets

This paper considers a continuous model of two-person poker, where the maximal amount of betB is assumed and the player who acts first chooses the amount of bet in the game. We analyze a model, in which the range of the amount of bet is a finite interval [0,B], 0B<+, to obtain a saddle point of the payoff function as a pair of optimal strategies among mixed strategies. We compare our results with those of Karlin and Restrepo and those of Newman.The author wishes to thank Professors M. Sakaguchi and T. Kurisu of Osaka University for suggesting the problem as well as for guidance and encouragement.