A model for real poker with an upper bound of assets (Q1062928)

This paper considers a continuous model of two-person poker, where the maximal amount of bet B 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 \(\beta\) is a finite interval [0,B], \(0\leq B<+\infty\), 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 \textit{S. Karlin} and \textit{R. Restrepo} [Contrib. Theory of Games, Vol. 3, Ann. Math. Studies 39, 337-363 (1957)] and those of \textit{D. J. Newman} [Oper. Res. 7, 557-560 (1959)].