The symmetric 4-Player gambler’s problem with unequal initial stakes

Abstract This research advances the 4-player gambler’s ruin problem for the case of arbitrary initial stakes. The aim of the research is attained by offering simple expressions using the difference equation approach and thus providing closed form solution to the problem. Moreover, the existing technique of Chang [A game with four players, Statist. Probab. Lett. 23(2) (1995), 111–115] dealing with equal initial stakes is demonstrated as a sub-case of the newly devised scheme. The legitimacy of the proposed formulation is further verified by considering various parametric settings.