A game based on successive events

Abstract

In this article, we provide the general expressions for the classic two‐player gambler's ruin problem when the decision process relies on the occurrence of successive and nonoverlapping events. The rationale of the proposed strategy is motivated by its exhibition in various sports events. For example, in tennis, a player is required to win two successive serves to win a game after achieving deuce. Similarly, in cricket, a bowler needs three wickets in three successive balls to secure the prestigious hallmark of a hat trick. The advantage of the proposed scheme is two‐folded. It provides ample opportunity for the competitors to come back in the game. Second, the decision process favours the player with a better skill set and reduces the chances of win or loss based only on luck. We provide expressions of ruin probability and expected and conditional durations of the game. The results are generalized for any number of successive events, say . The devised portfolio is then verified through rigorous simulation studies by considering more practical values of , that is, and .