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 $m$ 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 $m$. The devised portfolio is then verified through rigorous simulation studies by considering more practical values of $m$, that is, $m=2$ and $m=3$.

中文翻译：

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基于连续事件的游戏

在本文中，当决策过程依赖于下注的发生时，我们提供了经典的两人赌徒破产问题的一般表达。 $米$连续事件和不重叠事件。提议的策略的基本原理是由其在各种体育赛事中的展示所激发的。例如，在网球比赛中，要求球员在获得平局后赢得两连胜才能赢得比赛。同样，在板球比赛中，投球手需要在三个连续的球中使用三个小门，以确保帽子戏法的声名显赫。提议的方案的优点有两个。它为竞争对手提供了重返游戏的充足机会。其次，决策过程有利于拥有更好技能的玩家，并仅根据运气降低获胜或失败的机会。我们提供了破产概率以及游戏预期和条件持续时间的表达式。结果适用于任意数量的连续事件，例如$米$。然后，通过考虑更实际的价值，通过严格的仿真研究来验证设计的产品组合。$米$， 那是， $米=2$ 和 $米=3$。