In the standard definition of the classical gambler's ruin game, a persistent player enters in a stochastic process with an initial budget $b_0$, which is, round after round, either increased by 1 with probability p, or decreased by 1 with probability $1-p$. The player wins the game if the budget reaches a given objective value g, and loses the game if the budget drops to zero (the gambler is ruined). This article introduces the decisional gambling process, where the parameter p is hidden, and the player has the possibility to stop the game at any round keeping earnings. In this case, the best a player can do is to maintain an estimate of p based on the observed outcomes, and use it to decide whether is better to stay or quit the game. The main contribution of this article is to bring the question of finding the optimal stopping time to the gambler's ruin game. Different heuristics are analyzed and evaluated according to their performance in maximizing the gambler's expected final budget.

在经典赌徒破产游戏的标准定义中，顽固的玩家以初始预算进入随机过程${乙}_0$，即一轮又一轮，要么以概率p增加 1，要么以概率减少 1$1-磷$. 如果预算达到给定的目标值g，则玩家赢得游戏，如果预算降至零（赌徒被毁），则游戏失败。本文介绍了决策赌博过程，其中参数p是隐藏的，玩家有可能在保持收益的任何回合停止游戏。在这种情况下，玩家可以做的最好的事情是根据观察到的结果保持对p的估计，并用它来决定是留下还是退出游戏更好。这篇文章的主要贡献是把寻找最优停止时间的问题带到赌徒的灭亡游戏。根据它们在最大化赌徒的预期最终预算方面的表现来分析和评估不同的启发法。