（游戏）战争何时结束？
When will (game) wars end?
AI总结：
本文分析纸牌游戏“战争”的多种渐近变体，证明当牌数为$n$时其期望终止时间均为$n^2$量级，与经典“赌徒破产”过程一致。
摘要：
我们研究了经典纸牌游戏“战争”的若干变体。正如玩过这款游戏的人都知道的那样，游戏可能需要一段时间才会结束，但通常确实会终止。在这里，我们分析了该游戏的多种渐近变体，其中纸牌数量为$n$，并证明所有变体的期望终止时间均为$n^2$量级。这与每一回合由公平抛硬币决定哪位玩家赢得一张牌的游戏具有相同的期望终止时间；后者被称为“赌徒破产”（Gambler's Ruin），曾由 Pascal、Fermat 等人在十七世纪研究。
英文摘要：
We study several variants of the classical card game war. As anyone who played this game knows, the game can take some time to terminate, but it usually does. Here, we analyze a number of asymptotic variants of the game, where the number of cards is $n$, and show that all have expected termination time of order $n^2$. This is the same expected termination time as in the game where at each turn a fair coin toss decides which player wins a card, known as Gambler's Ruin and studied by Pascal, Fermat and others in the seventeenth century.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
