In its simplest form, the Robin Hood game is described by the following urn scheme: every day the Sheriff of Nottingham puts s balls in an urn. Then Robin chooses r (r < s) balls to remove from the urn. Robin's goal is to remove balls in such a way that none of them are left in the urn indefinitely. Let T n be the random time that is required for Robin to take out all s · n balls put in the urn during the first n days. Our main result is a limit theorem for T n if Robin selects the balls uniformly at random. Namely, we show that the random variable T n · n -s/r converges in law to a Fréchet distribution as n goes to infinity.

中文翻译：

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罗宾汉游戏的极限定理

以最简单的形式，罗宾汉游戏由以下瓮方案描述：每天诺丁汉警长将 s 个球放入瓮中。然后罗宾选择 r (r < s) 个球从瓮中取出。罗宾的目标是以这样一种方式移除球，即它们都不会无限期地留在骨灰盒中。设 T n 是 Robin 在前 n 天取出所有放入瓮中的 s·n 个球所需的随机时间。如果 Robin 随机均匀地选择球，我们的主要结果是 T n 的极限定理。即，我们表明，随着 n 趋于无穷大，随机变量 T n · n -s/r 在法律上收敛于 Fréchet 分布。