Alice plays the following game, loosely based on the card game "21". Alice starts with 0 points and draws numbers while she has less than k points. During each draw, she gains an integer number of points randomly from the range [1, maxPts], where maxPts is…

我们对 0 到 255 之间的整数进行采样，并将结果存储在数组 count 中：count[k] 就是整数 k 在样本中出现的次数。 计算以下统计数据:

There are two types of soup: type A and type B. Initially, we have n ml of each type of soup. There are four kinds of operations:

你有两种汤，A 和 B，每种初始为 n 毫升。在每一轮中，会随机选择以下四种服务操作中的一种，每种操作的概率为 0.25，且与之前的所有轮次 无关：

You have two soups, A and B, each starting with n mL. On every turn, one of the following four serving operations is chosen at random, each with probability 0.25 independent of all previous turns:

爱丽丝参与一个大致基于纸牌游戏 “21点” 规则的游戏，描述如下： 爱丽丝以 0 分开始，并在她的得分少于 k 分时抽取数字。 抽取时，她从 [1, maxPts] 的范围中随机获得一个整数作为分数进行累计，其中 maxPts 是一个整数。 每次抽取都是独立的，其结果具有相同的概率。 当爱丽丝获得 k 分 或更多分 时，她就停止抽取数字。 爱丽丝的分数不超过 n 的概率是多少？ 与实际答案误差不超过 10-5 的答案将被视为正确答案。

Alice plays the following game, loosely based on the card game "21". Alice starts with 0 points and draws numbers while she has less than k points. During each draw, she gains an integer number of points randomly from the range [1, maxPts], where maxPts is…