4569: Dexterina’s Lab

Dexterina and Womandark have been arch-rivals since they’ve known each other. Since both are super-intelligent teenage girls, they’ve always been trying to solve their disputes in a peaceful and nonviolent way. After god knows how many different challenges they’ve given to one another, their score is equal and they’re both desperately trying to best the other in various games of wits. This time, Dexterina challenged Womandark to a game of Nim.
Nim is a two-player game in which players take turns removing objects from distinct heaps. On each turn, a player must remove at least one object, and may remove any number of objects from a single heap. The player who can't make a turn loses. By their agreement, the sizes of piles are selected randomly from the range [0,x]. Each pile's size is taken independently from the same probability distribution that is known before the start of the game.
Womandark is coming up with a brand new and evil idea on how to thwart Dexterina’s plans, so she hasn’t got much spare time. She, however, offered you some tips on looking fabulous in exchange for helping her win in Nim. Your task is to tell her what is the probability that the first player to play wins, given the rules as above.

2 2
0.500000 0.250000 0.250000

0.62500000

Dexterina和Womandark自从认识以来就一直是劲敌。由于两人都是超级聪明的十几岁女孩，他们一直试图以和平和非暴力的方式解决争端。在上帝知道他们给了彼此多少不同的挑战之后，他们的分数是相等的，他们都在拼命地在各种智力游戏中击败对方。这一次，Dexterina挑战Womandark玩尼姆游戏。

尼姆是一款双人游戏，玩家轮流从不同的堆中移除物体。在每个回合中，玩家必须移除至少一个对象，并且可以从单个堆中移除任意数量的对象。不能转弯的选手会输。根据他们的协议，桩的尺寸从范围[0，x]中随机选择。每个桩的大小独立于游戏开始前已知的相同概率分布。

Womandark想出了一个全新的邪恶想法来阻止Dexterina的计划，所以她没有太多空闲时间。然而，她为你提供了一些看起来很棒的技巧，以换取帮助她在尼姆获胜。你的任务是告诉她，根据上述规则，第一个上场的球员获胜的概率是多少。