有这么一个猜拳游戏，猜拳的双方姑且叫他们“小单”和“小双”，单数和双数的单双。猜拳时只能出两种手势，就是出一个大拇指，表示一，或者出四个手指，表示四。然后把双发的手势数字加起来，单数时小单赢，双数时，小双赢。而且赢得分数就是双方手势数字之和。比如一个人出了1，另一个出了4，那么加起来是5，那小单赢了5分。如果两个人都出了1，那么加起来是2，是双数，那么小双赢了2分。现在的问题就是这个游戏是公平的游戏吗？该游戏的纳什均衡点在小单以13/20的概率出1，7/20的概率出4，如此的话，小单平均每局可赢0.45分。计算过程如下：设小单出1的概率是p，小双出1的概率是q。则小单每局的得分期望值是：–2pq+5(1 –p)q+5p(1 –q)–8(1–p)(1–q)=13p+13q–20pq–8现在的目标是无论q是多少，确定一个最佳的p值，则可将q作为变量，p作为常量，将上式化为：q(13–20p)–(8–13p)则可注意到当13-20p=0时，上式将不依赖于q。则可解得p=13/20时，上式值为0.45。即为纳什均衡点时，小单的单局得分期望值。
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