ABSTRACT

What is the probability two distinct ranks (say, a king and a five) will appear within a card of one another in a shuffled deck? An old bar bet is predicated on it being nearly guaranteed. By modeling the outcome using a finite automaton, we construct the probability generating function for card rank separation. We then derive the corresponding probability mass function, mean, and variance. We conclude with an unimpressive modification to make the scam a virtual lock.

中文翻译：

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小额下注和生成功能：两个不同卡等级的分离分布

摘要

在经过打乱的牌组中，两个不同等级（例如，国王和五个）出现在彼此的牌中的概率是多少？可以保证几乎可以保证旧的下注。通过使用有限自动机对结果进行建模，我们构造了用于卡等级分离的概率生成函数。然后，我们得出相应的概率质量函数，均值和方差。最后，我们进行了令人印象深刻的修改以使该骗局成为虚拟锁。