桥牌完美牌（13 张同花）概率

Perfect Bridge Hand

专题: Strategy / 策略
难度: L4
来源: QuantQuestion

题目详情

We often read of someone who has been dealt 13 spades at bridge. With a well-

shuffled pack of cards, what is the chance that you are dealt a perfect hand (13 of one suit)? (Bridge is played with an ordinary pack of 52 cards, 13 in each of 4 suits, and each of 4 players is dealt 13. )

解析

从 52 张牌中发 13 张给你，总手牌数为 $\binom{52}{13}$ 。

“完美牌”指 13 张全同一花色。可选花色 4 种，每种只有 1 种手牌。

所以概率为

\boxed{\frac{4}{\binom{52}{13}}}

（等价写法： $\frac{12!\,39!}{51!}$ ）。