Bridge is a Card game played with a normal deck of 52 cards. The number of possible distinct 13-card
hands is

where is a Binomial Coefficient. While the chances of being dealt a hand of 13 Cards (out of 52) of the same suit are

the chance that one of four players will receive a hand of a single suit is

There are special names for specific types of hands. A ten, jack, queen, king, or ace is called an ``honor.'' Getting the
three top cards (ace, king, and queen) of three suits and the ace, king, and queen, and jack of the remaining suit is
called 13 top honors. Getting all cards of the same suit is called a 13-card suit. Getting 12 cards of same suit with ace
high and the 13th card *not* an ace is called 2-card suit, ace high. Getting *no* honors is called a Yarborough.

The probabilities of being dealt 13-card bridge hands of a given type are given below. As usual, for a hand with probability , the Odds against being dealt it are .

Hand | Exact Probability | Probability | Odds |

13 top honors | 158,753,389,899:1 | ||

13-card suit | 158,753,389,899:1 | ||

12-card suit, ace high | 367,484,697.8:1 | ||

Yarborough | 1,827.0:1 | ||

four aces | 377.6:1 | ||

nine honors | 104.1:1 |

**References**

Ball, W. W. R. and Coxeter, H. S. M. *Mathematical Recreations and Essays, 13th ed.*
New York: Dover, pp. 48-49, 1987.

Kraitchik, M. ``Bridge Hands.'' §6.3 in *Mathematical Recreations.* New York: W. W. Norton,
pp. 119-121, 1942.

© 1996-9

1999-05-26