## Bridge Card Game

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

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