Bridge Card Game
Bridge is a Card game played with a normal deck of 52 cards. The number of possible distinct 13-cardhands is
where
is a Binomial Coefficient. While the chances of being dealt a hand of 13 Cards (out of52) 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 thethree top cards (ace, king, and queen) of three suits and the ace, king, and queen, and jack of the remaining suit iscalled 13 top honors. Getting all cards of the same suit is called a 13-card suit. Getting 12 cards of same suit with acehigh 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 withprobability 
, 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.
- Swinnerton-Dyer Conjecture
- Swinnerton-Dyer Polynomial
- Swirl
- Sylow p-Subgroup
- Sylow Theorems
- Sylvester Cyclotomic Number
- Sylvester Graph
- Sylvester Matrix
- Sylvester's Determinant Identity
- Sylvester's Four-Point Problem
- Sylvester's Inertia Law
- Sylvester's Line Problem
- Sylvester's Sequence
- Sylvester's Signature
- Sylvester's Triangle Problem
- Symbolic Logic
- Symmedian Line
- Symmedian Point
- Symmetric
- Symmetric Block Design
- Symmetric Design
- Symmetric Function
- Symmetric Group
- Symmetric Matrix
- Symmetric Points