*

Bridge is a card game played through a typical deck that 52 cards.The number of possible unique 13-card hand is


*

where

*
is a binomial coefficient. While the possibilities of being dealt a hand of 13 cards (out of 52) of the very same suit are


*

(Mosteller 1987, p.8), the opportunity that at the very least one of four players will receive a hand that a solitary suit is


*

*

(Gridgeman 1964; Mosteller 1987, p.8).

You are watching: How many possible bridge hands are there

There space special names because that specific varieties of hands. A ten, jack, queen, king, or ace is referred to as an "honor." obtaining the three optimal cards (ace, king, and also queen) of 3 suits and also the ace, king, and also queen, and also jack that the staying suit is dubbed 13 optimal honors. Getting all cards of the same suit is referred to as a 13-card suit. Acquiring 12 cards of exact same suit through ace high and the 13th card no an ace is dubbed 2-card suit, ace high. Obtaining no honors is dubbed a Yarborough.

The probabilities of being dealt 13-card bridge hands of a given type are given below. Together usual, because that a hand with probability

*
, the odds against being handle it are
*
.

handexact probabilityprobabilityodds
13 peak honors
*
*
*
13-card suit
*
*
*
12-card suit, ace high
*
*
*
Yarborough
*
*
*
four aces
*
*
*
nine honors
*
*
*

SEE ALSO: connected Graph, Bridgeless Graph, Cards, Graph Bridge, Poker
REFERENCES:

Ball, W.W.R. And Coxeter, H.S.M. MathematicalRecreations and also Essays, 13th ed. Brand-new York: Dover, pp.48-49, 1987.

Bizley, M.T.L. Letter come the Editor. Amer. Stat. 18, 31,Apr. 1964.

Gridgeman, N.T. "The secret of the missing Deal." Amer. Stat. 18,15-16, Feb.1964.

Kraitchik, M. "Bridge Hands." §6.3 in MathematicalRecreations. New York: W.W.Norton, pp.119-121, 1942.

Mosteller, F. "Perfect leg Hand." trouble 8 in Fifty difficult Problems in Probability with Solutions. New York: Dover, pp.2 and also 22-24, 1987.

Norton, H.W. Letter to the Editor. Amer. Stat. 18, 30-31, Apr.1964.

Reese, T. Bridgefor bright Beginners. Brand-new York: Dover, 1973.

Rubens, J. TheSecrets of winning Bridge. Brand-new York: Dover, 1981.


Referenced ~ above chathamtownfc.net|Alpha: Bridge
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