


Updated 10th June 2019  


STATISTICS &MORE STATISTICS

Hand Patterns  

Pattern (any suit order)  Probability (%)  Pattern (any suit order)  Probability (%) 
4432  21.55  6520  0.65 
4333  10.54  6610  0.072 
4441  2.99  7321  1.88 
5332  15.52  7222  0.51 
5431  12.93  7411  0.39 
5422  10.6  7420  0.36 
5521  3.17  7330  0.27 
5440  1.24  7510  0.11 
5530  0.895  7600  0.0056 
6322  5.64  8221  0.19 
6421  4.7  8311  0.12 
6331  3.45  8410  0.045 
6430  1.33  8500  0.0031 
6511  0.71  9211  0.018 
9310  0.01 
and even more Stats :
Probability that either partnership will have enough to bid game,
assuming a 26+ point game = 25.29% (1 in 3.95 deals)
Probability that either partnership will have enough to bid slam,
assuming a 33+ point slam = .70% (1 in 143.5 deals)
Probability that either partnership will have enough to bid grandslam,
assuming a 37+ point grand slam = .02% (about 1 in 5,848 deals)
Number of different hands a named player can receive = 635,013,559,600
Number of different hands a second player can receive = 8,122,425,444
Number of different hands the 3rd and 4th players can receive =
10,400,600
Number of possible deals = 52!/(13!)^4 =
53,644,737,765,488,792,839,237,440,000
Number of possible auctions with North as dealer, assuming that East
and West pass throughout = 2^36  1 = 68,719,476,735
Number of possible auctions with North as dealer,
assuming that East and West do not pass throughout =
128,745,650,347,030,683,120,231,926,111,609,371,363,122,697,557
Odds against each player having a complete suit =
2,235,197,406,895,366,368,301,559,999 to 1
Odds against receiving a hand with 37 HCP (4 Aces, 4 Kings, 4 Queens,
and 1 Jack) = 158,753,389,899 to 1
Odds against receiving a perfect hand (13 cards in one suit) =
169,066,442 to 1
Odds against a Yarborough = 1827 to 1
Odds against both members of a partnership receiving a Yarborough =
546,000,000 to 1
Odds against a hand with no card higher than 10 = 274 to 1
Odds against a hand with no card higher than Jack = 52 to 1
Odds against a hand with no card higher than Queen = 11 to 1
Odds against a hand with no Aces = 2 to 1
Odds against being dealt four Aces = 378 to 1
Odds against being dealt four honors in one suit = 22 to 1
Odds against being dealt five honors in one suit = 500 to 1
Odds against being dealt at least one singleton = 2 to 1
Odds against having at least one void = 19 to 1
Odds that two partners will be dealt 26 named cards between them =
495,918,532,918,103 to 1
Odds that no players will be dealt a singleton or void = 4 to 1