The La Plata Mountains as seen from above the authorís
            home.


Durango Bill's

Bridge Probabilities and Combinatorics



Bridge Probabilities and Statistics - Suit Splits

What is the probability of various possible splits given that you and dummy have "N" cards?

   Math notation is generally the same as that used in Microsoft's Excel. The MathNotation link will also give examples of the notation as used here.

   The tables below show the number of possible combinations and the probability of having the opponent's cards split in any possible way given that you and dummy have a combined total of "N" in a suit. These calculations are only valid for random hands. Both the bidding and play of the hand reveal addition knowledge and will modify the results shown here.

   Each line has 2 COMBIN() functions. The first is for the split in the suit of interest while the second fills out the remainder of the hand using the 3 other suits in the remainder of the deck.

   Note: For all combinations, there are COMBIN(26,13) = 10,400,600 possible hands for a specific opponent after 26 cards have been removed from the deck for you and dummy.


You and dummy have a combined total of 11 cards in the suit.

Split          Number of possible hands           Probability
-------------------------------------------------------------
"2,0"    COMBIN(2,0) * COMBIN(24,13) =  2,496,144       .2400
"1,1"    COMBIN(2,1) * COMBIN(24,12) =  5,408,312       .5200
"0,2"    COMBIN(2,2) * COMBIN(24,11) =  2,496,144       .2400
Total    COMBIN(26,13)               = 10,400,600      1.0000


You and dummy have a combined total of 10 cards in the suit.

Split          Number of possible hands           Probability
-------------------------------------------------------------
"3,0"    COMBIN(3,0) * COMBIN(23,13) =  1,144,066       .1100
"2,1"    COMBIN(3,1) * COMBIN(23,12) =  4,056,234       .3900
"1,2"    COMBIN(3,2) * COMBIN(23,11) =  4,056,234       .3900
"0,3"    COMBIN(3,3) * COMBIN(23,10) =  1,144,066       .1100
Total    COMBIN(26,13)               = 10,400,600      1.0000


You and dummy have a combined total of 9 cards in the suit.

Split          Number of possible hands           Probability
-------------------------------------------------------------
"4,0"    COMBIN(4,0) * COMBIN(22,13) =    497,420       .0478
"3,1"    COMBIN(4,1) * COMBIN(22,12) =  2,586,584       .2487
"2,2"    COMBIN(4,2) * COMBIN(22,11) =  4,232,592       .4070
"1,3"    COMBIN(4,3) * COMBIN(22,10) =  2,586,584       .2487
"0,4"    COMBIN(4,4) * COMBIN(22, 9) =    497,420       .0478
Total    COMBIN(26,13                = 10,400,600      1.0000


You and dummy have a combined total of 8 cards in a suit.

Split          Number of possible hands           Probability
-------------------------------------------------------------
"5,0"    COMBIN(5,0) * COMBIN(21,13) =    203,490       .0196
"4,1"    COMBIN(5,1) * COMBIN(21,12) =  1,469,650       .1413
"3,2"    COMBIN(5,2) * COMBIN(21,11) =  3,527,160       .3391
"2,3"    COMBIN(5,3) * COMBIN(21,10) =  3,527,160       .3391
"1,4"    COMBIN(5,4) * COMBIN(21, 9) =  1,469,650       .1413
"0,5"    COMBIN(5,5) * COMBIN(21, 8) =    203,490       .0196
Total    COMBIN(26,13)               = 10,400,600      1.0000


You and dummy have a combined total of 7 cards in a suit.

Split          Number of possible hands           Probability
-------------------------------------------------------------
"6,0"    COMBIN(6,0) * COMBIN(20,13) =     77,520       .0075
"5,1"    COMBIN(6,1) * COMBIN(20,12) =    755,820       .0727
"4,2"    COMBIN(6,2) * COMBIN(20,11) =  2,519,400       .2422
"3,3"    COMBIN(6,3) * COMBIN(20,10) =  3,695,120       .3553
"2,4"    COMBIN(6,4) * COMBIN(20, 9) =  2,519,400       .2422
"1,5"    COMBIN(6,5) * COMBIN(20, 8) =    755,820       .0727
"0,6"    COMBIN(6,6) * COMBIN(20, 7) =     77,520       .0075
Total    COMBIN(26,13)               = 10,400,600      1.0000


You and dummy have a combined total of 6 cards in a suit.

Split          Number of possible hands           Probability
-------------------------------------------------------------
"7,0"    COMBIN(7,0) * COMBIN(19,13) =     27,132       .0026
"6,1"    COMBIN(7,1) * COMBIN(19,12) =    352,716       .0339
"5,2"    COMBIN(7,2) * COMBIN(19,11) =  1,587,222       .1526
"4,3"    COMBIN(7,3) * COMBIN(19,10) =  3,233,230       .3109
"3,4"    COMBIN(7,4) * COMBIN(19, 9) =  3,233,230       .3109
"2,5"    COMBIN(7,5) * COMBIN(19, 8) =  1,587,222       .1526
"1,6"    COMBIN(7,6) * COMBIN(19, 7) =    352,716       .0339
"0,7"    COMBIN(7,7) * COMBIN(19, 6) =     27,132       .0026
Total    COMBIN(26,13)               = 10,400,600      1.0000


You and dummy have a combined total of 5 cards in a suit.

Split          Number of possible hands           Probability
-------------------------------------------------------------
"8,0"    COMBIN(8,0) * COMBIN(18,13) =      8,568       .0008
"7,1"    COMBIN(8,1) * COMBIN(18,12) =    148,512       .0143
"6,2"    COMBIN(8,2) * COMBIN(18,11) =    891,072       .0857
"5,3"    COMBIN(8,3) * COMBIN(18,10) =  2,450,448       .2356
"4,4"    COMBIN(8,4) * COMBIN(18, 9) =  3,403,400       .3272
"3,5"    COMBIN(8,5) * COMBIN(18, 8) =  2,450,448       .2356
"2,6"    COMBIN(8,6) * COMBIN(18, 7) =    891,072       .0857
"1,7"    COMBIN(8,7) * COMBIN(18, 6) =    148,512       .0143
"0,8"    COMBIN(8,8) * COMBIN(18, 5) =      8,568       .0008
Total    COMBIN(26,13)               = 10,400,600      1.0000


You and dummy have a combined total of 4 cards in a suit.

Split          Number of possible hands           Probability
-------------------------------------------------------------
"9,0"    COMBIN(9,0) * COMBIN(17,13) =      2,380       .0002
"8,1"    COMBIN(9,1) * COMBIN(17,12) =     55,692       .0054
"7,2"    COMBIN(9,2) * COMBIN(17,11) =    445,536       .0428
"6,3"    COMBIN(9,3) * COMBIN(17,10) =  1,633,632       .1571
"5,4"    COMBIN(9,4) * COMBIN(17, 9) =  3,063,060       .2945
"4,5"    COMBIN(9,5) * COMBIN(17, 8) =  3,063,060       .2945
"3,6"    COMBIN(9,6) * COMBIN(17, 7) =  1,633,632       .1571
"2,7"    COMBIN(9,7) * COMBIN(17, 6) =    445,536       .0428
"1,8"    COMBIN(9,8) * COMBIN(17, 5) =     55,692       .0054
"0,9"    COMBIN(9,9) * COMBIN(17, 4) =      2,380       .0002
Total    COMBIN(26,13)               = 10,400,600      1.0000



Return to Bridge Combinatorics main page

Web page generated via Sea Monkey's Composer HTML editor
within  a Linux Cinnamon Mint 18 operating system.
(Goodbye Microsoft)