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Bridge Probabilities and Combinatorics



Bridge Probabilities - Bidding Combinatorics and Statistics
Computer Program by Bill Butler

(How many ways are there to bid a set of four hands) 
 
   When we calculate the number of bidding combinations, we are only looking at legal sequences of bids. What cards are in the four hands has no relevance. The players could just as easily be bidding without looking at their cards.

   Each line in the table below gives the total number of combinations that are possible for any given number of suit bids. If there are no suit bids, then only the single sequence of "Pass, pass, pass, pass" is possible. If there is one suit bid, then the 980 combinations are calculated as follows:

Zero, 1, 2, or 3 leading "passes"  (4 combinations)    times
35 possible suit bids (Any of 7 quantities times 5 suits)    times
7 trailing combinations (mixed "passes", "double", and "redouble")
equals 4 times 35 times 7 = 980 combinations

See the "How to" section for more details.

Number of         Number  of
Suit Bids        Combinations
-----------------------------
   0                        1
   1                      980
   2                  349,860
   3               80,817,660
   4           13,577,366,880
   5        1,767,773,167,776
   6      185,616,182,616,480
   7            1.614861 E+16
   8            1.186923 E+18
   9            7.477613 E+19
  10            4.082777 E+21
  11            1.948598 E+23
  12            8.184111 E+24
  13            3.040712 E+26
  14            1.003435 E+28
  15            2.950099 E+29
  16            7.744010 E+30
  17            1.817565 E+32
  18            3.816886 E+33
  19            7.171727 E+34
  20            1.204850 E+36
  21            1.807275 E+37
  22            2.415177 E+38
  23            2.866710 E+39
  24            3.010046 E+40
  25            2.781282 E+41
  26            2.246420 E+42
  27            1.572494 E+43
  28            9.434965 E+43
  29            4.782551 E+44
  30            2.008671 E+45
  31            6.803565 E+45
  32            1.785936 E+46
  33            3.409514 E+46
  34            4.211752 E+46
  35            2.527051 E+46
Total      1.28745650347 E+47




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