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
Return to Bridge
Combinatorics main page
Web page generated via
KompoZer