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Percentages in Card Division
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This is not a convention, but a few people asked me whether I might give them some information about the percentage splits
of the cards. Although this should go without saying, the percentages reflect splits in both hands (i.e., a 3-1 and a 1-3 split are the same
these tables). Also, this assumes no other available information about the lay of the cards.
In the table below, the odds of a 3-2 division of 5 cards between two hands is found at the intersection of row 3 and column 2 (or row 2 and column 3) and is 67.8%
Card Division Probability Table
| X |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| 0 |
% |
100% |
48% |
22% |
9.6% |
3.9% |
1.5% |
0.5% |
0.2% |
0.1% |
0.05% |
| 1 |
100% |
52% |
78% |
49.7% |
28.3% |
14.5% |
6.8% |
2.9% |
1.1% |
0.4% |
0.1% |
| 2 |
48% |
78% |
40.7% |
67.8% |
48.5% |
30.5% |
17.1% |
8.6% |
3.8% |
1.4% |
0.5% |
| 3 |
22% |
49.7% |
67.8% |
35.5% |
62.2% |
47.1% |
31.3% |
18.9% |
9.5% |
4.2% |
1.6% |
| 4 |
9.6% |
28.3% |
48.5% |
62.2% |
32.7% |
58.9% |
46.2% |
31.8% |
19.1% |
9.8% |
|
| 5 |
3.9% |
14.5% |
30.5% |
47.1% |
58.9% |
31.2% |
57.2% |
45.8% |
31.9% |
|
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| 6 |
1.5% |
6.8% |
17.1% |
31.3% |
46.2% |
57.2% |
30.5% |
56.6% |
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|
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| 7 |
0.5% |
2.9% |
8.6% |
18.9% |
31.8% |
45.8% |
56.6% |
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|
|
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| 8 |
0.2% |
1.1% |
3.8% |
9.5% |
19.1% |
31.9% |
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| 9 |
0.1% |
0.4% |
1.4% |
4.2% |
9.8% |
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| 10 |
0.05% |
0.1% |
0.5% |
1.6% |
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If you want to find the probabilities for the distribution of 3 hidden hands, I would recommend you look up
Mathematical Tables in The Official Encyclopedia of Bridge (Henry G. Francis, Alan F. Truscott, eds.).