Percentages in Card Division

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.BR>

Probability with 2 hidden hands

2 cards 1-1 52%
2-0 48%

3 cards 2-1 78%
3-0 22%

4 cards 3-1 49.7%
2-2 40.7%
4-0 9.6%

5 cards 3-2 67.8%
4-1 28.3%
5-0 3.9%

6 cards 4-2 48.5%
3-3 35.5%
5-1 14.5%
6-0 1.5%

7 cards 4-3 62.2%
5-2 30.5%
6-1 6.8%
7-0 0.5%

8 cards 5-3 47.1%
4-4 32.7%
6-2 17.1%
7-1 2.9%
8-0 0.2%

9 cards 5-4 58.9%
6-3 31.3%
7-2 8.6%
8-1 1.1%
9-0 0.1%

10 cards 6-4 46.2%
5-5 31.2%
7-3 18.9%
8-2 3.8%
9-1 0.4%
10-0 0.05%

11 cards 6-5 57.2%
7-4 31.8%
8-3 9.5%
9-2 1.4%
10-1 0.1%
11-0 0.002%

12 cards 7-5 45.8%
6-6 30.5%
8-4 19.1%
9-3 4.2%
10-2 0.5%
11-1 0.02%
12-0 0.0003%

13 cards 7-6 56.6%
8-5 31.9%
9-4 9.8%
10-3 1.6
11-2 0.1%
12-1 0.003%
13-0 0.00002%

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.).