The statistical data for the number of trumps for both side under the general condition (no any special knowledge of the hands) is only import as an academic or theoretical interest. In actual bidding of the hands there are extra information's for you to get a better set of statistical possibilities of the number of trumps on both side. I'll cover some of those situations in other sections. But it turns out this general case is extremely useful for many actual bidding situations. The Law applies only if both side has about the same HCP. All discussions in this section assumes both side has about the same number of HCP. All discussions assume no adjustments to the Law is required like double suit fit and minor honors and bad internal cards for the trump suit etc. (Please refer to Larry Cohen's book for detail)
I run a simulation of 100 million random bridge hands and the result is in the sample output section. A summary of the trump distribution is as follows:-
| 7 | 8 | 9 | 10 | 11 | 12 | 13 | ||
| total | 15.74% | 45.75% | 28.08% | 8.68% | 1.57% | 0.16% | ||
| 7 | 15.74% | 10.49% | 5.25% | |||||
| 8 | 45.74% | 5.25% | 26.92% | 11.47% | 1.97% | 0.13% | ||
| 9 | 28.10% | 11.48% | 11.69% | 4.10% | 0.76% | 0.07% | ||
| 10 | 8.68% | 1.97% | 4.10% | 2.03% | 0.51% | 0.07% | ||
| 11 | 1.57% | 0.13% | 0.76% | 0.51% | 0.15% | 0.02% | ||
| 12 | 0.15% | 0.06% | 0.07% | 0.02% | ||||
| 13 |
The first observation is that about 46% of the time you will have 8 trumps and 28% of the time you will have 9 trumps. So you should pay more attention to this 2 situations then others. The ability to differentiate between the 2 is extremely important in your bidding system.
The second observation is that the more trump you have the more trump your opponent may have statistically. Let's say you have 10 trumps (use data under column with 10). You opponent has 22.7% (1.97%/8.68%) chance to have 8 trumps, 47% chance to have 9 trumps, 23.4% chance to have 10 trumps, 6% chance to have 11 trumps.