Ranking the pairs in a bridge match - what precision?


by haruspex
Tags: bridge, match, pairs, precision, ranking
haruspex
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Feb15-13, 04:46 PM
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Quote Quote by AlephZero View Post
In practice, I would guess most hands would be played approximately the same number of times, so the realistic range is 1/lcm(M,N) where M is fairly close to N.

For eaxmplle lcm(1,2, ... 30) = 2^4.3^3.5^2.7.11.13.17.19.23.29 = 2.33 x 10^12.
But lcm(27,28,29,30) is only 2^2.3^3.5.7.29 = 109620.

Also, there will be some complcated constraints on the number of times different hands are played, because (presumably) each player or pair of players can only play their games sequentially, and may have to wait for their next opponents to finish. As an extreme (and completely unrealistic) example, it is probably impossible to have 29 hands each played 30 times and one hand only played once.
Yes, that's not bad. This suggests a prepass which computes the LCM to use based on the actual numbers of times each hand was played.
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