Ingo, I actually built a simulator for this once. I could assign ELO ratings to the players and they would win or lose based on their probability of winning as predicted by the ELO system. It was indeed a good way to get a feel for this. I tried things such as random pairings (not taking into consideration their ratings) and comparing this to proper pairings. I would run the same tournament 10,000 times to see how often the "best" player actually won. This was not a formal proof but it was certainly a good empirical proof that it's important to pair properly.
If I can find that code I will present some data. The ELO ratings were assigned in the shape of the bell curve to make it more realistic. My formula was something like (random(3000) + random(3000) + random(3000) ) / 3 and 1500 will tend to be the average rating and there will be relatively few player a lot stronger or a lot weaker. That is at least more realistic that just setting the ratings randomly. Don On Mon, May 9, 2011 at 7:33 AM, "Ingo Althöfer" <[email protected]>wrote: > Hello Nick, > > > You are proposing that the tournament should start by pairing strong > > players with weak players, and claiming that this is more likely to > > result in the strongest player winning the tournament. I don't see it. > > A formal proof for the general case. "Only" special cases (for instance > with one top player, (n-1) semi-strong players, n weak players) have > been proven. > > However, one can run "some" simulations to get a feeling for it. > The following model (with wins and losses only) will do: > For each player i a positive number r[i] is given, his rating. > When i plays j, i will win with prob > r[i] / ( r[i] + r[j] ), > and j will win with > r[j] / ( r[i] + r[j] ). > For simplicity we assume that different games run independently of > each other. > > Select some set of 2*n strengths and try > different pairing schemes to see, how often > which player wins. > > Ingo. > -- > Empfehlen Sie GMX DSL Ihren Freunden und Bekannten und wir > belohnen Sie mit bis zu 50,- Euro! https://freundschaftswerbung.gmx.de > _______________________________________________ > Computer-go mailing list > [email protected] > http://dvandva.org/cgi-bin/mailman/listinfo/computer-go >
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