Author: Peter Fendrich
Date: 16:07:04 12/20/02
Go up one level in this thread
On December 20, 2002 at 12:16:25, Uri Blass wrote: >On December 20, 2002 at 11:03:14, Peter Fendrich wrote: > >>On December 20, 2002 at 04:10:35, Rémi Coulom wrote: >> >>>On December 19, 2002 at 19:28:01, Peter Fendrich wrote: >>>> >>>>I did, some 15-20 years ago, in the Swedish "PLY" a couple of articles that >>>>later became the basics for the SSDF testing. >>>>A year or so ago you posted a question about how to interpret results with very >>>>few games. In a another thread I posted a new theory for this as an answer >>>>"Match results - a complete(!) theory (long)". >>>>I also made a program to use for this that can be found at Dann's ftp site. >>>>/Peter >>> >>>Hi Peter, >>> >>>If you had not noticed it, you can take a look at a similar program I have >>>implemented: >>>http://remi.coulom.free.fr/WhoIsBest.zip >>>Basically, I started with the same theory as you did, but I went a bit farther >>>in the calculations. In particular, I proved that the result does not depend on >>>the number of draws, which is intuitively obvious once you really think about >>>it. I also found a more efficient way to estimate the result. I checked the >>>results of my program against yours and found that they agree. >>> >>>Rémi >> >>Hi, >>For me it's not so obvious that you can through the draws out. >>I just took a short look at your paper and maybe I misunderstood some of it. >> >>Take this example: A wins to B by 10-0 >>Compared with: A wins to B by 10-0 and with additional 90 draws. >>Not counting the draws will get erronous results. >> >>The results between our programs shouldn't agree, I think, because I heavily >>relies on the trinomial distribution (win/draw/lose). One can use the binomial >>function (win/lose) and add 0.5 to both n1 and n0 for draws. That will probably >>give a fairly good approximate value but the only correct distribution is the >>trinomial. >> >>/Peter > >If the target is only to find which programs is better we can throw draws. > >You can imagine the following game chessa: > > >One game of chessa includes at least one game of chess. > >chessa is finished only when a chess game is finished in a win. >if a chess game that is played as part of chessa is finished in a draw then >chessa continues and the sides play chess with opposite colors. > >By these rules in both cases the winner won 10 games of chessa with no draws >(draw in chessa cannot happen). > >Uri In that case you don't need anything more than the result. What I'm doing is producing a statment like: A is better than B with the probability of x%. The 10-0 result will raise x very high but the 55-45 result will lower the probability even if A is still regarded as the best. /Peter
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