Author: Uri Blass
Date: 11:01:46 05/26/02
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On May 26, 2002 at 06:17:45, Martin Schubert wrote: >On May 26, 2002 at 05:02:43, Uri Blass wrote: > >>On May 26, 2002 at 02:46:42, Martin Schubert wrote: >> >>>>That means that at this time Fritz7 has the most probability to be the best. So >>>>it must be listed as number one. >>> >>>That's not true. There is no probability for Fritz7 being the best. You can't >>>calculate any probability for that because the statistical assumptions are that >>>the ratings are unknown but solid. >> >>We can talk about probabilities because we do not know and the question is what >>is our chances to be correct in guessing. > >You're wrong. We don't know the true rating. But there are now probabilities for >that. Statistically we have assumptions of solid unknown ratings. The >probabiilities are lying in the results of the games. After having finished the >games there is no chance anymore (is "chance" the right english word in this >context? I mean the german "Zufall"). So you can't talk about probabilities in >this context. My point is that there is a meaning for the probability that we believe that X is better than Y. If you need to make a guess which program is better, then there is a meaning to the question what is the probability that you believe that you are right. Let assume for the discussion that the rating of Fritz is distributed normally with average of 2720 and standard deviation of 50. Let assume the same is for tiger except average 2700. These assumptions are before seeing games because we need to assume apriory distribution and it is logical to assume that Fritz is probably better based on previous expereince when Fritz was the program that was leading the ssdf list more often than Tiger. let use the variable X for the rating of Fritz and the varaible Y for the rating of Tiger. X and Y are constants but for us they are not constants because we do not know them. We ask the question what is the probability that X>Y. Before having games we can say that it is slightly more than 1/2 based on our assumptions. After having games we can have better knowledge about X and Y and we may change our opinion. I agree that the fact that Fritz has better rating than Tiger does not mean that the probability that we believe that Fritz is best is more than 50% because it is important to know also what is our previous opinion and in case that our previous opinion was that tiger is best we may continue to believe that Tiger is best even if Fritz is leading and the difference is small enough. Uri
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