Author: Bruce Moreland
Date: 14:36:08 06/08/00
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On June 08, 2000 at 15:25:22, Amir Ban wrote: >On June 07, 2000 at 19:05:30, Bruce Moreland wrote: > >>On June 06, 2000 at 15:53:44, Wayne Lowrance wrote: >> >>>All of the probobability details boil down to Junior having about as much >>>chance of beating Crafty 10-0 as I do winning the lotto, ok, exagerated but the >>>result from my perspective is wrong, something is wrong, I agree with Dr Bob's >>>assessmenmt. I am a educated EE (retired)and If one of my staff engineers came >>>to me with a similiar test result of his project, well, he would know better not >>>to come to me with it, Period. >> >>You would be being too harsh. >> >>It's true that if you pick a random string of results, you shouldn't expect to >>see an improbable outcome. >> >>But if you can search through a series of sub-strings, looking for one that has >>an improbable outcome, you might very well find one, since you give yourself a >>lot of chances. >> >>I wrote a program that allowed me to test this. I did a series of matches. >>Each match was 30 tests. If a 60/40 probability came back on the 60 side, I >>scored a given test a success. If there was a string of 10 successes in a row >>in any match, I counted this match. It should have been very possible to >>predict the probabilities here exactly, but I figured a Monte Carlo simulation >>would be good enough. >> >>I ran 1,000,000 trials and 55,000 of them had a series of 10 successes in a row. >> Which is 5% of them, which sounds like not a lot, but it is really quite a lot >>given how rare a string of 10 successes in a row should be. >> >>If I use a 50/50 probability, I only get about 10,000 matches counted, and if I >>up it to 75/25, I get over 300,000, which is 30% of the matches. It seems like >>small differences in the probabilities used have a large effect upon the >>outcome. >> >>This doesn't simulate chess very well, since we have draws, but I think that >>I've shown the test shouldn't be summarily dismissed as unfair. It may have >>been an improbable outcome, but not necessarily so improbable that you'd suspect >>the test. >> >>The only thing I'm a little suspicious of is that the string was the last ten >>games, so I'd wonder if Crafty was a little sick or something. That could bear >>some investigating. >> >>bruce > >Ok, here's my two cents: > >The most likely estimate for the game outcome is the overall match result >(33.5/41). The probability for any *particular* sequence of 10 games (say the >last 10) to be 10-0 is (33.5/41)^10 = 13.3%. > >If you want probability for any sequence anywhere, the probability is larger, as >you point out. > >If you suspect the 10-0 result, you can argue that the most likely estimate >should discount this result, so this gives you a probability of (23.5/31)^10 = >6.3%. Again, much larger if you look at *any* sequence. There's not much to say >for this argument, because it discounts the 10 games on the premise that the >result is improbable, but still finds that the result is probable. > >Amir As Uri pointed out, it's hard to relate this to chess, since there are draws. If you score 75% against someone, that isn't enough information. If you score 75% by winning three out of four, the odds of 10 wins in a row are (3/4)^10, which is 5.6% If you score 75% by winning half the games and drawing the rest, your odds of 10 wins in a row are (1/2)^10, which is only 0.10%. That's a dramatic difference. My guess is that ten wins in a row, given an evident ability to score about 75%, isn't so far out of the question that I'd doubt the test. That was the point I was suggesting to the fellow I responded to. bruce
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