Author: Amir Ban
Date: 12:25:22 06/08/00
Go up one level in this thread
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
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