Author: John Sidles
Date: 14:07:12 02/18/06
Go up one level in this thread
On February 18, 2006 at 16:52:34, John Sidles wrote: Here's the same table, with total score instead of the (less well-defined) "plus score" nGame = 10, confidence = 95.%, score = 7.5/10 nGame = 10, confidence = 99.%, score = 8./10 nGame = 10, confidence = 99.9%, score = 9./10 nGame = 20, confidence = 95.%, score = 13.5/20 nGame = 20, confidence = 99.%, score = 14.5/20 nGame = 20, confidence = 99.9%, score = 16./20 nGame = 30, confidence = 95.%, score = 19.5/30 nGame = 30, confidence = 99.%, score = 20.5/30 nGame = 30, confidence = 99.9%, score = 22./30 nGame = 40, confidence = 95.%, score = 25./40 nGame = 40, confidence = 99.%, score = 26.5/40 nGame = 40, confidence = 99.9%, score = 28.5/40 nGame = 50, confidence = 95.%, score = 30.5/50 nGame = 50, confidence = 99.%, score = 32.5/50 nGame = 50, confidence = 99.9%, score = 34.5/50 nGame = 75, confidence = 95.%, score = 44.5/75 nGame = 75, confidence = 99.%, score = 46.5/75 nGame = 75, confidence = 99.9%, score = 49./75 nGame = 100, confidence = 95.%, score = 58./100 nGame = 100, confidence = 99.%, score = 60.5/100 nGame = 100, confidence = 99.9%, score = 63.5/100 >On February 18, 2006 at 03:50:09, Uri Blass wrote: > >>My question is based on your experience what is the biggest result that A beat B >>in match of 100 games(Noomen match or match based on other positions like Albert >>Silver's postions) but still A is not better than B against other programs. > >Here's a table for how large a plus score you need to see, by either A or B, for >you >to be confident (at the given level of confident) this plus score was not due to >luck. > >Here "luck" means that A and B actually each have 1/3 chance of win, lose and >draw, >but that either program was simply lucky enough to achieve a plus score. > >nGame = 10, confidence = 95.%, score = +2.5 >nGame = 10, confidence = 99.%, score = +3. >nGame = 10, confidence = 99.9%, score = +4. >nGame = 20, confidence = 95.%, score = +3.5 >nGame = 20, confidence = 99.%, score = +4.5 >nGame = 20, confidence = 99.9%, score = +6. >nGame = 30, confidence = 95.%, score = +4.5 >nGame = 30, confidence = 99.%, score = +5.5 >nGame = 30, confidence = 99.9%, score = +7. >nGame = 40, confidence = 95.%, score = +5. >nGame = 40, confidence = 99.%, score = +6.5 >nGame = 40, confidence = 99.9%, score = +8.5 >nGame = 50, confidence = 95.%, score = +5.5 >nGame = 50, confidence = 99.%, score = +7.5 >nGame = 50, confidence = 99.9%, score = +9.5 >nGame = 75, confidence = 95.%, score = +7. >nGame = 75, confidence = 99.%, score = +9. >nGame = 75, confidence = 99.9%, score = +11.5 >nGame = 100, confidence = 95.%, score = +8. >nGame = 100, confidence = 99.%, score = +10.5 >nGame = 100, confidence = 99.9%, score = +13.5 > >So for example, in a 10 game tournament, if either >program achieves a +4 score (or higher), you can be >99.9% confident that such a high score was *not* >due to luck. > >Note: these were calculated by brute force in >Mathematica.
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