Author: Bruce Moreland
Date: 22:17:14 01/30/01
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On January 30, 2001 at 21:53:55, Dann Corbit wrote: >On January 30, 2001 at 21:24:13, Robert Hyatt wrote: >[snip] >>I think that 1000 game match might well be way off from 50%. IE it is not >>unlikely that one side will pull ahead a significant amount, and then they >>start playing equally for the rest of the match. But there is nothing in >>statistics that says after you flip a coin and get 100 consecutive heads, >>that sometime later you will get 100 consecutive tails to offset them. It >>is more likely that this series will simply end with heads being ahead 100 >>counts... > >You can have a bad run anywhere. For instance, for two perfectly even engines, >one can win ten in a row [including against itself, for example]. The >probability of this happening right off the bat is identical to it happening one >million games into a very long trial. Over a very long run, the bad runs will >cancel each other out (on average). And if you have one after one million >games, 10/1000000 is a very small percentage so it won't hurt much. All that happens if you have a run of good or bad luck is that you shift your location within the normal distribution to the left or to the right a little bit, which is kind of the point of the normal distribution. If you do 1000 tests you probably do not end up with +500 -500, but all the silliness *approximately* cancels out, and most of the time you end up pretty close to the mid point, and almost all the time you end up within a reasonable distance from it. bruce
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