> If you don't see why that it is false, consider this more extreme example. > "I will toss it 1000 times, look for the run of 100 tosses that has the most > heads, and look up the results for that run in a ststistical table and > announce its significance level."
to beat a dead horse... moreover, somewhat long runs will occur with high probability. many people assume that an unbiased coin will (when examined at any point during the experiment) give exactly half heads and half tails with high probability. this would only be true if the sequence alternated heads and tails. which is as unlikely as getting all heads or all tails. to convince yourself to the contrary, toss a coin 100 times, writing down the sequence of H and T's. note that any other sequence with the same number of H's and T's is equally likely, such as the one where all of the H's come first, followed by all of the T's. also note that the sequences with *no runs* greater than 1 are less likely than those with *at least one run* greater than 1. further, assuming that it did not come out exactly 50/50, note that relabelling H's and T's as one another will result in a sequence with equal probability of occurring as the one you generated, or any of its permutations. however (and this is the part that takes some more detailed math), most experiments of this sort will, if evaluated after every coin toss, result in a temporary run that is skewed far outside the actual bias of the coin. for an unbiased coin, you can count on n/2 +- sqrt(n) heads for moderate values of n, and not really much else. s. _______________________________________________ Computer-go mailing list [email protected] http://dvandva.org/cgi-bin/mailman/listinfo/computer-go
