Author: Michael Yee
Date: 14:04:48 10/12/04
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On October 12, 2004 at 10:28:16, Graham Laight wrote: [snip] >How does one explain such a poor performance by Junior, which had massively >superior hardware to Fritz? Should we ask the Junior programmers to forward >their program to to Franz Morsch for advice and improvement? > >-g If the variance of a random variable is low, maybe then you could expect the outcome to be close to the expected value most times. But it's not true in general. For instance, consider the experiment of 3 flips of a binary coin (0/1). The 8 possible outcomes are: 000 001 010 011 100 101 110 111 Some probabilities of getting n flips: P(0 flips) = 1/8 P(1 flip ) = 3/8 P(2 flips) = 3/8 P(3 flips) = 1/8 Notice in this case that P(E[x] = 1.5 flips) = 0! (That is, it's impossible to get the expected value in this case in one run of the experiment.) Also note that P(< 1.5 flips) = 0.5 (since the distribution is symmetric). To bring this back to the bilbao results... I would just say that to expect Junior to consistently play at a certain level (say 8/10, 8/10, 8/10, etc.) is asking too much. In fact, maybe Junior's style of play introduces more variance over short runs (6/10, 10/10, 8/10). Michael
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