Author: Steven J. Edwards
Date: 01:59:00 08/07/98
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On August 07, 1998 at 01:09:56, Danniel Corbit wrote: >All this masterful pounding of plies... It is an interesting exercise in >itself. But I wonder how many of those legal permutations are actually useful. >Did you find any interesting positions in the mix, or are you just throwing them >away without bothering to look at them? At eight microseconds per pathway, there's not much time for analysis. I have found an earlier reference to the enumeration of eight ply long trajectories from the initial array. In the 1949 book _The Fireside Book of Chess_ edited by Chernev and Reinfeld, there is on page 106 an estimate by Edwin Anthony. A figure of 318,979,584,000 is given, a value which is too high by a factor of about 3.75. Well, fifty years ago I guess that logarithms were high tech. Another figure is given for the twenty ply enumeration; it's 169,518,829,100,544,000,000,000,000,000. Yes; that's fifteen significant digits. It may not be that far off; I'd guess that the real answer is somewhere is the neighborhood of 10 to the 30th power. I may do some more work with this using a variant of transposition tables to store position subtree enumerations. This could make an attempt at nine ply enumeration reasonable. Maybe even ten ply with enough memory. -- Steven (sje@mv.mv.com)
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