Author: Dann Corbit
Date: 14:09:41 05/27/99
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On May 27, 1999 at 16:56:22, KarinsDad wrote: [snip] >2) Due to the "tricks" being used to decrease the number of bits, the actual >number of legal positions may be greater than 2^x where x = minimum number of >bits it can be fit into. For example, if I had a 4x4 chess board and only one >piece to place on it, it is obvious that there would be 16 possibilities or 4 >bits required to represent it normally (assuming the piece had to be on the >board). If I could then use some compression trick to drop it down to 3 bits, it >would not mean that the number of possibilities dropped from 16 to 8, it would >just mean that I was clever. If you have some mapping from a large set of bits to a smaller one, then it does completely number the possibilities or you have an error. I am assuming that a binary string of n bits can be translated to a unique board position. If this is true, and all board positions can be generated using *whatever* function you wish to apply to the bit string, then the count of bits will absolutely be a way to determine the limit of legal board positions. I won't be hasty to dismiss his methodology until I have seen it in total. The work of J. Niervegelt does, indeed, indicate that there may be only about 100 bits of information in a chess position. However, I don't think any 18 queen positions were tried, so I'll withhold judgement on that one. At any rate, a correct and compact coding will have important theoretical value.
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