Author: Bruce Moreland
Date: 13:50:16 05/28/99
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On May 27, 1999 at 16:56:22, KarinsDad wrote: >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. No, it would mean that you were wrong. If you have 16 unique values there is no way to store them in less than 4 bits. If you stop and think about this for a second, perhaps you'll understand. Now, if you have a series of values between 0..15, and you need to store them, you may be able to store them in less than 4 bits each on average, because you can make use of information regarding the frequency with which given values appear. The only way to store in less than log2(legal_positions) bits would be to compress the data based upon frequently occuring patterns. That is a different problem entirely. If the goal is to make a method of encoding *any* legal chess position in some minimum number of bits, you're not going to do any better than assigning each legal position a Godel number and putting it in a word that has that many bits. bruce
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