Author: KarinsDad
Date: 09:28:15 05/21/99
Go up one level in this thread
On May 20, 1999 at 14:13:34, Dann Corbit wrote: >On May 20, 1999 at 13:44:08, J. Wesley Cleveland wrote: > >>On May 19, 1999 at 19:24:48, Dann Corbit wrote: >> >>>On May 19, 1999 at 18:47:25, Brett Clark wrote: >>> >>>>There are more possible moves in a chess game than there are molecules in the >>>>universe. For that reason, I don't think that we'll ever see a computer play >>>>"1. e4, mate in 50". >>>That may be an overestimate. There are (according to some sources) only 10^52 >>>possible chess board positions [You don't need to know all the moves if you know >>>all the positions -- transpositions are unimportant]. There are (according to >>>other sources) about 10^82 elementary particles in the observable universe. It >>>would be a bit strange if the average molecule had 10^30 particles in it. >>> >>>OTOH, I suspect you are right about "1. e4, mate in 50" being a long way off. >>> >>>I think that we should always be careful to say what is impossible or possible. >>>There are sometimes new ways of looking at things. >> >>The thread about representing positions in the minimum number of bits is also >>about setting an upper bound on the maximum number of chess positions. 160 bits >>is 2^160 or ~= 10^48. >Yes, what a fascinating rejoinder! In this case, if 10^52 is correct, then 173 >bits should be the minimum, since 2^173 = 1.197e52 >If we can encode in less, then the number of board positions is less than we >thought (or we have an error in our thinking and the scheme won't work). Actually, I think that this estimate is based on the number of combinations of piece placement on a board (regardless of whether any set of legal moves can get you to that position), not the legal number of positions that can be achieved via legal moves. An example of this would be black having a pawn on a2, white having pawns on a3, a4, a5, a6, and a7 without having at least 5 captures somewhere along the way (and at least 4 of those captures had to be white captures of black pieces). You could have a lot of positions with just this example alone where the position is not legal, but it has pieces all on legal squares for those particular pieces (e.g. if you had this example with all 32 original pieces still on the board). A simpler example is having your king in check when it is your opponent's turn to move. This cannot occur via legal moves, but may not be excluded at all times in the calculations. KarinsDad :)
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