Author: KarinsDad
Date: 08:28:51 05/19/99
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On May 19, 1999 at 02:40:34, Dave Gomboc wrote: >On May 19, 1999 at 01:54:47, KarinsDad wrote: > >>Dann, >> >>Here is the Shirov Kasparov game I mentioned. I just picked a random game. As >>can be seen, this game maxed out at 142 bits (if Shirov would have castled, say >>at move 13, it could have been 150 bits or slightly higher). The two numbers on >>the left are the number of bits required after each move. The entire advantage >>of this schema is that most black pieces do not require a color bit until a >>white piece or pawn is taken. Once this happens, (in this game at move 3 since >>it was a Sicilian), that condition no longer holds. However, only 2 pawns or one >>piece have to be taken in the entire game to basically ensure that 160 bits is >>the maximum, so by move 4 in this game, the chances of it going above 160 bits >>are negligible. >> >>It would be interesting if someone could find a position from a real game that >>could get to 161 bits or more, but I doubt that will happen. >> >>KarinsDad :) >> >>125 125 1.e4 c5 >>126 126 2.Nf3 d6 >>126 137 3.d4 cxd4 >>135 136 4.Nxd4 Nf6 >>137 137 5.Nc3 a6 >>139 139 6.Be3 Ng4 >>139 139 7.Bg5 h6 >>139 139 8.Bh4 g5 >>139 140 9.Bg3 Bg7 >>141 141 10.Be2 h5 >>137 133 11.Bxg4 hxg4 >>141 142 12.0-0 Nc6 >>142 138 13.Nf5 Bxc3 >>134 135 14.bxc3 Qa5 >>134 134 15.Qxg4 f6 >>134 132 16.Rab1 Qxc3 >>132 132 17.Rfd1 Ne5 >>128 124 18.Bxe5 Qxe5 >>124 124 19.g3 b5 >>124 122 20.c4 bxc4 >>122 122 21.Qf3 c3 >>122 123 22.Rbc1 Bb7 >>121 119 23.Qxc3 Bxe4 >>117 113 24.Nxd6+ exd6 >>113 109 25.Re1 Qxc3 >>106 106 26.Rxc3 d5 >>106 114 27.f3 Kf7 >>110 110 28.fxe4 Rhe8 >>110 110 29.Rc7+ Kg6 >>110 108 30.Rf1 dxe4 >>110 108 31.Rc6 Rf8 >>108 108 32.Re6 Rae8 >>108 108 33.Rfxf6+ Rxf6 >> 98 98 34.Rxe8 Kf5 >> 98 98 35.Kf2 Rh6 >> 98 98 36.Rf8+ Ke5 >> 98 98 37.Re8+ Kf5 >> 98 98 38.Rf8+ Ke5 >> 1/2-1/2 > >What a waste of bits! :) The entire game should have been storable in far >fewer. To know exactly how many, take the number of legal moves from each >position, multiple them all together to get a big number, P. Find n such that P >/ 2^n < 0. n = the number of bits you need to store the raw positions (no >1/2-1/2, player names, etc.) > >I didn't do it for this game, but n will likely be in the low hundreds. You are >using several thousand bits to represent the game. > >Dave The point of the data structure is to store any position when you DO NOT have an entire game, but just a position. The illustration above was only being used to show how difficult it will be in real games to go over the 160 bit limit in the structure. As can be seen (and, of course, this is only one game), most of the positions in this game could be represented in 140 bits or less (considerably less than the 160 bits). For example, you could use this structure to store a bunch of interesting positions in a database. The suggested moves after the position would be stored in a different format. Of course you can store a game in much fewer bits! That was not the point of it. The point of it was whether you could store a position in fewer bits. KarinsDad :)
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