Author: Mark Young
Date: 23:10:00 07/17/04
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On July 17, 2004 at 23:54:49, Stuart Cracraft wrote: >[D]3qk3/8/8/8/8/8/PPPPPPPP/RNBQKBNR w - - 0 1 > >White to play and mate. > >Is this a joke or real? > >Stuart FEN: [d]3qk3/8/8/8/8/8/PPPPPPPP/RNBQKBNR/ w White to play and mate: 1. ? Results Program CPU/Mhz Hash table Move Value Plys/Max Time Notes Chess Master 5000 P100/Win 95 unknown <32 Mb e2-e4 +32.68 12 48:00:00 1.700.000.000 pos. Rebel Decade 2.0 P100 512 Kb e2-e4 +31.73 12 04:38:53 235.754.343 posit. Crafty 12.7 P100 24+5 Mb e2-e3 +36.258 15 63:27:31 3.778.604.670 pos. Chess Master 5500 Pentium Pro 200 Mhz ? e2-e3 +31.76 10 00:07:27 mate not found Chess Genius 5.0 PII/266 16 Mb e2-e4 +35.24 13/25 09:22:00 can't see mate Notes: Despite its simple, innocent aspect, this is an incredibly computationally expensive mate problem, inspired by Test 12, a problem proposed by english problemist Henry Dudeney where the object was to mate the lone king in 6 moves. Here, he is not alone, but has his powerful wife to help. This makes the task much more difficult. Of course, it has to be a mate in some number of moves, but I have been yet unable to determine in how many, and which move begins the mating sequence. My best conjecture is that it's a mate in 12 moves, but I have yet to prove it. For this one, no endgame tablebases will save the day. It has to be solved by computing muscle alone, and the number of possible moves at each ply is large. Chess Master 5000, running under Windows 95 on a Pentium 100 with 32 Mb of RAM, set to Infinite time, Brute Force, looks at 1.700.000.000 positions (yes, 1.7 billion positions !) in some 48 hours, but even so, it´s unable to find the mate. By the way, though 1.700.000.000 positions seem a lot, they can be examined by Deep Blue in less than 9 seconds, you know. Rebel Decade 2.0 goes to 12 ply-depth, examines a modest (in comparison) 235.754.343 positions in less than 5 hours, but fails to see the mate, just the obvious large advantage. Crafty 12.7, running on a Pentium at 100 Mhz, and with 24 Mb for the main hash table and 5 extra Mb for the pawn structures hash table, cannot find the mate either, after searching to a depth of 15 plies in some 63 hours. It looks at 3.778.604.670 positions (almost 4 billion positions, it would take Deep Blue nearly 20 seconds to examine that many), of which only 1.217.302.718 are evaluated, but the best it finds is that 1. e3 leads to a gain of at least +36.258. No good. It should be mate, nothing else will do. Just for fun, Kai Luebke let Chess Master 5500 look at this position for some 7 minutes on his powerful hardware, and it reached 10 plies no less. At that depth, its evaluation of the move was significantly less, and of course, it found no mate at all. Perhaps letting it look at the position for some weeks could prove useful !. Ed Panek also tried his hand at this position with Chess Genius 5.0, running on a very fast computer with a large 16 Mb hashtable. After more than 9 hours it reached 13/25 plies, yet it couldn't find the mate. However, not to be outdone, Ed tried a different approach. See the Addendum below. Incidentally, this could be a good way to completely solve the game of chess. Just keep adding new men to help the Royal Couple, one at a time, and determine the minimun number of moves to give checkmate. When you have added some 14 men, that's it. Simple, isn't it ? Addendum: Kai Luebke sent e-mail about this position, and told me this: " ... BTW, none of my programs solved Test 91 in under 1 hour (I also tried MChess at "mate in 12" level). Maybe a special mating solver like Alybadix can do it, but I doubt even Rebel 9 or MChess 7 will find this under 10 hours. Maybe Cray Blitz ..." Ed Panek, who also tried very hard at this position, sent an e-mail telling me his further efforts after the unsuccessful attempt. He let Chess Genius 5.0 play both sides continuously, game after game, for a total of 12 games, at 1 min. per move. The results, in his own words: " ... Genius never mates in under 12 full moves or over 13 moves, but always finds mate. I would conclude that there are many mates in 12, and maybe a few in 11 ... Unsure for now ... Wait for next generation of processors to come out, or until I go on vacation and let the computer run all time ! ..."
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