Last update: 05/03/97

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, itīs 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 ! ..."

92.- "Surrounded" - Proposed by V. Albillo

FEN: rnbQKbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBqkBNR/w

White to play and mate in 12: 1. Nb1-c3

Results

Program	CPU/Mhz	Hash table	Move	Value	Plys/Max	Time	Notes
Rebel Decade 2.0	P100	512 Kb	Nb1-c3	+6.35	11	06:28:11	can't see mate
Crafty 12.9	P100	6 Mb + 1Mb	Nb1-c3	+6.857	15/21	144:02:46	can't see mate
Chess Genius 5.0	PII/266	16 Mb	Nb1-c3	+8.96	12/24	16:10:00	can't see mate
CHEST	Solaris/P166?	70 Mb	Nb1-c3	Mate12	?	36:00:00	shortest mate

Notes: Another extremely computationally intensive position, where both royal couples start completely surrounded by the enemy, and must try to checkmate, while avoiding being checkmated themselves, just as in the normal starting position. Only this time is real frenzy !. In fact, there are so many mating combinations for both sides in this position, that chess engines have a real hard time trying to decide who wins. White has a decisive advantage, being first, but just the slightest failure to maintain it, and it's suddenly lost. For instance, the almost "obvious" move 1. Ng1-f3+, which leaves Black with one and only one forced response, results in White (not Black) being checkmated !. See the Addendum below for further details. Rebel Decade 2.0 suffers a lot with this kind of highly combinatorial positions because of its small hash table. When looking at up to 10 plies, it prefers the losing (but very tempting) 1.Ng1-f3+, but fortunately it selects the probably correct first move, 1. Nb1-c3 when looking at 11 plies in some 6 hours. It examined 373.291.281 positions and evaluated the selected move at +6.35. Chess Genius 5.0 running in a fast computer with a large hashtable, looks at 12/24 plies, taking more than 16 hours to reach that depth, but cannot see mate. All it sees is a large +8.96 advantage for White. It selects the probably correct first move (not proved), 1. Nb1-c3. However, see Ed Panek further comments in the Addendum below. Crafty 12.9, running on a P100 and with reasonably large hashtables, goes deeper, at 15/21 plies, yet it doesn't see mate either, just a large advantage, +6.857 for White, after playing the same move, 1. Nb1-c3. However, it took more than 144 hours to get there ! That's 6 days of continuous running, yet it still doesn't see the forced mate !. CHEST is a special-purpose chess program which specifically searches for mates. It was written by Heiner Marxen, , who is unafraid of Bizarre Positions, Unsolved Positions, etc., and thus tried this position with his program. CHEST, running under Solaris (Unix) and using a 70 Mb transposition table, found the shortest, forced mate in 12 with 1. Nb1-c3 in some 36 hours. You can have a look at another CHEST's great performance in cracking the extremely difficult Bizarre Position Test 75. Amazing ! Addendum: Ed Panek sent an e-mail stating that the Principal Variation predicted by Chess Genius 5.0 after looking at 12/24 plies is: b1c3, g8f6+, e8xf7,e1xf1, g1f3+, f1xg2, h1xd1, b8c6, d1g1+, g2xf2 But then Ed tried the position resulting after these moves are made and discovered that: " ... now when CG5.0 is walked to this point it predicts: c3d1+, f2xe2, f3d4+, c6xd4, d8xc7, d7d6, c7c4+, e2f3, c4d3+, f3f4, d3e3+, f4f5, g1g5++ ... [so it seems to be a] mate in 12 ... " Kai Luebke also liked the position, and tried it very tentatively with some of his best programs, MChess 7 and Rebel 9, just to have a quick look. He reports this: " ... Very nice position, you're surely an inventive guy! :-). Here's a quick first glance from my top programs: MChess 7: move depth time value Nf3+, 5 ply, 1:37, +6,57 Nf3+, 6 ply, 2:44, +6,57 Rebel 9: Nf3+, 8 ply, 0:12, +4,31 Nf3+, 9 ply, 1:01, +5,01 Playing the first two obvious moves (1.Nf3+ Kxf2) and then continuing the analysis didn't help a lot ... " My reply to this last statement was: VA: " ... It will surprise you, no doubt, but if White plays the "obvious" 1. Nf3+, it get's mated. . This was discovered both by Crafty and CG 1.0 and they switch to 1. Qxc7, then to 1.Nc3. I am not sure that White wins, both kings are in real danger, and in the Principal Variation calculated so far (15/18), White had to give its Queen ... " Here's a resume of Crafty 12.9's analysis of this position. Note that the disastrous 1. Ng1-f3+ is considered best at depths 6, 7, 8, 9, 10, 11, and 12. At depth 13, the winning 1. Nb1-c3 is discovered, but notice that it is listed without any Principal Variation, just the first move by itself. It continues to be considered best at depths 14 and 15, this time listed with an usable Principal Variation. Though the last timing listed is 8642:46 (i.e, more than 6 days), actually I let it go up to 13000:00 (more than 9 days), but it didn't change its mind, nor did it find the forced mate. depth time score variation (1) 5-> 4.31 2.080 Qxc8 Qxc1 Qxb7 Nf6+ Kxf7 Kxf1 Qxa8 Qxb2 6-> 9.92 4.372 Nf3+ Kxf2 Ne5 Nf6+ Kxf7 Qxf1 Rxf1+ Kxf1 Qxc8 Kxg2 Qxb7+ 7-> 11.88 4.671 Nf3+ Kxf2 Ne5 Nf6+ Kxf7 Qxf1 Rxf1+ Kxf1 Qxc8 Kxg2 Qxb7+ 8-> 22.69 3.310 Nf3+ Kxf2 Ne5 Nf6+ Kxf7 Qxf1 Nd3+ Kxg2 Rxf1 Ne4 Nf4+ Kxf1 Qxc8 9-> 1:50 5.048 Nf3+ Kxf2 Qxc7 d6 Qc4 Bd7+ Kxf8 Nf6+ Kxg7 Rg8+ Kxf7 Rg4 Nc3 Qxc2 10-> 10:01 3.555 Nf3+ Kxf2 Qxc7 d6 Qc4 Bd7+ Kxf8 Nf6+ Kxg7 Rg8+ Kxf7 Rg4 Nc3 Qxc1 Rxc1 Rxc4 Kxe7 11-> 17:15 5.687 Nf3+ Kxf2 Qxc7 d6 Qc4 Bd7+ Kxf8 Nh6+ Kxg7 Nf5+ Kxh8 Be6 Qc3 Nd7+ Kxh7 Nf6+ Qxf6 exf6 12-> 114:33 4.515 Nf3+ Kxf2 Qxc7 d6 Qc4 Bd7+ Kxf8 Nh6+ Kxg7 Nf5+ Kxh8 Be6 Qxe6 fxe6 Na3 h6 13-> 845:02 4.814 Nc3 14->2260:06 6.188 Nc3 Qxc2 d3 Kxf1 Qxc7 Nf6+ Kxf7 d6 Qxc8 Nbd7 Nf3+ Kxg2 Ne1+ Kh3 Qxa8 Nb6 Nxc2 Nxa8 15->8642:46 6.857 Nc3 Qxc2 d3 Kxf1 Qxc7 Nf6+ Kxf7 d6 Qxc8 Nbd7 Nf3+ Kxg2 Ne1+ Kxh1 Qxb7+ d5 Nxc2 Re8 Bf4+ Kg2 Qxa7