Last update: 05/03/98

Results

Program	CPU/Mhz	Hash table	Move	Value	Plys/Max	Time	Notes
Chess Genius 1.0	P100	320 Kb	Rc2xc7	Mate9	6/18	00:05:30	seen at 2:32
Chess Genius 5.0	PII/266	8 Mb	Rc2xc7	Mate9	5/17	00:00:24
Chess Genius 5.0	PII/266	8 Mb	Rc2xc7	Mate8	6/18	00:01:02
Chess Genius 5.0	PII/266	8 Mb	Rc2xc7	Mate7	7/19	00:03:10	shortest mate
Rebel Decade 2.0	P100	512 Kb	Re2xe7+	Mate9	8/17	00:18:58	seen at 18m 1s
Crafty 12.7	P100	6 Mb	Re2xe7+	Mate9	9/17	00:19:49	seen at 16:56

Notes: A Rook is a major piece, and has always been considered far stronger than a Knigth, for instance, no doubt about it. How about testing it for real ? In this bizarre position, White has only Rooks, Black only Knights. As it happens to be, all 8 Knights can do little to defend Black against the powerful Rooks: White plays and mates Black in 9 moves or less. In fact, there are several solutions for a mate in 9, and it can be proved that it's indeed a mate in 8 or less, maybe even a mate in 7, though I haven't proved that yet. A possible Principal Variation for an hypothetical mate in 7 goes like this, but I don't know if all Black responses are the best: 1. Rc2xc7 Nb7-d6; 2. Rh2xh7 Na7-c6; 3. Rd2xd6 Ng7-f5; 4. Rd6xd7 Nf7-e5; 5. Re2xe5 Nc6xe5; 6. Ra2-a8+ Ne7-c8; 7. Ra8xc8++ Chess Genius 1.0 with its usual small hashtable but its great programming, finds quickly the mate in 9 while looking at only 6 full plies, the search extensions do the rest. It even sees that it's a mate in 9 in nearly half the time it requires to actually stop the search and play it across the board. Crafty 12.7, with a much larger 6 Mb hashtable needs to look at 9 full plies, but it does find a different move that also gives mate in 9. It takes nearly four times longer than CG1.0 but then nobody's perfect. It looks at 36.595.934 positions, but only evaluates 432.539 of them. Rebel Decade 2.0 behaves almost exactly like Crafty 12.7: it finds the same move evaluated too as a mate in 9, and takes nearly the same time, though looking at one ply less, 8 plies. It had to examine 23.340.325 positions to find the mate. Chess Genius 5.0 needs a ply less than CG1.0, 5/17, to find the same mate in 9, and does it in an incredibly short time, many times faster than Chess Genius 1.0, not to mention Crafty 12.7. Going one ply deeper, at 6/18, it discovers a shorter mate in 8, still much faster than the other programs. But most amazingly, one ply more, 7/19, and it discovers the shortest possible mate in 7, and even so, nearly two times faster than CG1.0's mate in 9, and 6 times faster than Crafty's. Ed Panek let it go yet another ply deeper, 8/20, which took 9 min. 38 sec., but alas, no shorter mate is possible. If you want to have a look at the mate-in-7 Principal Variation and some other interesting comments, see the Addendum below. On the other hand, if you are interested or want to check your favourite program, here's Crafty's analysis: depth time score variation 5-> 1.98 24.721 Rxc7 6-> 6.73 25.020 Rxc7 7-> 32.43 28.008 Rxc7 Nhf6 Rxa7 Nbc5 Rxg7 Nfe4 Ra8+ Nd8 8-> 2:16 28.304 Rxc7 Nbd6 Rxh7 Nac8 Rhxg7 Kd8 Rbc2 Nc4 9 16:56 Mat09 Rxe7+ Kxe7 Rxf7+ Kxf7 Rxd7+ Ke6 Rgxg7 Nd5 Rce2+ Kf5 Rdf7+ Nhf6 Rhf2+ Nf4 Rxf4+ Kxf4 Rxf6# 9-> 19:49 Mat09 Rxe7+ Kxe7 Rxf7+ Kxf7 Rxd7+ Ke6 Rgxg7 Nd5 Rce2+ Kf5 Rdf7+ Nhf6 Rhf2+ Nf4 Rxf4+ Kxf4 Rxf6# time: 19:49 cpu:100% mat:18 n:36595934 nps:30753 ext-> checks:3979005 recaps:0 pawns:0 1rep:447691 predicted:0 nodes:36595934 evals:432539 endgame tablebase-> probes done: 0 successful: 0 hashing-> trans/ref:11% pawn:0% used:w99% b99% Crafty will mate in 9 moves. Addendum: Ed Panek sent the following comments with his result for Chess Genius 5.0: " ... [the mate-in-7 Principal Variation is:] c2xc7, b7d6, h2xh7, d6f5, f2xf5, a7c6, g2xg7, f7e5, h7h8+, e7g8, h8xg8+, d7f8, g8f8++ Apparently the problem is that Black must defend against the pin on e7 knight, and prevent the Rooks from storming the flanks. Note: Genius does not see mate until 24 seconds ... till then it has a +30 advantage :) . This is what Richard Lang (the author of Genius) calls a "cook" to find mate :) . This is what is improved over earlier versions of Genius ..."

72.- Proposed by Valentin Albillo, 1997

FEN: 4k3/bbbbbbbb/8/8/8/8/RRRRRRRR/4K3/ w

White to play and win: 1. Ra2xa7

Results

Program	CPU/Mhz	Hash table	Move	Value	Plys/Max	Time	Notes
Chess Genius 1.0	P100	320 Kb	Ra2xa7	+37.45	8/20	05:02:18	can't see mate
Chess Genius 5.0	PII/266	16 Mb	Ra2xa7	Mate10	7/19	00:32:45	sees Mate11 at 25m
Chess Genius 5.0	PII/266	16 Mb	Ra2xa7	Mate8	9/21	02:47:22	shortest mate
Rebel Decade 2.0	P100	512 Kb	Ra2xa7	+26.86	9	01:42:02	can't see mate
Crafty 12.7	P100	6 Mb	Rc2xc7	Mate12	12/23	08:24:35	sees mate

Notes: In Test 71 above we saw a convincing demonstration that Rooks are in fact stronger than Knights, forcing a mate in 9 moves or less (in fact, in 8 moves and maybe even in just 7). But perhaps Bishops can defend their King more efficiently. As a matter of fact, a Bishop can be considered as a kind of "Rook of the diagonals", and being four of each color, they can make double (quadruple!) attacks on a given point. To test the point, in this bizarre position White has only Rooks, Black only Bishops. We will see that actually, Bishops defend their King better than Knights, presenting much more resistance to the Rooks. But in the bitter end, resistance is futile: White plays and mates Black in 12 moves or less. Maybe as little as 8 moves !. Chess Genius 1.0 does what it can with this difficult position, but its small hashtable does it no good for this kind of combinatorial positions where each side has a lot of possible, very similar moves. After looking at 8/20 plies taking a very long time, it does not see the mate. To accomplish that, it would need to look at least 3 plies deeper, and that would take an inordinate amount of time. Crafty 12.7, with its larger 6 Mb hashtable, is capable of looking at 12/23 plies using only 60% more time than CG1.0, but this is just sufficient to discover a forced mate in 12 moves. This time Crafty's large hashtables and comprehensive search extensions outperformed CG1.0 ostensibly, allowing it to search extremely deep along selected lines, in a necessarily large, but quite reasonable amount of time. Rebel Decade 2.0 fails to find any mate. After looking at 9 plies, and examining 133.669.180 positions, it finds the correct move but fails to recognize it as a mate. Chess Genius 5.0 once again steals the show. It goes on looking deeper and deeper, until, by the time it reaches 7/19 plies, in 25 min., it sees a mate in 11 with 1. Ra2xa7. 7 min. later, still at 7/19 plies, it finds a shorter mate in 10 with 1.Rc2xc7. But for the best result it needs to look still two plies deeper, 9/21, where it finds the shortest mate in 8 in 2h 47m 22s. Continuing the search to 10/22 plies takes 3h 34m 29s, and going still further, to 11/23 plies takes 10h 14m 28s, but no shorter mate is possible. For additional comments and the Principal Variation, see the Addendum below. For the sake of completeness, as usual, here's a resume from Crafty's analysis: depth time score variation 4-> 1.21 18.018 Rxf7 Kxf7 Rxg7+ Kxg7 Rxe7+ Kf6 Rhxh7 5-> 2.57 18.018 Rxf7 Kxf7 Rxg7+ Kxg7 Rxe7+ Kf6 Rhxh7 6-> 8.10 18.279 Rxf7 Kxf7 Rxe7+ Kf6 Rxc7 Bxg2 Rcxd7 7-> 54.07 20.870 Rxa7 Bxh2 Rxd7 Bhe4 Rxe7+ Kd8 Rfxf7 Bxb2 8-> 3:05 21.044 Rxa7 Bxb2 Rxc7 Bd3 Rxb2 Bde6 Rh8+ Bg8 Rbxb7 Bxe2 9-> 43:21 23.731 Rxa7 Bxb2 Rxc7 Bhe4 Rxb2 Bbc6 Rh8+ Bf8 Rb8+ Ke7 Rxc6 10-> 100:34 28.175 Rxc7 Kf8 Rxf7+ Kxf7 Rdxd7 Bc3+ Rxc3 Bhe4 Rbxb7 Bxb7 Rexe7+ Kf6 Rxb7 11-> 288:01 30.897 Rxc7 Bgd4 Rxa7 Bxf2+ Rgxf2 Kf8 Rxh7 Kg8 Rfxf7 Bh4+ Rxh4 Kxf7 Rcxd7+ Kf8 12 504:35 Mat12 Rxc7 Bgd4 Rxe7+ Kxe7 Rxd7+ Kxd7 Rxf7+ Ke6 Rh6+ Kxf7 Rxb7+ Ke8 Re6+ Kf8 Rdf2+ Bxf2+ Rgxf2+ Bxf2+ Rxf2+ Bf5 Rxf5+ Kg8 Re8# Crafty will mate in 12 moves Addendum: Ed Panek sent the following comments with his result for Chess Genius 5.0: " ... [the mate-in-8 Principal Variation is:] a2xa7, h7f5, c2xc7, f7e6, g2xg7, e8f8, d2xd7, f8xg7, d7xe7+, g7f6, e7xe6+, f6g5, c7g7+, f5g6, g7xg6++ In this position, as opposed to the Knights vs Rooks [Test 71], there is a tangible threat to the Rooks immediately. However, the Rooks pose an immediate pin on e7 again while the Bishops have no pin against the White King ... it is only a question of calculating which Bishop to pick off first to achieve the fastest mate :) ..." Also, just for the record, here are the results when 8 Rooks battle eight other pieces in this arrangement. The mate in minus 5 means that even though the side with the Rooks moves first, the Queens mate in 5 moves ! . 8 Rooks against: 8 Pawns 8 Knights 8 Bishops 8 Rooks 8 Queens Mate in 4 Mate in 7 (see Test 71) Mate in 8 (see Test 72) Mate in 15 or less Mate in minus 5

73.- Proposed by Valentin Albillo, 1997

FEN: nnn5/nkn5/nnn5/8/8/5QQQ/5QKQ/5QQQ/ w

White to play and win: Qg3-g7

Results

Program	CPU/Mhz	Hash table	Move	Value	Plys/Max	Time	Notes
Chess Genius 1.0	P100	320 Kb	Qg3-g7	Mate9	7/19	01:58:11	sees mate
Chess Genius 5.0	PII/266	16Mb	Qh3xc8+	Mate11	8/20	00:18:53	longer mate
Chess Genius 5.0	PII/266	16Mb	Qh3xc8+	Mate9	9/20	04:48:00	shorter mate
Rebel Decade 2.0	P100	512 Kb	Qf2-a2	+51.20	8	03:27:28	doesn't see mate

Notes: In Test 71 above, we saw how 8 Rooks could easily defeat 8 Knights, giving mate in 7, at most. Having 8 Queens instead of 8 Rooks against the Knights, results in an even faster defeat, as the Queens are able to give a mate in 2. But a large part of the disadvantage comes not from the fact that the Knight is much weaker than the Queen or the Rook, but from the fact that the stronger side moves first, and the Knights are not protected in the initial arrangement, so that Black loses several of them before they can protect themselves. To test this, let's see what happens given the initial position of this Test. Here, each Knight is well protected, by other Knights, and by the King. Even though they have to fight 8 Queens, they offer far more resistance, so that in this position White can give mate in 9 or less. Just for comparison, and to help appreciate Knights as they deserve, exchanging in this same position the Knights for Bishops, White can give mate in 2, while exchanging the Knights for Rooks, allows White to give mate in 3. So the Knights defends its King better !. There's something in this position that's very interesting for testing purposes, and that's the fact that, due to the symmetric nature of the arrangement, there exist two identically winning moves, with the exact same evaluation, each one the mirror of the other with respect to the large diagonal. Thus, all pruning, refutations, etc, have to deal with the inconvenient fact that there's one other move who cannot be refuted, because there are two identical co-best moves ! This doesn't make it any easier to find the best move, but much harder. Chess Genius 1.0 finds a mate in 9 after looking at 7/19 plies, which is nearly the minimum number of plies a program needs to look at to recognize a mate in 9 (17). It takes a long time, increased by the symmetrical, non-refutable solution (1. Qf2-b2). Quite oddly, Chess Genius 5.0 needs to look one ply deeper to see any mate at all, at 8/20 plies, and even then, it finds one of the correct moves (not the one found by CG1.0), but evaluates it as a longer mate in 11. Letting it search still another ply deeper, 9/20, it finds the very same move, but this time correctly recognized as a shorter mate in 9. Why it needs two more plies than CG1.0, and more than double the time even though it runs in a computer 3 or 4 times faster, and with a much larger hash table, really beats me !. See the Addendum below for further comments and the Principal Variation. Finally, freeware Rebel Decade 2.0 fails to find the mate. Even though it searches one ply deeper than CG1.0 taking nearly double the time, it does not find any of the correct moves, and also does not evaluate the chosen move as a mate. It examined 156.344.214 positions, but to no avail. Addendum: Ed Panek sent the following comments with this result for Chess Genius 5.0: " ... [letting it continue to see if there's a shorter mate] no change after 8 hours and depth 9/20 and 5 move queries from depth 10/22 (almost depth 10) [so no shorter mate seems possible. The Principal] Variation is: h3xc8+, a7xc8, h2h8, c7d5, f3xd5, b6xd5, h8xc8+, b7xc8, h1h3+, c8b7, f1b5+, a8b6, f2xb6+, d5xb6, g1xb6+, b7a8, b6b7++ [It was a] big problem for my computer... even though it is fast I let it run all day while I was at work (8 hours) and it could not get to depth 10 ... too many queens ..."

74.- "Melee", proposed by Valentin Albillo, 1997

FEN: RnBqkBnR/PPppppPP/8/8/8/8/ppPPPPpp/rNbQKbNr/ w

White to play and mate in 8: h7xg8=N !!

Results

Program	CPU/Mhz	Hash table	Move	Value	Plys/Max	Time	Notes
Chess Genius 1.0	P100	320 Kb	h7xg8=N	Mate8	6/18	00:03:13	shortest mate
Chess Genius 5.0	PII/266	8 Mb	h7xg8=N	Mate8	7/19	00:03:26	shortest mate
Rebel Decade 2.0	P100	512 Kb	h7xg8=Q	+17.86	8	01:15:05	can't see mate
Crafty 12.7	P100	12+5 Mb	h7xg8=Q	Mate10	9/19	01:08:50	longer mate
Crafty 12.7	P100	12+5 Mb	h7xg8=N	Mate7	9/13	01:22:57	Bug !?

Notes: Chess is a finely balanced game, where both players start from a symmetrical initial position, and White, having the first move, has thus a slight advantage. But not all symmetrical initial positions are so fair. In fact, one can be surprised by the amazing results one can get when starting from some altered initial positions. For instance, in this Bizarre Position, "Melee", all pieces are on the same squares as on the standard initial position, except for the fact that their colors alternate symmetrically for Black and White. The resulting position is perfectly symmetrical, yet White can mate in 8 moves, starting with an amazing non-checking underpromotion to a Knight !. Chess Genius 1.0 finds the mate in 8 after looking at 6/18 plies in a short time. Notice that recognizing a mate in 8 requires to look at at least 15 plies for certain variations, and CG1.0 is achieving this with only 6 plies of full-width search, plus 12 extra for relevant extensions. In this case, at least 9 extension plies are explored. The Principal Variation predicted is: 1. h7xg8=N Bc1xd2+; 2. Ke1xd2 f7-f6; 3. Ng8xf6+ Ke8-f7; 4. g7-g8=Q+ Kf7xf6; 5. Rh8-h6+ Kf6-f5; 6. e2-e4+ Kf5xe4; 7. Qd1-f3+ Ke4-e5; 8. Bf8-g7++ Surprisingly, Chess Genius 5.0 needs to go one ply deeper, 7/19 to find the same shortest mate, and it takes slightly longer. This is surprising, because it's a far newer version, it's running in a machine at least 3 times faster, and it's using a much larger hashtable. Nevertheless, it saw the correct underpromotion at a depth of 6/18, in just 45 sec. but evaluated as a mate in 9. Just to make sure there wasn't a shorter mate, Ed Panek let it run till it reached an amazing depth of 17/29 plies, taking no less than 8 hours 17 min. and 15 seconds, for good. The move was still evaluated as a mate in 8, the very shortest possible. Rebel Decade 2.0 is the only program tested which fails to find any mate. It searches to a depth of 8 plies in nearly the same time that Crafty 12.7 took to search 9 plies (more than an hour), and it finds the same move as Crafty, but fails to recognize it as a mate. It examined 60.527.375 positions in all. Crafty 12.7, on the other hand, behaves very oddly with this position. First, though it uses a 12 Mb hashtable for transpositions, plus a 5 Mb hashtable for pawn structures, it needs to look as deep as 9/19 plies to discover an inferior move, 1. h7xg8=Q which it evaluates as a longish mate in 10, and does it more than 20 times slower than the shortest mate in 8 found by Chess Genius 1.0. But letting it search a little longer, still at 9/13 plies, it finally discovers the correct underpromotion to a Knight, 1. h7xg8=N, but evaluates it as a mate in 7, which it is not !. I searched the position with several programs, and even coded a special exhaustive mate search, and I can confidently state that it's a mate in 8, and no mate in 7 or less can be forced in this position. What gives ? Perhaps some Crafty 12.7 evaluation bug ?. Seems likely. Just for its possible usefulness in tracing the bug, here's an extract of Crafty 12.7's faulty analysis: depth time score variation 8-> 2:05 17.252 hxg8=Q hxg1=Q Bxe7+ Kxe7 Qxd8+ Kd6 Qf6+ Kd5 Nc3+ Kc4 Qf4+ Kc5 Qf5+ d5 Qxd5+ Kb6 axb8=Q 9 3:16 ++ hxg8=Q!! 9 68:50 Mat10 hxg8=Q Bxd2+ Kxd2 hxg1=Q Qxf7+ Kxf7 g8=Q+ Kf6 Qg7+ Ke6 Qg6+ Ke5 Bg7+ Kd5 Kc3+ Kc5 Qd4+ Kb5 Qb4# 9 82:51 Mat07 hxg8=N f6 Nxf6+ exf6 g8=Q Bxd2+ Kxd2 axb1=N+ Qxb1 Qe7 Bg7+ Qf8 Qxf8# 9-> 82:57 Mat07 hxg8=N f6 Nxf6+ exf6 g8=Q Bxd2+ Kxd2 axb1=N+ Qxb1 Qe7 Bg7+ Qf8 Qxf8# time:82:58 cpu:100% mat:21 n:91285026 nps:18338 ext-> checks:17642216 recaps:40821 pawns:2743444 1rep:4872883 predicted:0 nodes:91285026 evals:486395 endgame tablebase-> probes done: 0 successful: 0 hashing-> trans/ref:15% pawn:-26% used:w99% b99% Crafty will mate in 7 moves.

75.- "The Ring", proposed by Valentin Albillo, 1998

FEN: 8/2pPpP2/1P1qk1p1/1p4P1/1P4p1/1p1QK1P1/2PpPp2/8/ w

White to play and mate in 12: 1. f7-f8=Q

Results

Program	CPU/Mhz	Hash table	Move	Value	Plys/Max	Time	Notes
CHEST	Solaris/P166?	70 Mb	f7-f8=Q	Mate12	?	31:30:00	shortest mate
Crafty 12.9	P100	6+1 Mb	Qd3xd6+	+10.509	8/13	04:23:40	can't see mate
Chess Genius 5.0	PII/266	12 Mb	f7-f8=Q	No mate found	18/19	16:00:00	Special mate levels

Notes: In this Bizarre Position, "The Ring", we have a very unstable symmetrical position where not only the Royal Couples are very near, but also there are a number of pawns about to promote. This is both an interesting, aesthetically beautiful position by itself, and also a good test of chess engines and special mate programs, as the number of possible promotions, underpromotions, and checking threats is very large. Crafty 12.9 cannot find the mate. It takes extremely long to perform even a very shallow search, more than 4 hours to reach 8 plies, and, as explained in the Addendum below, 30 full hours aren't enough to reach 9-ply depth. It selects 1. Qxd6+ evaluated at +10.509, no mate. CHEST is a special-purpose chess program which specifically searches for mates. It was written by Heiner Marxen, , who kindly ran this Bizarre Position and sent me the result. As you can see, CHEST, running under Solaris (Unix) and using a 70 Mb transposition table, could find the shortest, forced mate in 12 with 1. f7-f8=Q in some 31 hours. See Heiner's interesting comments on both his program and the result in the Addendum below. Chess Genius 5.0 running on a powerful PII/266, and set to it's Special Mate Levels (not Infinite level), goes to 18/19 plies in 16 hours, but cannot find any mate in 9 or less. It suggest the correct move, 1. f7-f8=Q, however, as the best candidate found. Addendum: Here's an extract of Crafty 12.9's analysis: depth time score variation 2-> 2.72 5.912 f8=N+ Kf7 Qxd6 f1=Q Qxg6+ 3-> 12.21 7.783 Qxd6+ exd6 f8=Q d1=N+ Kd2 Kxd7 bxc7 Kxc7 Kxd1 bxc2+ Kxc2 4-> 36.87 8.467 Qxd6+ exd6 f8=Q d1=N+ Kd2 Kxd7 Kxd1 b2 Qf7+ Kc6 Qxc7+ 5-> 2:01 9.577 Qxd6+ cxd6 f8=Q d1=Q d8=Q f1=N+ Kf2 Qd4+ Kxf1 Qd1+ Kf2 Qd4+ Kg2 Qe4+ Kf2 bxc2 Qfxe7+ 6-> 10:20 10.179 Qxd6+ cxd6 f8=Q Kxd7 Kxd2 Kc6 Qxf2 b2 Qg1 b1=Q Qxb1 Kxb6 7-> 28:14 10.175 Qxd6+ cxd6 f8=Q d1=N+ Ke4 f1=Q Qxf1 Kxd7 Qxd1 Kc6 Qd5+ Kxb6 8 263:40 10.509 Qxd6+ cxd6 f8=Q d1=N+ Kd2 f1=Q Qxf1 Kxd7 Qxd1 Kc6 Qg1 b2 Kd3 The attempt seems somewhat short, but I let it run till it reached 1800 minutes (30 hours) without it printing any more lines (i.e.: it didn't reach 9 plies). As you can see, it does not find the mate, nor does it find the conjectured correct first move 1. f7-f8=Q (this was found with old Chess Genius 1.0: it didn't see mate in 12, but when playing both sides it did deliver a mate in 11 without too much trouble). Heiner Marxen tried this position on his own special mate-searcher, CHEST, and was able to solve it, demonstrating that it is a mate in 12 (and no less) in some 31 hours. In his own words: "... I let CHEST run during the Christmas holidays, and it cracked "The Ring" ... it is a forced mate in 12, with 1. f8=Q (as you already expected). No other key move leads to a forced mate in 12, and there is no way to force a mate in less than 12 moves. Running on a P-166 (guessing) and using a 70MB transposition table, it needed ca 31.5 hours to be sure of the key move, and another 7.5 hours to print the top 7 plies of the complete solution tree ... ... although CHEST cracked this one, it was a really tough job, and there might have been some luck involved. This is the high end job CHEST can do in reasonable time on a fast machine. Some (arbitrary) statistics: searches in transposition table: ca 600 million found in transposition table: ca 135 million mate in 2 jobs: ca 202 million mate in 2 computed (not in TT): ca 162 million moves done/undone: ca 1300 million Some other 32-bit statistics counters did overflow (several times) ... Hope you enjoyed my analysis of "The Ring" (I did :-). So long!."