1. L. Stiller, 1991 White wins in 255 moves |
2. L. Stiller, 1991 White wins in 246 moves |
(NB 29 January 2014: This was written a very long time ago. Some things are outdated. See below for an explanation of the difference between the 'win in 246' on the right and the mate in 262 on the left. Also see entry 393 in Open Chess Diary.)
The above diagrams have a certain notoriety. The one on the left is the longest longest shortest forced win in an endgame, meaning that the shortest path to mate is longer than all other shortest paths with the same material - and longer than all known longest shortest paths with any other material. (The unusual captions 'White wins in n moves' are explained at the bottom of this article.)
The moves leading to mate have been found by the database technique, initiated in 1970 by the German Ströhlein, and later developed mainly by Ken Thompson of Bell Laboratories. The idea is that a database is made with all possible positions with a given material. Then a subdatabase is made of all positions where Black is mate. Then one where White can give mate. Then one where Black cannot stop White giving mate next move. Then one where White can always reach a position where Black cannot stop him from giving mate next move. And so on, always a ply further away from mate until all positions that are thus connected to mate have been found. Then all of these positions are linked back to mate by the shortest path through the database. That means that, apart from 'equi-optimal' moves, all the moves in such a path are perfect: White's move always leads to the quickest mate, Black's move always leads to the slowest mate.
Thompson analysed 4- and 5-man endgames in this way; Stiller was the first to explore 6-man endgames. Theory was refuted in the process: endgames like 2B vs. N; Q vs. 2B or Q vs. 2N, which were thought to be generally drawn, turned out to be wins in more than 90 % of the cases. The endgames above were also considered to be draws until Stiller showed 95 % of the positions are won for White. (The 50-move rule would prevent winning these endgames over the board, but as they have never occurred in games, and probably never will, and couldn't be won by humans anyway, there is no need for a special 250- or 300- move rule.)
What one sees in Stiller's Monsters is Perfect Chess, but there is a
more practical side to perfect chess.
When Kasparov announced his idea of 'Advanced Chess'
a few years ago, where players can consult computers during the game, my
initial reaction was one of dismay: where would all the wonderful blunders
go?
The elimination of blunders, however, turned out
to be the whole point.
How strange, this phobia of mistakes in the very
greatest. Fischer invented his clock for that, so the work of hours would
never again be undone in a second. And now Kasparov wants to bring his
computer. The idea that blunders do not belong in chess, that chess is
a game of iron logic where chance should play no part, is apparently only
shared by laymen and the great champions.
To all other chessplayers, the mistake, not the
pawn, is the soul of chess. Without mistakes no wins. Long live the blunder!
What would chess be without all the hung pieces, the mates in one, the
blindness, the Fingerfehler, the mix-ups of move-order, the Nf5xd6
of Amsterdam 1956, the d4-d3 of Havana 1965?
The Advanced Chess match between Kasparov and Topalov
was not very exciting, but for a while, I thought Kasparov's idea might
lead us to the Perfect Game. However, I soon I realised this would be a
pretty boring game. Because in the light of perfection, what is a mistake?
In most positions with R+N vs. N, you can hang your Rook and
it does not change the result. It was a draw and it still is a draw. In a
higher sense, it is not a mistake at all.
The same with the initial position. It is a draw,
and any move after which it is still a draw must be seen as perfect. And
such moves are very easy to find - in fact, I don't even need a board to
type the moves of a game that consists purely of perfect moves: 1.d4
d5 2.Bf4 c6 3.Nf3 Nf6 4.e3 e6 5.Ld3 Bd6 6.Bxd6 Qxd6 7.0-0 0-0 8.c3 b6 9.Nbd2
Bb7 and so on: the kind of game you sometimes see between weak
club players. The Perfect Game is not worth looking at.
But the Perfect Game of the database endgames is
another matter altogether. The moves are beyond comprehension.
A grandmaster wouldn't be better at these endgames than someone who had
learned chess yesterday. It's a sort of chess that has nothing to do with
chess, a chess that we could never have imagined without computers. The
Stiller moves are awesome, almost scary, because you know they are the
truth, God's Algorithm - it's like being revealed the Meaning of Life,
but you don't understand a word.
If you're not going to play over these
moves - have a look at them at least, just to see what Truth looks like
typographically.
Diagram 1: 1.Ka6 Nb4+ 2.Ka5 Nc6+ 3.Ka4 Nc4 4.Rh2 Nb6+ 5.Ka3 Nc4+ 6.Ka2 Nb4+ 7.Ka1 Ne5 8.Kb2 Nc4+ 9.Kc1 Kc3 10.Bd1 Nd3+ 11.Kb1 Nd2+ 12.Ka1 Nb3+ 13.Ka2 Nbc5 14.Ka3 Nb4 15.Rh3+ Nbd3 16.Bg4 Kd4 17.Bf5 Nf2 18.Rh6 Nfd3 19.Ka2 Ke5 20.Bg6 Kd4 21.Kb1 Kc3 22.Bh7 Kd2 23.Rh2+ Kc3 24.Bg8 Kd4 25.Kc2 Nb4+ 26.Kd1 Ne4 27.Be6 Ke3 28.Bf5 Nd5 29.Kc1 Nd6 30.Bd7 Kd4 31.Kb2 Ne3 32.Rh4+ Kd5 33.Ba4 Ndf5 34.Rh8 Nd6 35.Rh5+ Kd4 36.Bc6 Ndc4+ 37.Kb3 Nd2+ 38.Kb4 Ne4 39.Ba8 Nc2+ 40.Kb5 Ne3 41.Kc6 Nf6 42.Rh4+ Ke5 43.Kc5 Nd7+ 44.Kb5 Nf6 45.Bh1 Nf5 46.Ra4 Nd6+ 47.Kc5 Nfe4+ 48.Kc6 Ng3 49.Bg2 Nde4 50.Ra8 Kd4 51.Rd8+ Ke5 52.Rd5+ Kf4 53.Ra5 Nc3 54.Kc5 Nf5 55.Bc6 Ne3 56.Kd4 Ne2+ 57.Kd3 Nc1+ 58.Kc3 Ne2+ 59.Kb4 Nf5 60.Ba8 Neg3 61.Kc3 Ne4+ 62.Kd3 Ng5 63.Bc6 Nf7 64.Ra4+ Ke5 65.Ra7 N5d6 66.Ra8 Kf4 67.Ra4+ Ke5 68.Bd7 Nb7 69.Re4+ Kd6 70.Rd4+ Ke5 71.Bc6 Nbd6 72.Bg2 Nf5 73.Re4+ Kd6 74.Ra4 Ke5 75.Bh3 Ng3 76.Rg4 Nf5 77.Re4+ Kf6 78.Re1 N7d6 79.Re2 Kg7 80.Re5 Kf6 81.Rd5 Ke6 82.Rc5 Kf6 83.Ke2 Nd4+ 84.Ke3 Ne6 85.Rd5 Nc4+ 86.Kf2 Ng7 87.Ke2 Ne6 88.Rf5+ Ke7 89.Kd3 Nb2+ 90.Kc3 Na4+ 91.Kb4 Nac5 92.Kc4 Nd7 93.Ra5 Nb6+ 94.Kc3 Nc5 95.Kb4 Nd3+ 96.Kb5 Nd5 97.Bf5 N3f4 98.Kc6 Kf6 99.Bb1 Ne3 100.Ra6 Ne2 101.Kd7+ Ke5 102.Re6+ Kf4 103.Re4+ Kf3 104.Re8 Ng3 105.Ke6 Nef1 106.Bc2 Kf4 107.Rf8+ Ke3 108.Rd8 Nh2 109.Ra8 Ngf1 110.Ra3+ Kf4 111.Bd1 Nd2 112.Kd5 Nhf1 113.Kd4 Ng3 114.Ra4 Nde4 115.Kd5 Ke3 116.Ke5 Kd2 117.Bh5 Nc5 118.Ra2+ Ke3 119.Bg6 Nd7+ 120.Kd6 Nf6 121.Ra3+ Kf4 122.Ra4+ Kg5 123.Bd3 Ng4 124.Ba6 Nf5+ 125.Ke6 Ng7+ 126.Kf7 Nf5 127.Be2 Ngh6+ 128.Ke6 Ng3 129.Bd1 Ngf5 130.Rb4 Ne3 131.Bf3 Nef5 132.Bg2 Ng7+ 133.Kd5 Nh5 134.Rb5 Kf4 135.Ke6 Ng3 136.Rb4+ Kg5 137.Bh3 Ne2 138.Ke5 Ng3 139.Ra4 Ne2 140.Be6 Ng3 141.Bd7 Nf7+ 142.Kd4 Nd6 143.Bh3 Ndf5+ 144.Ke5 Nh6 145.Ra5 Kh4 146.Bg2 Kg5 147.Ba8 Ng4+ 148.Ke6+ Kf4 149.Ra3 Nh2 150.Bb7 Ne2 151.Ra4+ Ke3 152.Re4+ Kf2 153.Kd6 Nf3 154.Re8 Ned4 155.Kc5 Kg3 156.Be4 Ne2 157.Bc2 Nf4 158.Kc4 Kf2 159.Ba4 Ng6 160.Kd5 Ng5 161.Kd4 Nf4 162.Bc6 Nf3+ 163.Ke4 Ne6 164.Re7 Nc5+ 165.Kd5 Nb3 166.Be8 Nbd2 167.Bh5 Kg3 168.Re3 Kf2 169.Rd3 Ke2 170.Rc3 Kf2 171.Bg4 Kg2 172.Rd3 Kf2 173.Ke6 Ke2 174.Ra3 Kf2 175.Kf5 Nd4+ 176.Kg5 Nf1 177.Rd3 Ne2 178.Rf3+ Ke1 179.Bh5 Nd4 180.Ra3 Ne2 181.Ra7 Nfg3 182.Bg6 Kd2 183.Rb7 Ke3 184.Kg4 Nf1 185.Rh7 Nd2 186.Re7+ Kf2 187.Bd3 Nc1 188.Ba6 Ndb3 189.Kf4 Nc5 190.Bb5 N1d3+ 191.Kf5 Nb4 192.Re8 Kf3 193.Be2+ Kf2 194.Bh5 Kg3 195.Re3+ Kf2 196.Re2+ Kg3 197.Rd2 Nc6 198.Rd6 Nb4 199.Ke5 Nbd3+ 200.Kd4 Nf4 201.Bf7 Ncd3 202.Ra6 Nf2 203.Ra3+ Kh4 204.Ke3 N2h3 205.Bb3 Kg5 206.Ke4 Kh4 207.Ba4 Nh5 208.Bc2 Ng7 209.Bb3 Nh5 210.Ra4 Kg5 211.Kf3 Ng1+ 212.Kf2 Nh3+ 213.Kg2 N3f4+ 214.Kf3 Nh3 215.Ra5+ Kh6 216.Ra6+ Kg5 217.Be6 N3f4 218.Ra5+ Kh6 219.Bf7 Ng6 220.Ra6 Nhf4 221.Kg4 Kg7 222.Be8 Kh7 223.Bxg6+ Nxg6 224.Kg5 Nf8 225.Kf6 Nd7+ 226.Ke7 Ne5 227.Ke6 Nf3 228.Kf5 Nh4+ 229.Kg5 Nf3+ 230.Kg4 Nd4 231.Kf4 Ne2+ 232.Kg5 Kg7 233.Ra7+ Kg8 234.Rc7 Kf8 235.Kf6 Kg8 236.Rg7+ Kf8 237.Rf7+ Kg8 238.Kg6 Nd4 239.Rf6 Ne2 240.Rf3 Nd4 241.Rc3 Kf8 242.Kf6 Ke8 243.Re3+ Kd7 244.Rd3 Kc6 245.Rxd4 Kc5 246.Ke5 Kc6 247.Rd5 Kc7 248.Rd6 Kb7 249.Ke6 Kc8 250.Rc6+ Kb7 251.Kd7 Kb8 252.Rc7 Ka8 253.Kc6 Kb8 254.Kb6 Ka8 255.Rc8 mate
Diagram 2: 1.Ke6 N6b4 2.Ke5 Nd3+ 3.Ke4 Nf2+ 4.Kf3 Nd3 5.Ke2 Ncb4
6.Ke3 Kb2 7.Kd4 Nf4 8.Kc4 Nbd5 9.Rh7 Ne3+ 10.Kd4 Nc2+ 11.Ke4 Ne6 12.Ke5
Ng5 13.Rh5 Ne1 14.Kf5 Ngf3 15.Ke4 Nd2+ 16.Ke3 Nb3 17.Rh1 Nc2+ 18.Kd3 Nc1+
19.Ke4 Nb3 20.Rh3 Nc5+ 21.Ke5 Ne1 22.Nf6 Ned3+ 23.Kd6 Nb7+ 24.Kc7 Nbc5
25.Kc6 Kc2 26.Rh2+ Kb3 27.Kd5 Kb4 28.Kd4 Nf4 29.Rh4 Kb5 30.Ne8 Nb3+ 31.Ke4
Ng6 32.Rh7 Nc5+ 33.Kd4 Nf4 34.Nd6+ Kc6 35.Rh6 Nb3+ 36.Ke4 Ne6 37.Ke5 Ned4
38.Rh3 Nc5 39.Nc8 Nc2 40.Rc3 Nb4 41.Kd4 Nba6 42.Rc2 Kd7 43.Nb6+ Kd6 44.Nc4+
Kc6 45.Ne3 Kd6 46.Nf5+ Ke6 47.Ng7+ Kf7 48.Nh5 Ne6+ 49.Ke5 Nb4 50.Re2 Nd3+
51.Ke4 Nb4 52.Rb2 Kg6 53.Ng3 Ng5+ 54.Kd4 Ne6+ 55.Kc4 Na6 56.Rf2 Ng5 57.Rf1
Nc7 58.Ne2 Nf7 59.Nf4+ Kg5 60.Kd4 Nb5+ 61.Kc5 Nbd6 62.Ne6+ Kg6 63.Nf8+
Kg5 64.Kd5 Nf5 65.Rb1 Ng3 66.Rb7 Nh6 67.Rg7+ Kf4 68.Ne6+ Kf3 69.Rb7 Nh5
70.Rb4 Nf6+ 71.Kd4 Nh5 72.Kd3 Ng4 73.Ng5+ Kg3 74.Ne4+ Kh4 75.Ra4 Nf4+ 76.Kd4
Ne6+ 77.Kd5 Nf4+ 78.Kd6 Nh3 79.Ra8 Ngf2 80.Nc5 Kg5 81.Ke5 Ng4+ 82.Kd4 Nf4
83.Ne4+ Kg6 84.Ra6+ Kf5 85.Ra5+ Ke6 86.Nc5+ Ke7 87.Ra7+ Kf6 88.Ke4 Kg5
89.Ra5 Nh5 90.Ne6+ Kg6 91.Rb5 Kf7 92.Nc5 Ke7 93.Rb2 Kd6 94.Nb7+ Ke7 95.Ra2
Ng7 96.Re2 Kd7 97.Rg2 Ne8 98.Kf4 Ngf6 99.Ke5 Ke7 100.Re2 Kd7 101.Na5 Ng4+
102.Kf5 Nh6+ 103.Kg6 Ng8 104.Nc4 Nc7 105.Kf7 Nh6+ 106.Kf6 Ng8+ 107.Ke5
Ne7 108.Rd2+ Kc6 109.Rc2 Na6 110.Ne3+ Kd7 111.Rd2+ Kc6 112.Rd6+ Kb5 113.Rh6
Nc8 114.Kd4 Nb4 115.Rh5+ Kc6 116.Nc4 Ne7 117.Rh6+ Kc7 118.Rh7 Kd7 119.Ke5
Nbd5 120.Nd6 Kc6 121.Ne4 Ng6+ 122.Kf5 Nf8 123.Rh6+ Kc7 124.Rh1 Nd7 125.Rb1
Nb8 126.Ke5 Ne3 127.Kd4 Nf5+ 128.Kd5 Ne3+ 129.Kc5 Nd7+ 130.Kd4 Ng4 131.Rc1+
Kd8 132.Re1 Ngf6 133.Ng5 Kc7 134.Nf7 Nf8 135.Rf1 Ng4 136.Rg1 Nf6 137.Re1
Kd7 138.Ke5 Ne8 139.Nh8 Ke7 140.Kd5+ Kd7 141.Rf1 Nc7+ 142.Ke5 Nfe6 143.Ng6
Nc5 144.Rb1 Kc6 145.Ne7+ Kd7 146.Nf5 Kc6 147.Nd4+ Kd7 148.Rd1 N7a6 149.Nf5+
Kc6 150.Rh1 Nb4 51.Rh6+ Kd7 152.Kd4 Ne6+ 153.Kc4 Na6 154.Rh7+ Kc6 155.Rh1
Nac7 156.Rd1 Ne8 157.Ne7+ Kc7 158.Kd5 Nf8 159.Ng8 Kd7 160.Kc5+ Ke6 61.Re1+
Kd7 62.Re7+ Kd8 163.Ra7 Nd7+ 164.Kc6 Ne5+ 165.Kd5 Ng6 166.Rh7 Nc7+ 167.Kc6
Ne5+ 168.Kd6 Nc4+ 169.Kc5 Ne5 170.Rh5 Nf7 171.Kc6 Ne6 172.Ra5 Ke8 173.Nf6+
Ke7 174.Nd5+ Kf8 175.Kd7 Nd4 176.Nf4 Nh6 177.Rd5 Ndf5 178.Ke6 Ng7+ 179.Kf6
Ng8+ 180.Ke5 Nh6 181.Ra5 Ng4+ 182.Kd4 Kf7 183.Ra7+ Kf6 184.Ke4 Ne8 185.Ra6+
Kg7 186.Rb6 Ngf6+ 187.Kf5 Nd7 188.Ne6+ Kf7 189.Ng5+ Kf8 190.Ra6 Ng7+ 191.Kg6
Ne5+ 192.Kh7 Ne8 193.Re6 Nf7 194.Nf3 Nfd6 195.Kg6 Nf5 196.Re1 Ne7+ 197.Kg5
Kf7 198.Ne5+ Kg7 199.Ng4 Kf8 200.Nh6 Nd5 201.Nf5 Kf7 202.Re2 Nb6 203.Re7+
Kf8 204.Re1 Nd5 205.Re5 Nb6 206.Kg6 Nc7 207.Nd6 Nbd5 208.Re1 Ne6 209.Kf5
Nec7 210.Ke5 Nb4 211.Rf1+ Ke7 212.Rf7+ Kd8 213.Nb7+ Kc8 214.Nc5 Nb5 215.Rg7
Kd8 216.Rb7 Nc6+ 217.Ke6 Kc8 218.Rh7 Nb4 219.Na4 Na6 220.Kd5 Nbc7+ 221.Kd6
Ne8+ 222.Ke7 Nec7 223.Rh6 Nb8 224.Nb6+ Kb7 225.Nc4 Nc6+ 226.Kd6 Nb4 227.Rh8
Nba6 228.Rh7 Kc8 229.Na5 Kd8 230.Nc6+ Kc8 231.Ne7+ Kd8 232.Nd5 Ne8+ 233.Kc6
Nb8+ 234.Kb5 Nd6+ 235.Kc5 Nc8 236.Rh8+ Kd7 237.Nf6+ Kc7 238.Rh7+ Kd8 239.Rb7
Na6+ 240.Kc6 Ne7+ 241.Kb6 Nb4 242.Rd7+ Kc8 243.Rxe7 Nd5+ 244.Nxd5 Kd8 245.Kc6
Kc8 246.Re8 mate
NB: In an earlier version of this story, the caption read 'White
to play and mate in n'. But as some readers pointed out, that was not
correct - and neither is my phrasing when I say that the shortest path
to mate is sought. What is sought, is the shortest path to conversion
- in this case the reduction to a winnable 5-man endgame. In a few cases,
you should read 'conversion' where I wrote 'mate.' In diagram 1, the first
conversion takes 223 moves, the second 22 moves, and then mate takes 10 more moves.
In diagram 2, conversion takes place at move 243, immediately followed by a
further conversion one move later and then mate in 2 more moves. But you cannot
simply add these numbers - Black can perhaps allow a quicker initial conversion
for a slower further conversion, or White can find a slower conversion to
a faster further conversion. The shortest path directly to mate from the
diagrammed positions has not been computed and might be a few moves shorter
than the 246 and 255 moves.
In fact, as one reader, Michel van der Stappen,
pointed out, this is illustrated dramatically at the end of the solution
to diagram 2. There, with 243.Rxe7, White executes the conversion he has been
aiming at for such a long time, but misses the quicker mate with 243.Rc7+ Kd8 (Ka8
244.Nd7+ and 245.Ra7 mate) 244.Kb7 and 245.Rd7 mate. Still, 243.Rxe7 is
perfect in the sense that it is the quickest winning conversion possible at that
point.
So - the moves above are perfect in a slightly lesser
way. That makes those solutions vaguely resemble chess after all: White
does not go for mate from move 1, but for intermediate goals.
PS: In 2000, Ken Thompson and Peter Karrer found that the direct perfect road to mate in diagram 2 is 262 moves. Up to White's 205.Re5 the moves are the same as above; with 205...Nec7 Black diverges. This DTM (Depth to Mate) of 262 was then the greatest DTM found, and it still is the record for 6-man endgames. The moves can be played over on the left. Also see entry 60 in Open Chess Diary, Play chess with God.