Something about the imagery in Tim Krabbe’s quote below from April 2000 on ultra-long computer database-generated forced mates has stuck with me, long years after I first came across it; something about poetically expressing what superhuman intelligence in a constrained setting might look like:
The moves below are awesomely beautiful. Or ugly—hard to say. They’re the longest “database endgame” mate, 262 moves.
In 1991, Lewis Stiller already made the surprising discovery that this endgame, King plus Rook and Knight versus King plus two Knights (KRNKNN in databasese) is won for the strongest side in 78 % of the cases. He gave the longest win, which was 243 moves—but that was the distance to conversion (the reduction to a smaller endgame), not to mate. From that conversion to mate it was a further 3 moves; a total of 246 moves for the entire win. But for the fastest mate, you could not simply add those numbers, because Black could perhaps allow a quicker conversion to a slower mate, or White could perhaps allow a slower conversion to a faster mate. (See my story Stiller’s Monsters on this site.)
It was expected that the direct path to mate, where both sides only care about the distance to mate, would be shorter than 246 moves. Surprisingly, it turned out to be longer: 262 moves. We owe this discovery to Ken Thompson, who constructed the (93 Gigabyte) database, and Peter Karrer, who found this longest mate in it.
Playing over these moves is an eerie experience. They are not human; a grandmaster does not understand them any better than someone who has learned chess yesterday. The knights jump, the kings orbit, the sun goes down, and every move is the truth. It’s like being revealed the Meaning of Life, but it’s in Estonian. On Thompson’s Website, where this and other endgame databases can be found, he has named the link to them: ‘Play Chess with God.’
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 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. …
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.
In 2014 Krabbe’s diary entry announced an update to the forced mate length record at 549 moves:
In entry 316 of this Diary, in May 2006, I gave a record 517-move win, found by Marc Bourzutschky and Yakov Konoval, in the 7-man endgame of Queen and Knight vs. Rook, Bishop and Knight, also known as KQNKRBN. Now Guy Haworth at the University of Reading, in an update of his Chess Endgame Records, publishes, among 91 sometimes very lengthy longest shortest wins in up to 7-man endgames, the deepest known mate: 549 moves, in the endgame KQPKRBN. It was found by a team of programmers at the Lomonosov Moscow State University.
All the moves below are perfect, but not always in the same way. … As in all longer Endgame Tables sequences, the moves are incomprehensible. Haworth writes. “These extreme positions are the outposts, the Everests or Mariana Trenches of chess’s state space: they should be hailed, visited and contemplated not only because they are there but because the lines from them can perhaps be analysed and explained in terms of some chessic principles.”
Very perhaps, I’m afraid. In the 1097 moves above, there are at least 1000 that I could never understand. If White is following an infallible path to mate, shouldn’t it at least be possible to put the positions below (all with White to play) that are reached on this path, in the right order?
To me, all five seem equally distant from any win. But they represent huge leaps of progress—from left to right, they arise after Black’s 100th, 200th, 300th, 400th and 500th move. It is unfathomable that in the 200-move eternity between the 200- and 400-move diagrams, White should have improved his position—if anything, Black seems freer after 400 moves than after 200.
It is hard to see a shred of conventional strategy. There is no forcing Black’s King to the edge or the corner—it is chased (or just goes) to corners, edges and the center in seemingly random fashion. In fact, the fatal position after move 508, where Black cannot avoid the loss of the exchange, occurs quite suddenly when his King is on c5. White’s King too, marches all over the board—it only leaves 12 squares unvisited.
Krabbe of course includes all the move sequences in his diary entries at the links above, I haven’t reproduced them here.
Something about the imagery in Tim Krabbe’s quote below from April 2000 on ultra-long computer database-generated forced mates has stuck with me, long years after I first came across it; something about poetically expressing what superhuman intelligence in a constrained setting might look like:
And from that linked essay above, Stiller’s Monsters—or perfection in chess:
In 2014 Krabbe’s diary entry announced an update to the forced mate length record at 549 moves:
Krabbe of course includes all the move sequences in his diary entries at the links above, I haven’t reproduced them here.