Just one of 17,823,400,766 positions

4/1/2002 – Imagine this: a relatively simple endgame position, six pieces on the board, with a study-like win. The problem is that White must find 262 accurate moves in order to achieve his goal. In most cases the slightest inaccuracy leads to an immediate draw. We refer to the longest known six-piece ending, as calculated by the endgame databases of Ken Thompson and Eugene Nalimov. Take a deep breath before you proceed to the details here...

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Longest six-piece endgame

You probably know what endgame databases (or "tablebases") are. People like Ken Thompson and Eugene Nalimov have actually taken certain endgames and generated every single position that can occur in them. Working backwards from mate they record the status of every position, and store the results in a database. With help of these databases programs like Fritz, Junior or Shredder can play absolutely perfect chess, at least in those ending. In any position with the given material they are able to say whether it is a win, draw or loss, and how many moves to mate.

One of the first endgames that was exhaustively calculated was the four-piece ending queen vs rook. It was done by Ken Thompson back in the early eighties. He generated every legal position with K+Q Vs K+R – 1,900,000 in all – and working backwards from mates created a list in which every position contained information with the distance to mate (the longest was 61 moves).

In the subsequent years Ken Thompson and others worked out all five-piece endings, which have between 212 and 335 million positions each. If you buy one of our chess programs, they will already play a number of four and five-piece endings (e.g. Q Vs R or R+P Vs R) perfectly. With the "Endgame Turbo" (ChessBase shop, click "Fritz programs"), which is delivered on four CDs, our programs will play all important five-piece endings perfectly. They will in fact use the endgame knowledge in the search, so that games against the computer these days usually end in mate announcements in 20 or more moves!

Thompson and Nalimov have also calculated the most interesting six-piece endgames. These are not available on CDs, since each is between one and two Gigabyte in size. A painful download on the Internet is the only option. However, Fritz and other ChessBase programs are already equipped to use these databases. And Shredder actually has a special "endgame oracle" which allows you to do extensive research with these databases.

Helmut Conrady, a German computer chess journalist, has been experimenting with six-piece endings, using Shredder to find special positions and records. One of his most remarkable discoveries (with the help of Ken Thompson) was the following position:

Longest six-piece ending

White to move

This is the longest know win in a six-piece ending. White needs to play 262 accurate moves to mate the opponent, assuming perfect play by both sides. You can replay the solution below, but before you do so here are some interesting (actually "depressing" would be more apt) facts about the the endgame and the above position.

  1. The number of positions in the endgame K+R+N Vs K+N+N with White to move is exactly 17,823,400,766. They have all been calculated and are all contained in the database. 70.08% of them are winning for White.

  2. The above position is the only one (excluding its mirror positions) in this ending that requires 262 moves to mate. All other of the thousands of billions of positions are shorter wins (or drawn).

  3. In the course of the solution White exceeds the fifty-move rule no less than five times.

  4. If the black king were on a1 instead of b1 in the above position the number of moves to mate is reduced by 141 moves (to 121 moves). If it were on a2, b2 or c1 the position would be a draw.

  5. It is quite likely that nobody will ever understand the point of the moves which the computer tells us are necessary. If you replay the solution you will feel that White sometimes makes no progress for dozens of moves. Then he seems to restrict the black knights, only to let them go for the next 30 or 40 moves.

  6. Of the first 14 moves in the solution to the above position eleven white moves are absolutely forced. This means that if White does not find the only accurate move the game is immediately drawn. There is a phase from move 125 to move 134 in which White has to make ten accurate moves. Any deviation from the forced line loses half a point.

In the above position the only move that wins (= mates in 262 moves) is 1.Ke6!! Helmut Conrady writes: "Only the chess god Caissa knows why in a position without enemy contact or direct threats exactly this one unique move must be played." The best black reply is 1...N6b4! If he plays anything else he shortens the game by at least 143 moves, e.g. 1...Kc1 = mate in 119, 1...N6d4 = mate in 117 or 1...Na5 = mate in 106.

In our analysis any move with two exclamation marks indicates that it is the only white move that retains the win. Every other move draws. A single exclamation mark (!) indicates that this move leads to the shortest mate – all other moves will delay the win unnecessarily. For Black a single exclamation mark means this is the only move that doesn't shorten White's win.

The first eight moves of the solution are 1.Ke6!! N6b4! 2.Ke5!! Nd3+! 3.Ke4!! Nf2+! 4.Kf3!! Nd3! 5.Ke2! Ncb4! 6.Ke3!! Kb2! 7.Kd4!! Nf4! 8.Kc4! Nbd5!

Here's a depressing question: which is the next move that White must play in order to keep the win. There is only one single move he must find, all others lead to a position in which Black can draw. Write down five candidate moves and then check whether the correct one is among them when you play through the solution.

You can play through the main line of this endgame on our Javascript board. If you want full analysis with replayable variations you can download the game in CBV format (41 KB), which can be read by ChessBase, Fritz or any compatible chess program. Maybe we are wrong, maybe with a few decades of intense work you will be able to understand this endgame.



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