Perfect endgame play, longest direct mate

Perfect endgame play (3)

By Frederic Friedel

In the first part of our series we told you how endgame databases (or "tablebases") worked, using the example of the four-piecer king+queen vs king+rook. It was the first endgames that was exhaustively calculated, by Ken Thompson back in the early eighties. He generated every legal position with the given material and working backwards from mates created a list in which every position contained information on the distance to mate. His program used this list to play the queen vs rook ending with absolute perfection – "as well as god", Ken once quipped. In the subsequent years Thompson and others worked out all five-piece endings, which we described in the second part of our series.

If you have bought 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 (see below), which is delivered on four CDs, the engines will play all important five and six-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!

Since a majority of our readers will have a chess program with access to five-piece endings we have decided to give you a weekend puzzle that requires a little more than firing up the engine and pressing a key. It is a position that Thompson dug up in 1986, when he was fooling around with his first five-piece endings.

Ken discovered that with the above material on the board there is only one square on which the white king can be placed so that the position is winning by force. Really, only one square – put the white king on any other and Black is able to force a draw. You are invited to solve this using your five-piece tablebases. But do not post the solution in our discussion section below, if and when you have found it.

Longest direct mate problem

Endgame databases can, with the given material on the board, instantly tell you if a position is won, lost or drawn, and how many moves it is to mate. But the mate they announce – often in dozens or even scores of moves – is not like that of a chess problem: it denotes the number of moves the attacking side will require against the best possible defence by the defender. But there are many alternatives, many different paths to reach the same goal. In chess problems of the "Mate in three" variety there needs to be one single move at each stage for the attacker to reach the goal. If any deviation is possible the alternative move is called a "cook" of a "dual". It generally spoils the problem.

So what is the longest mate problem, one in which every single move of the attacker is forced and where there is no alternative for each move, no variation that would not lead to the goal of the problem being met in a (even slightly) different way. In 1976 the longest whistle-clean direct mate problem was published:

In the above position it is White to play and mate in 203 moves, would believe it? We will not mention the name of the composer yet, to encourage you to think about the problem for a while, instead of searching the Internet for the pre-digested solution (damn you Google!). Make copious use of your computer, and run the strongest engines you have. Here in fact is the FEN description to make it easier for you:

6n1/p1BN3b/p1p3np/p1p2rpq/6kr/K1P4p/2PP4/7Q w - - 0 1

It is possible to work out the general idea of the problem with a regular chess engine, but you will have to also think about how Black can delay the inevitable for as long as possible – 203 moves, to be exact. Feel free to discuss it in the feedback section below. We will show you the solution during the coming week, with expert annotations provided by the supreme problemist John Nunn.

Incidentally there have been attempts to construct longer dual-free direct mates since the above position was published, back in 1976. But none to our knowlege was as clean an free of any possible deviation than the one given above.

Endgame databases for notebook computers

In the years after the pioneer work with four-piece endings Ken Thompson and others worked out all five-piece endgames, which have between 212 and 335 million positions each. And then came the six-piece endings, which required truly massive computing power to calculate – and plenty of hard disk space to store. Russian programmer Eugene Nalimov created a new format that required eight times less space than the previous versions. And in 2013 Ronald de Man developed the "Syzygy Bases" that were in turn seven times smaller than the Nalimov tablebases. For the first time it was possible (or practical) to provide users six-men tablebases on DVDs.

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 Endgame Turbo the programs will play all important five and six-piece endings perfectly. They will in fact use the endgame knowledge in the search, so that positions with many more than six pieces that can be traded down to advantageous six or five-piece endings will be handled perfectly as well.

Endgame Turbo 4 contains all five and 27 of the most important six-piece endgames in the Syzygy format, which can be used with top engines like Komodo 8 or Houdini 4. Endgame Turbo 4 consists of four DVDs with the following endgames:

You can order Endgame Turbo 4 in the ChessBase shop here.
Price: €59.90 – €50.34 without VAT (for customers outside the EU) and $54.03 (without VAT).

Expect to read more about five and six-piece endgame databases in a future report.