What's What in Endgames

Continuing with A Brief History of Endgame Theory, where I reproduced the preface to Averbakh's 'Comprehensive Chess Endings' (CCE), an advantage in having this work in digital format (see Averbakh's Convekta for details) is being able to analyze the critical points of endgame research. For example, the following table shows the number of positions in CCE with a certain number of pieces.

4- :    412
5   : 1404
6   : 1020
7   :   487
8   :   222
9+ :   599

In other words, CCE has 412 positions with four pieces or less, 1404 with exactly five pieces, and 599 with nine pieces or more. As I mentioned in the Convekta post, CCE has 'over 4100 examples in total', while the number of positions in the table totals over 4400. Why the difference? The reason is that many CCE examples consist of a key, numbered diagram to illustrate a main theme. These are followed by text descriptions that shift a piece, perhaps the Black King, to different squares in order to illustrate variations on the main theme. In the book, only the numbered diagram is counted as a position, while in the digital file each shifted position is also counted once.

When the Convekta version of CCE was released, tablebases covered five-piece endgames. A few years later the first six-piece tablebase became available, and a seven-piece version is in the works today. GM Pal Benko's column 'Endgame Lab' in the December 2011 issue of Chess Life had this to say (p.48).

Progress with the Seven-Piece Database : The six-piece endgame database, a marvel in its own right, is now in danger of being overtaken exponentially by the arrival of a seven-piece database.

This month I am providing a short review of recent endgame database progress. The remarkable six-man database, now in the public domain (available at www.k4it.de), has even shown a record 243-move win. The team of Americans Mark Bourzutschky and Russian Yakov Konoval have worked together to aim for even higher peaks. As early as 2006, among other interesting records, they reported an unbelievable 517(!)-move win in a King, Queen, Knight versus King, Rook, Bishop, and Knight seven-man endgame. But these are positions without Pawns -- very rare in real games.

Their newest article (in EG 2011) presents piece and Pawn endgames too. Much more challenging for optimal play because of possible Pawn promotions and en passant moves, these endings are much more useful for practical players. Bourzutschky and Konoval gladly answered me and provided some analysis for Chess Life readers.

[...]

I asked them about their future plans. "We are not sure whether we even want to generate all the seven-man endgames, because many will not be interesting but still take up a lot of space. Better analysis of the databases generated so far, and moving to interesting eight-man endgames may be more relevant."

While I don't agree that the six-piece tablebase is 'in danger' of anything, the backend of chess is in danger of losing its mystery. But what can you do? That's progress. Over 60% of the CCE positions are already subject to exact solution and their numbers will increase in a few years.