Computer Challenge 01 – analysis

by Karsten Müller
5/2/2023 – Last week we presented a Computer Challenge. It's a position in which even the best chess engines will not find the solution — even if you run them for a very long time. Our readers were asked to come up with the logic and strategy of the solution themselves, and then confirm everything with the help of the computer. The result: success? Here is the full truth on the historical endgame puzzle.

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When proofreading Mark Dvorestky's Endgame Manual for the 5th edition in 2019 I had noticed that Mark's winning proof was not convincing. As neither I nor my engines could find a win or drawing proof I decided to leave it out as there were other examples on such fortresses in the book.

The first correct and convincing published win was given by Peter Prohaszka in two excellent articles in American Chess Magazine 21/2021, p.67-73 (this is the second part with the solution). The following by Wolfram Schön based on the comments of the ChessBase readers is a version of it:

Here's the full game in which the position occurred, and the solution worked out by Michael Taktikos. In the following you can click (or tap) on any move or any diagram to get a special replayer, where you can start an engine and explore the moves even further.

The plan to smash the black fortress in a nutshell:

  1. The knight "wants" (via b2) to square d3, from where it can occasionally sacrifice itself on e5 or c5, or quickly change direction from d3 and act via c1 and b3 on a5.
  2. The queen "wants" to support him from square c3, from where she can act on a5 and e5
  3. The king wants to move to the kingside, last not least making room for the correct positioning of the former pieces.

Which of the engines can find the win? Their evaluation is deceptive, since almost all show a win evaluation without recognizing the fortress, and with 1. Nxb6? are immediately caught up in the draw vortex. Among the engines that recognize the fortress and start with 1.Kb3!, Lc0 v0.30.0-rc1 with the NN BT2-768x15smolgen-12h-do-01-3650000 is the one who consistently follows the described plan and evaluates the planned move significantly better than other moves. From this one is the main variant in the pgn (on a GPU 3060ti, roughly 15 sec/move)

The second best is Crystal 5 KWK, and the third place goes to Stockfish XI-r1 FD (fortress detection). The latter two also start right away with 1.Kb3, but in their 4 HV they show roughly the same (winning) evaluation for almost all moves and do not follow the plan in a straight line, but only after lengthy maneuvering and some repetitions of the position. The side variants mentioned in the pgn come from these engines (on a CPU Ryzen 9 3900x, set to 22 threads, roughly 15 sec/ move).

Karsten Müller is considered to be one of the greatest endgame experts in the world. His books on the endgame - among them "Fundamentals of Chess Endings", co-authored with Frank Lamprecht, that helped to improve Magnus Carlsen's endgame knowledge - and his endgame columns for the ChessCafe website and the ChessBase Magazine helped to establish and to confirm this reputation. Karsten's Fritztrainer DVDs on the endgame are bestsellers. The mathematician with a PhD lives in Hamburg, and for more than 25 years he has been scoring points for the Hamburger Schachklub (HSK) in the Bundesliga.

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