For those that aren't aware of the Nalimov Tablebases, they provide a complete assessment (win, loss, draw) of every position involving 6 pieces or less. This task has been progressing for years, starting with 3 piece endings (eg K+PvK). As computing power has increased, positions with more material has been investigated. The method for generating these results is to start with the final position (and assessment) and then work backwards to generate a set of positions that lead to the final position.
Nalimov Tablesbases are much beloved by computer chess programmers as they can be incorporated into a chess program, removing the need to actually teach a program what to do in a number of endgame positions. Personally I find this a sign of laziness on behalf of a programmer, but it does make the program play perfect chess in these endings, resulting in better results.
Another use of Tablebases is to check endgame analysis from books like Basic Chess Endings (Fine) or Pawn Endings (Averbakh and Maizelis). Indeed in the later book the diagrammed position is of interest.
The book gives 1.d5! as winning, which it does, but states that White can also win with 1.a4. However the website states that this is a draw after 1. ... Ke4! 2.a5 Kd5 3.Ke2 Kc6 4.Ke3
At this point the book leaves off with an etc, implying that the win is a matter of technique, but the tablebase shows that every move for Black, with the exception of 4. ... e5, still holds the draw.
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