W : Kg2 , Pa2, b2, c2

S : Kb7 , Pf7, g7, h7

White to move

[fen "8/1k3ppp/8/8/8/8/PPP3K1/8 w - - 0 1"]

Houdini's shootout ended in a black win with depth 23 Ply and a white win with depth 25 Ply.

  • 3
    An extremely similar position is the subject of an earlier question. – ETD Mar 14 '15 at 14:39
  • 1
    @ETD With kinds at d1 and e8 this would be "The Little Game of Chess" analyzed by Captain Evans (of gambit fame) in the 19th century. – bof Mar 16 '15 at 3:20
  • @bof, very interesting! From some (very) light searching I can't tell if the text of Evans' analysis exists; I'd like to think it does. Do you know? (I've noticed at MO that you sometimes have things like logic preprints from decades past at the ready. Perhaps it's the same with Evans' work?) – ETD Mar 16 '15 at 3:42
  • 1
    @ETD Sorry, that's all I know! I recalled reading about "The Little Game of Chess" 50 or 60 years ago, in a book I no longer have (Frey's New Complete Hoyle), but I didn't remember where the kings were placed. So I tried Googling and the site I linked to was my first success. It says Capt. Evans found the win "independently".I suppose the other analyst was probably some noted chessmaster or problemist of the day. But I was so happy to find that position on the web that I didn't look any further. – bof Mar 16 '15 at 4:28

Analysis of this general endgame appears in Staunton's Handbook, in the section "King and Three Passed Pawns against King and Three Passed Pawns."

In the preceding section of the book, "King against Three Passed Pawns," Staunton provides analysis indicating that a lone king battling the three connected passers in isolation (without assistance from their own king) can stop a promotion by getting to the so-called master square, which are here g3 for White, b6 for Black.

When considering these KPPP vs. KPPP endgames, he asserts a general rule about the kings' starting points for those positions in which one or both kings are within 3 squares of their respective master squares:

Victory will be in the hands of the party who can first play his King into its master square.

Staunton goes into some detail explaining the general logic behind play, and gives some examples. I won't try to elaborate here, but instead refer the reader to Staunton's text if interested. According to the rule, the OP's position would indeed be a win for White.

Among the examples Staunton considers, one is "Greco's position," which is identical to the OP's but with kings on e1 and e8. According to Staunton, that position was long considered drawn, but analysis given by Szén revealed it to be a win (in accordance with the rule above). Staunton further considers the position with kings on d1 and e8, calling it "Szén's position," and presenting analysis he credits to Evans (consistent with bof's comment to the OP) showing this also to be a win for White (again in accordance with the master square rule).

For those interested in more beyond Staunton: there is a paper by Noam Elkies applying combinatorial game theory to chess endings, and which in particular considers cases where pawn endgames essentially reduce to distinct subgames wherein mutual Zugzwang might arise. It deals with some of these KPPP vs. KPPP endings near the end, including Szén's position and a nice study by Behting:

[fen "1k6/1P6/2P5/P7/5ppp/8/6K1/8 w - - 0 1"]
[White "White"]
[Black "to Win"]

It would be astonishing if White were in zugzwang in the initial position and it were a win for Black. It would be mildly surprising if it were a draw, because pawn endgames are so volatile.

Stockfish 5 at depth 40 evaluates it as +19 for White, which is convincing enough for me.

  • 2
    Stockfish is highly selective, and this is dangerous in an endgame where zugzwang can play a role. But the claim is supported by Houdini who reached a winning position at level 27 Ply. – Peter Mar 14 '15 at 15:03

It seems all symmetric positions like this, where both sides have 3 connected passed pawns are winning for first moving side, because, it's not possible to blockade(it is possible for a moment, but then zugzwang happens) and racing favors first moving side.

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