7

I heard that two bishops and two knights have good winning chances against the queen according to the 7-man tablebases. Unfortunately, even the pawnless 7-man tablebases are not available online. So, I am wondering if this special position is won for white.


[FEN "3qk3/8/8/8/8/8/8/1NB1KBN1 w - - 0 1"]
[TITLE "White to move and win?"]

Houdini's Shootout at Level 21 Ply :

[Event "Stellung ausspielen (Houdini15aw32, 21p)"]
[White "Neue Partie"]
[Black "Houdini 1.5a w32"]
[Result "1-0"]
[FEN "3qk3/8/8/8/8/8/8/1NB1KBN1 w - - 0 0"]

1. Nf3 Qa5+ 2. Nbd2 Qb4 3. Ne5 Qc3 4. Nd3 Qf6 5. Bb2 Qh4+ 6. Ke2 Qh2+ 7. Nf2

Qc7 8. Bd4 Kf8 9. Nfe4 Ke7 10. Ke3 Kd7 11. Bc4 Ke7 12. Bd5 Qd7 13. Nf6 Qc7 14.

Nf3 Qc1+ 15. Ke4 Qc8 16. Ng5 Qc2+ 17. Ke5 Qc7+ 18. Kf5 Qc2+ 19. Nge4 Qd1 20.

Bc5+ Kd8 21. Ke6 Qe1 22. Bb6+ Kc8 23. Ke7 Qe2 24. Kf7 Qf1 25. Nc5 Qf4 26. Bb7+

Kb8 27. Bc6 Qf5 28. Na6+ Kc8 29. Bd7+ Qxd7+ 30. Nxd7 Kxd7 31. Nb4 Kc8 32. Ke6

Kb7 33. Nd5 Ka6 34. Be3 Kb7 35. Kd6 Kb8 36. Kc6 Ka8 37. Nc7+ Kb8 38. Bb6 Kc8

39. Ba7 Kd8 40. Nd5 Ke8 41. Kd6 Kf7 42. Ne7 Kg7 43. Be3 Kf6 44. Bf4 Kf7 45. Bg5

Ke8 46. Nc6 Kf7 47. Ne5+ Ke8 48. Kc6 Kf8 49. Kd7 Kg7 50. Ke7 Kg8 51. Bh6 Kh7

52. Bf8 Kg8 53. Ng4 Kh7 54. Kf7 Kh8 55. Bg7+ Kh7 56. Nf6# 1-0
  • 1
    According to Reuben Fine in book "Basic Chess Endings", the endgame is always won by white (I guess, except for special circumstances where black can immediately mate or win a piece). It does not provide any analysis (other than the Kling & Horowitz position (see wikipedia for pawnless chess endings)) to support it though. – GloriaVictis Mar 14 '15 at 15:34
  • Stockfish can't replicate these results /cry – Tony Ennis Mar 14 '15 at 18:22
3

Theoretically yes, as a practical matter (for humans), no.

What is known is that a pawnless position cannot be won (barring unusual positional circumstances) if one side has an advantage of a bishop or knight, but it can be won if one side has the advantage of a rook (or a queen versus a rook).

The "old" wisdom is that three minor pieces are worth about a queen, so white has the advantage of one minor piece. As a matter of fact, three minor pieces may be worth more than a queen, pushing white's advantage closer to, say, queen versus rook.

The other thing is that with so many pieces and moving parts, White has "coordination" problems. That's why as a practical matter, human beings won't win with this kind of advantage. The advantage of a computer is that it can calculate its way around coordination problems. If the minor piece synergies indeed give the computer an advantage greater than a minor piece, the computer will find a way to bring this extra power to bear; a human being (other than a world champion caliber player), will not.

| improve this answer | |
  • 1
    "What is known is that a pawnless position cannot be won (barring unusual positional circumstances) if one side has an advantage of a bishop or knight, but it can be won if one side has the advantage of a rook (or a queen versus a rook)." That would be true in cases where there is no way to make progress other than making even trades (and so the aggressor then needs to have at least a rook extra). But in general, I don't know that what you claim is "known" is in fact true. In any case, can you speak to the specific position being asked about? – ETD Mar 14 '15 at 15:40
  • @ETD: I can speak to specific permutations. King and minor piece do not beat king. King and rook beat king. King and rook do not beat king and minor piece ("barring unusual positional circumstances.") King and queen can beat king and rook. From that, I infer that an advantage of three points is "not enough," to win five points is "enough," and maybe four (king and queen versus queen and rook). King and four minor pieces vs. king and queen is somewhat more than a minor piece advantage, but a computer is more likely to be able to realize this advantage than a human being. – Tom Au Mar 14 '15 at 19:17
  • 3
    Yes, again, my point was that the basic facts about what the minimal mating materials are is only pertinent if the only way to make progress is via even trades of material. And if you're making such a claim for this (or any other) position, it's not unreasonable for readers to expect concrete analysis to back it up. I'll leave it at that. – ETD Mar 14 '15 at 19:46
  • It is widely known that two bishops vs knight is winning for the bishops even if in some cases its more than 50 moves – Colin Hicks Jul 8 at 3:41
  • 1
    @ColinHicks: That's a construct I have never heard of, and don't understand. – Tom Au Jul 8 at 4:25

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