1

A single knight or bishop usually isn't enough to force checkmate. However, I know there are certain positions where the defending side has his king in front of a rook pawn where a win can be forced.

So I have two questions related to this:

  • What is the longest forced win where the winning side has only a knight or bishop?
  • Are there any nontrivial (i.e., not mate in 1) forced wins that don't involve the losing side having his king trapped in front of a rook pawn?
3

According to this website, the longest checkmate for K+B vs. K+P is a simple mate in one, e.g.

[FEN "8/8/8/8/8/8/p7/k1K1B3 w - - 0 1"]

The K+N vs. K+P case is slightly more interesting, the following position is mate in seven:

[FEN "8/8/8/8/p7/8/N7/k1K5 w - - 0 1"]

1. Nb4 a3 2. Nc2+ Ka2 3. Nd4 Ka1 4. Kc2 Ka2 5. Ne2 Ka1 6. Nc1 a2 7. Nb3#

You can play these endgames with online tablebases, e.g. this one from Shredder.

  • Oh, now that's a helpful website. Looking at the 5-man ones, there appears to be one that isn't just a forced simplification to the above two positions: KB vs KNP. Neat. – eyeballfrog Jan 24 '18 at 22:23

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