KBNK

[h.g.muller]

I was wondering, is KBNK a won end-game on any (even) size board, and perhaps even on an infinite board? There doesn't seem to be a faster-than-linear increase in the length of the longest mate, as one usually sees in end-games that at some point cease to be won (e.g. K+K vs K). For KBNK I find

6x6: 22
8x8: 33 (+11)
10x10: 47 (+14)
12x12: 64 (+17)
14x14: 78 (+14)

In KBNK you have one piece that outruns the King (Knight), and a slider that can always be positioned to restrain it in a single move. And although B+N probably cannot drive a bare King in a specific diagonal direction all by themselves, they can conceivably slow its progress in the opposite direction enough that their own King eventually can catch up. And the three of them could possibly do the job. So it could very well be that mate is possible on an infinite board (with one corner).

[byakuugan]

Using your Pieces-Only Tablebase Generator, I can generate 8x8, 4x4, and 3x3, but nothing else.

[syzygy]

I just came across this thread which seems to be along similar (but more general) lines:

http://mathoverflow.net/questions/63423 ... ega-moves/

[h.g.muller]

This chess on infinite edgeless boards is really something... It seems an active topic of math research, raising some very deep problems.

In the mean time I found this thread about KBNK:
http://chess.stackexchange.com/question ... ard-boards
It contains an optimal mate-in-92 on a 16x16 board. Apparently this is effected by first allowing the bare King to escape to the safe corner, followed by a repetitive drive along the edge towards the deadly corner, which manages to keep the bare King confined in a limited area next to the edge at all times.