Let White have the two bishops. Given any setup, has the maximum number of moves to forced mate been calculated? If not, are there any bounds on this number?

Of course, information on extensions of this problem to say any rectangular board, are also welcome.

I should note that for a 2xn board checkmate isn't possible. Also, for m >= 3, with n >= m without loss of generality, I'm not certain whether forced mate is always possible. I would say though that it is given m,n sufficiently large though.

To update let the bishops be on opposite colored squares, of course.

  • 1
    What do you mean by "without losing generality"? – hkBst Jul 27 '16 at 12:49
  • In this case those words shouldn't have appeared. – Paul Burchett Jul 29 '16 at 0:23

Mate could be forced sooner...[the] two bishops [can mate in up to] 19 [moves].

Source: Last paragraph from Daniel's answer to 'With only a king left, how many moves remaining until a draw?', with editing from me, seeing as I am taking just the part relevant to this question.

For a table of maximum number of moves to mate, see Wikipedia, which cites Batsford Chess Endings by Speelman, Tisdall and Wade.

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