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Let White have the two bishops. Given any setup, has the maximum number of moves to forced mate been calculated on an nxn board (for large enough n)? 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.

Update again: I noticed someone edited the question out. It isn't meant merely for the 8x8 board, but for any nxn board, where n is any sufficiently large natural number. I know R&K vs K has been solved in this way for any nxn board. I'm wondering whether the same has been done for K BB vs. K on any nxn board. Please watch what you edit next time. Also, an answer has been accepted to the edited question, not my intended question.

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    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
  • If you look at the edit history, you will see that nobody other than you has ever the edited the question, except for the tags. Since the question didn’t make it clear that you wanted an answer for general n×n, it’s not surprising that the existing answer got marked as accepted. – Stephen Aug 30 at 12:00
  • I don't remember editing the question out. It certainly wasn't my intention to edit it out. Also, it should've been clear that I was talking about a generalization, and not the standard 8x8 board. I did have the variables m and n in the post, after all. – Paul Burchett Aug 30 at 12:49
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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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    While I gave this a thumbs up for relevant information, it shouldn't have been accepted as an answer. It only deals with the 8x8 board. I was looking for a solution for general nxn. – Paul Burchett Aug 30 at 8:19

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