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Are there any possible moves to checkmate a Black opponent if we have a White bishop and king?

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    No, and most (if not all) online chess sites will end the game with at result as a draw at this point. – Akavall Jul 30 '20 at 20:47
  • No, but if your opponent has a pawn or a knight or a bishop of opposite colour of yours, you can checkmate him – jf328 Jul 31 '20 at 6:49
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No. There is no position you can construct in which the black king is in check (has to be from the bishop), white only has king and bishop and the black king can't move.

The closest you can get is this:

[fen "k7/1BK5/8/8/8/8/8/8 w - - 0 1"]

And the black king can move to a7.

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There is no way to force a win with KB vs K.

No way for them to blunder into it.

No way for them to help you selfmate.

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It is impossible. The Black king cannot be checkmated. In the case that the Black king goes into the 'right' corner, then it may be checked by the bishop. However, it must have at least 1 escape square. In the wrong corner, then Black cannot be checkmated no matter what.

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