Can a rook force a draw against three bishops?
One of the bishops is on a different coloured square than the other two.
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1 Answer
It's generally a win for the three bishops. However, it can be a rather long process.
The tablebase I consulted says that in this position with White to move, the best move for White is Kd3, which is a win for Black with DTZ of 87.
[FEN "8/2kb4/8/8/8/2K1b2b/8/3R4 w - - 4 3"]
In fact, in some positions, the 50 move rule will trigger, which could result in a draw with best play. Here, Kd5 results in a DTZ of 101:
[FEN "k7/3b4/8/8/2K5/7b/5b2/1R6 w - - 1 1"]
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It seems replacing the bishop with a knight (ensuring the other two bishops are on differently-coloured squares) also forces mate. A particularly difficult one is white[Kc3, Rh8] and black[Ka1, Bd1, Ba7, Na8] with black to move and win with DTZ of 133. Commented Mar 17 at 16:06
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And to be clear, the example I selected almost certainly isn't the longest DTZ. I just put the pieces down wherever.– D MCommented Mar 17 at 16:37
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Your "DTZ of 133" comment made me try some other positions... yeah, sometimes the DTZ goes above 100, meaning the side with the rook could potentially get a draw by 50 move rule. I edited that possibility in.– D MCommented Mar 17 at 16:44