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Position with KN vs KN aren't automatically drawn because checkmate is possible, even though it can't be forced; however, KN vs K is automatically drawn because checkmate isn't even possible with the lone king's co-operation.

If my opponent won't agree to a draw, can I force them to take my knight to reach the automatically drawn position, rather than having to wait for the 50-move rule?

This question is based on a comment on a question about KN vs KN.

David Richerby
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2 Answers2

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If you can fork your opponent's king and knight with your knight, then your opponent must either take your knight or allow you to take theirs on the next turn. Since that gets you down the KN vs K one way or the other, this forces the draw.

However, the answer to the literal question is no: there is no situation in KN vs KN where the only legal move is to take a knight. Here is a case analysis, assuming White to move.

  1. White is checkmated. Then, by definition, White can't take anything.

  2. White is in check, but not mated. The check must be from the knight, so White can't take it with their king. If white's king is not in the corner, they can simply move their king out of check (there are at least five adjacent squares; the black king might block three of those, and the white knight one more, but that still leaves an escape square). If the king is in the corner, the black king covers at most two of the three adjacent squares, and the third one can't be occupied by the white knight because that would be checkmate; so there's still an escape square.

  3. White is not in check.

    1. If the white knight is not in a corner, it can move to at least three squares. The white king could be on one of these squares, the black knight could be on another, but the black king can't be on any of them (it's White's move, so Black can't be in check). Therefore, white has at least one possible knight move that isn't taking the black knight.
    2. If the white knight is in a corner, there are two squares it can potentially move to. If either of these is empty, White has a non-capturing knight move. If they're both occupied, we're in a position such as the one below. Wherever the black king is, White has at least one king move that doesn't capture the knight. But note that this position is another one where the white knight can be captured on the following move.

 

[FEN "8/8/8/8/8/6n1/5K2/7N b - - 0 1"]

So perhaps the more interesting question is whether we can force the transition to KN vs K, rather than specifically forcing the opponent to take our knight. Again, the answer is no: as long as you keep your knight out of the corners and avoid having your king and knight forked, you can force the game to continue for 50 moves. The only way this could go wrong is if your knight starts in the corner and the opponent can force it off the board before you can get it out, as in the following position

[FEN "K7/8/2k6/8/4n3/8/8/7N b - - 0 1"]
David Richerby
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I'd like to present an alternate to what David Richerby says, which I agree with, but hopefully it's fun to have another way to look at things. While this isn't a rigorous proof, it seems like your opponent can be rather mean about dragging things out (or even flagging you to lose on time if they're REALLY ornery) if they want to be.

They should be able to

1) keep the king >4 squares (or >3 diagonally each way) away from your knight or, failing that,

2) keep the king on an opposite colored square from your knight, in case the two pieces are close by, which prevents a knight fork. The easiest way to do this would seem to be to place a knight on b2/g2/b7/g7, the opposite corner from their king. Even if your pieces corner the king, moving the knight back and forth would work, or you could move the knight 5 squares in 3 moves to one of the other squares to get even further away. 2L1D, 1L2U, 2L1D is one example, but you can mirror or rotate that as need be.

aschultz
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  • Any tournament director would declare this game drawn if asked. But if you are prepared to expend this much effort on forcing the exchange, why not expend far less effort on just playing it out? You have to cooperate to lose, and you're not going to do that are you? – Philip Roe Apr 30 '17 at 21:26
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    That's true. From a practical standpoint you can probably even just chase his knight with yours, then attack his knight if he checks your king. But in terms of establishing a way to say OK, here's a fortress, I figured this would be a way to expound on the detailed answer above. Also, in some blitz tourneys, people can--well, put competition ahead of sportsmanship. – aschultz Apr 30 '17 at 22:24