Chess Strategem
November 7, 2004 9:06 AM Subscribe
ChessFilter: A has only a king and a rook. B has only a king and a knight. If A plays perfectly, is he assured of victory? Or is it possible for B to force a draw, no matter how well A plays?
It's possible for A (or B) to force stalemate by getting B's king into a corner (say, h1). If A's rook is on g2, and A's king is adjacent to the rook, then there's nowhere to go for B. This is especially true since A's rook can sneak over there much quicker than B's knight.
posted by swift at 10:48 AM on November 7, 2004
posted by swift at 10:48 AM on November 7, 2004
With the knight, however, this would probably end up as a draw-by-repetition, not stalemate.
posted by swift at 10:49 AM on November 7, 2004
posted by swift at 10:49 AM on November 7, 2004
I dunno, swift. Seems to me you could keep B's king in check a lot easier with a rook. With a knight, you have to stay close to the king in order to "dance around" the piece when challenged by the rook. The rook, on the other hand, can be all the way on the other side of the board, but in a single move be used for defense. I'd say A has the advantage, and in practical terms (not "perfect playing") player A will win more times than B.
posted by Civil_Disobedient at 11:32 AM on November 7, 2004
posted by Civil_Disobedient at 11:32 AM on November 7, 2004
Of course, actually winning would be pretty difficult. The only way I can see it working is if the king is in the corner, blocked by their knight (h1, g2). It would be tough to orchestrate something like that. Once you get rid of the knight, the best you can hope for is stalemate.
posted by Civil_Disobedient at 11:36 AM on November 7, 2004
posted by Civil_Disobedient at 11:36 AM on November 7, 2004
It would actually not be too hard to get rid of the knight, by keeping the the king in check until the king ends up on the same rank/file as the knight.
Then stalemate.
posted by swift at 11:48 AM on November 7, 2004
Then stalemate.
posted by swift at 11:48 AM on November 7, 2004
Response by poster: Actually, if B loses the knight, then A (left with a king and a rook) wins for sure, if he knows what he's doing.
I'm just trying to figure out whether there is a known method by which A could win for sure even if B is savvy enough to keep the knight alive for as long as possible.
posted by bingo at 1:34 PM on November 7, 2004
I'm just trying to figure out whether there is a known method by which A could win for sure even if B is savvy enough to keep the knight alive for as long as possible.
posted by bingo at 1:34 PM on November 7, 2004
Barring a bizarrow position it's a draw. More here. In general this kind of simple endgame is solved in chess, mostly by exhaustive search.
posted by Nelson at 1:47 PM on November 7, 2004
posted by Nelson at 1:47 PM on November 7, 2004
Response by poster: swift: But how, with just a rook, can you keep putting the king in check while essentially forcing the king to move into alignment with the knight, but not in such a way that the two pieces are actually adjacent, and yet in such a way that you can, in one move, move the rook so that you're attacking the king from a safe distance (and, behind the king, the knight)?
posted by bingo at 2:30 PM on November 7, 2004
posted by bingo at 2:30 PM on November 7, 2004
The knight doesn't have to be behind the king. They just have to be in line with each other.
- N - - R - - K
The Knight and King could stay closer, but eventually they'd have to get in line to remain close. Otherwise, the Knight strays and you get the configuration above.
posted by swift at 4:01 PM on November 7, 2004
- N - - R - - K
The Knight and King could stay closer, but eventually they'd have to get in line to remain close. Otherwise, the Knight strays and you get the configuration above.
posted by swift at 4:01 PM on November 7, 2004
A question for ChessFi's -- let's say you have a piece cornered -- say, rook at H7 pushing the king back to row 8. Now, let's say the king is at E8. It's my move, and my king is at E6. Can I move my king to E7? I mean, technically I can't move myself into check, but since I've already got the rook guarding the 7th row, the opponent king can't attack without putting himself into check. In other words, can I move myself into a check position against a king if I have the position defended already?
I've never actually seen this come up, but just in case...
posted by Civil_Disobedient at 8:00 PM on November 7, 2004
I've never actually seen this come up, but just in case...
posted by Civil_Disobedient at 8:00 PM on November 7, 2004
Civil_Disobedient: No, you can't. I guess the way to think about it is that once the king is gone, the game is over immediately. In your hypothetical situation, it wouldn't matter how your king was protected. Once the player takes your king with his king, your troops would be leaderless and the battle ends immediately.
posted by gyc at 8:25 PM on November 7, 2004
posted by gyc at 8:25 PM on November 7, 2004
Response by poster: Nelson, thanks for the link, that's helpful.
This came up in a game I played recently, where I was player A, and, much to player B's annoyance, I persisted until he made a mistake that dropped the knight. But I wanted to find out whether I really had to depend on that mistake.
swift, I get what you're saying, although it seems to me that a careful player B could keep his king and knight from being on the same diagonal plane for a long time. Even if they must eventually be lined up, that might be timed so that A's rook won't be in position to take advantage.
posted by bingo at 10:45 PM on November 7, 2004
This came up in a game I played recently, where I was player A, and, much to player B's annoyance, I persisted until he made a mistake that dropped the knight. But I wanted to find out whether I really had to depend on that mistake.
swift, I get what you're saying, although it seems to me that a careful player B could keep his king and knight from being on the same diagonal plane for a long time. Even if they must eventually be lined up, that might be timed so that A's rook won't be in position to take advantage.
posted by bingo at 10:45 PM on November 7, 2004
Yes, in general (i.e., there are exceptions, but this makes up the large majority of cases), A cannot force B's king in line with his knight, until the king is close enough to defend the knight.
More generally, yes, rook vs. knight is a draw, although there are exceptions, and it can be hard for the player with the knight to pull off the draw.
Doing a bit of Googling, I found this fascinating game. On move 114 White underpromotes his pawn to a knight, giving check. (Promotion to any other piece results in 114... Rc8#, while moving the king loses the pawn.) The game is a theoretical draw at this point, but White subsequently blunders with 115. Ng4, moving the knight away from his king. (115. Ng8 holds the draw.) Black misses the quick win here with 115... Rh3; then any legal move would either a) allow Black to checkmate immediately; b) subject the knight to immediate capture; or c) place the king and knight on the same file, allowing Black to win the knight by moving his rook to that file. After dancing around a bit more, Black is able to force White into a position where he can't avoid losing his knight. But that's not possible from most positions.
posted by DevilsAdvocate at 10:15 AM on November 8, 2004
More generally, yes, rook vs. knight is a draw, although there are exceptions, and it can be hard for the player with the knight to pull off the draw.
Doing a bit of Googling, I found this fascinating game. On move 114 White underpromotes his pawn to a knight, giving check. (Promotion to any other piece results in 114... Rc8#, while moving the king loses the pawn.) The game is a theoretical draw at this point, but White subsequently blunders with 115. Ng4, moving the knight away from his king. (115. Ng8 holds the draw.) Black misses the quick win here with 115... Rh3; then any legal move would either a) allow Black to checkmate immediately; b) subject the knight to immediate capture; or c) place the king and knight on the same file, allowing Black to win the knight by moving his rook to that file. After dancing around a bit more, Black is able to force White into a position where he can't avoid losing his knight. But that's not possible from most positions.
posted by DevilsAdvocate at 10:15 AM on November 8, 2004
Once the player takes your king with his king, your troops would be leaderless and the battle ends immediately.
That's a great explanation. Thanks, gyc.
posted by Civil_Disobedient at 1:11 PM on November 8, 2004
That's a great explanation. Thanks, gyc.
posted by Civil_Disobedient at 1:11 PM on November 8, 2004
Correct play with 3, 4, and 5 pieces: Nalimov Tablebase Server (java applet)
posted by crunchburger at 6:43 PM on November 8, 2004
posted by crunchburger at 6:43 PM on November 8, 2004
This thread is closed to new comments.
posted by matteo at 9:31 AM on November 7, 2004