General Question

Paradox's avatar

Chess question (please read details).

Asked by Paradox (2570points) November 13th, 2010

I already know a queen and king can force checkmate against a king and bishop (and I think a knight as well) but can a king and queen force mate against a king and rook? I’m talking about forcing a mate before 50 moves with no pawns on the board or is this a situation that is similar to a lone king against two knights and a king where you have to hope your opponent makes a wrong move?

Is forcing a checkmate mathematically possible with a queen and king against a rook and king (with no pawns on the board) before 50 moves?

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11 Answers

Afos22's avatar

I thought it was a stalemate…

chielamangus's avatar

Yes. The strong side can force a position in which the weak side gets checkmated or has to lose the rook, after which the strong side delivers mate in a few more moves.

I learned K+Q vs. K+R in a psychiatric ward. When I knew I was checking in, I figured I’d have a lot of time for reading, so I carried along Averbakh’s Chess Endings: Essential Knowledge. The best way to learn from a chess book is to read it without sight of a board and pieces, so I read that section “blindfolded” for days. I was glad I took a chess book with me, because you wouldn’t believe the crappy books made available in a county loony bin.

JonnyCeltics's avatar

Yes, of course. You’ve just either got to have your opponent make a blunder, or work to fork, somehow, the rook and the king. Problem is, that is your opponent is a quality player, it’ll end in a draw, without a doubt.

chielamangus's avatar

it’ll end in a draw, without a doubt.

No, it’s a win for the queen. Take my word for it, or this guy’s, who quotes grandmaster Fine, grandmaster Averbakh, the Belle computer, and so on.

http://www.jimloy.com/chess/kq-kr.htm

poisonedantidote's avatar

It’s possible to win, but its very tricky. In that situation I’ll offer a draw just to be polite and get the next game going. Or maybe If i have the queen, and its a tournamet, ill drag it out just to win on time/points.

@Afos22 stalemate only happens a very specific way. stalemate does not happen when you can both still move but will dance around the board forever. Stalemate happens, when player X puts player Y in check, player Y moves their king, and then player X moves in such a way, that the king of player Y is not in check, but that they will be in check if they move any piece.

In other words, stalemate is when it’s your turn but you cant move because you would be in check, but you are not in check where you are. you cant move, so it cant be your opponents turn, and he cant move either. as neither of you can move, and neither of you are in check, it is stalemate.

chielamangus's avatar

ill drag it out just to win on time/points.

“Winning on points” is for people who don’t know how to play chess.

The Q=9 R=5 B=3 N=3 P=1 scale does not relate pieces to integers, but to pawns. A queen’s value is not roughly nine “points”, but nine pawns.

Paradox's avatar

Stalemate is what poisonedantidote says, when you can’t move any pieces or your king without placing it in check while the king is not in check.—Technically it’s possible to have all your peices on the board and still be stalemated.

Draw by insufficient material is still a draw but not a stalemate. This occurs when it is mathematically impossible to get a checkmate for both players. A lone king against a king and a bishop or two kings left on the board is an example of a draw by insufficient material.

There is a 50 move rule to guard against infinite moves on the chess board when checkmate is always possible (due to a moving blunder) but very unlikely because the mate can’t be forced mathematically. In the 50 move rule if there is no pawn advancement or piece capture within 50 moves for each player then the game is a draw (barring checkmate or stalemate occuring first).

You can force a mate (regardless of what the opposition does) when the situations are: lone king against a king, bishop and knight/ lone king against a king and two bishops/ a lone king against a king and rook/ a lone king against a king and queen or a lone king against 3 knights (rare scenerio however). I’m not getting into pawn or opposition considerations here.

However I know 2 knights and a king can’t force mate against a lone king unless the player makes a blunder. @chielamangus So it is possible to actually force a mate in the scenerio I’ve described (king and queeen vs king and rook). I would love to learn that strategy because this situation always seems to end up ending in a draw on the 50 move rule but thanks. I’m not considering wins by point values of pieces here but an actual forced mate strategy within the allowed 50 move limit.

chielamangus's avatar

I would love to learn that strategy because this situation always seems to end up ending in a draw on the 50 move rule

K+Q vs. K+R isn’t really that useful to know. It’s more helpful to know K+Q vs. K+P because that one arises more often. K+Q vs. K+R should only arise in the rare instance where one side manages to promote while the other side’s rook was busy elsewhere on the board.

Paradox's avatar

@chielamangus Ironically I don’t get into the king/queen vs king/rook scenerio too much against other people but I do find myself in it (frequently) playing against the computer.

chielamangus's avatar

I do find myself in it (frequently) playing against the computer.

That’s very, very odd. I’ve never had to play either side of that ending — which some say is the cosmic result of having learned it.

Next time it arises, or even gets close to arising, save the gamescore and send it to me. I bet there’s something to do long in advance of that ending that will enable you to win before it threatens to occur.

Paradox's avatar

@chielamangus I guess I’m not a great chess player then. I actually consider myself lucky if I can get to an endgame with that setup because I usually get mated before reaching the endgame. I don’t play chess as much as I used to when I was a kid but I do try to upgrade of playing level.

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