King and Queen vs. King and Rook

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King and Queen vs. King and Rook

This is what BCE (Basic Chess Endings, 1941 by Ruben Fine) has to say about this ending: "This is a win, but from the general position the process is rather complicated. In order to have drawing chances, Black must keep his rook near his king, for otherwise a check will capture the rook. The basic winning idea is to force Black into zugswang, so that he will have to move his rook away from his king." Of course "zugswang" is when it is your move, but you wish it were not, as you now have to damage your position in some way.

In 1978, this ending received some publicity, when Ken Thompson's program Belle (with this ending in its database) played this ending against Walter Browne. The conditions of the game were that Brown, with the queen, had to win the game under tournament conditions (I think they started with the position shown above left). In particular, the 50 move rule applied. And if Browne was not able to win, then Belle would be declared the winner of the challenge. Browne overstepped the 50 move limit, and lost the competition. Browne won a rematch, a second game played after Browne had some time to prepare, when he captured Belle's Rook on the 50th move.

Most of the critical positions had been seen before, and most of the published analysis was accurate to some extent. But, from a practical point of view, the ending was much more difficult than most people thought. Fine's advice, above, gives us a clue about this. "Black must keep his rook near his king, for otherwise a check will capture the rook." This is sometimes (maybe even more than once in a game) much more difficult than it sounds. There are numerous positions in which the rook can go to the opposite side of the board and never be forked without some time-consuming preparation which allows the rook to go somewhere else. Then White must resort to more subtle threats to make progress. And the effectiveness of these rook moves, away from the king, can be difficult to predict. But the defense must find at least one of these rook moves during play, in order to have a chance of benefitting from the 50 move rule.

Let me illustrate this by brutally criticizing some analysis by Yuri Averbakh of the above position (White moves) by Max Euwe (1958), in Queen v. Rook/Minor Piece Endings (1972), by Averbakh, V. Chekhover, and V. Henkin. This ragged (but mostly valid) analysis is typical of what was in print back then. This should give you a "small" taste of how difficult this ending can be. The following comments are mine, unless otherwise attributed:

Diagram #1: 1 Qa5 (Black threatened mate) 1...Re4! 2 Qd5+ (or 2 Qd2) 2...Rc4 3 Qd3+ (or 3 Qe6 or 3 Qe5) 3...Kb4 (not 3...Rc3?? 4 Qb5+ Ka3 5 Qb2+) 4 Kb2 (or 4 Qe3) 4...Kc5! 5 Kb3 Rb4+? (this wastes four moves! 5...Rd4! is better) 6 Kc3 Ra4 (or 6...Rb6) 7 Qf5+ Kd6 8 Qf8+ (Averbakh gives this an exclamation mark. 8 Kd3 is two moves faster. 8 Qf6 is the move shown by Euwe) 8...Kd7!! 9 Kd3 (Averbakh give this an exclamation. 9 Qb8 or 9 Qf5+ are two moves faster) 9...Ra5 10 Kc4 (10 Qf7+ is two moves faster) 10...Re5 (or 10...Ra4+) 11 Qf7+ (or 11 Kd4) 11...Kd6! 12 Qf6+ (12 Kd4 is two moves faster) 12...Re6 13 Qf4+ Kc6 14 Qd4 (or 14 Kd4) 14...Rd6 15 Qe4+? (15 Qf2 or 15 Qg4 are three moves faster) 15...Kb6? (15...Kd7!! is five moves better!) 16 Kb4 Rc6 17 Qd4+? (17 Qe7! is four moves faster) 17...Ka6? (17...Kc7!! is five moves better) 18 Qd8 (or 18 Qe3) 18...Kb7 (18...Rc7! is two moves better. This stalemate idea comes up every once in a while) 19 Kb5 Rc7 (or 19...Rc1) 20 Qd5+ (20 Qe8 is better) 20...Ka7? (20...Kc8 is three moves better) 21 Ka5? (21 Qe4 is better, as you will see in note A) 21...Rb7?(A) 22 Qd4+ Kb8 23 Ka6 Rc7 (23...Kc8 avoids mate but loses the rook) 24 Qd8+ (or 24 Qe5) 24...Rc8 25 Qb6+ Ka8 26 Qb7++, Averbakh 1972.

Black wasted 27 moves. So you can see that Averbakh (with all the time in the world to write his book) was in serious danger of overstepping the 50 move rule himself. Averbakh wrote this: "From this we can establish that, against the best defense, the win in this ending takes a maximum of from 25 to 30 moves." How true, but his defense was not close to "best." Let's look at my note A, off the above (at Black's 21st move), for some even greater difficulties in the following diagram:

A - [diagram #2] 21...Rh7!! (My move, which is not easy for either player to find; Averbakh didn't find it, and my computer didn't like it, so don't go into this ending thinking the defense will be easy) 22 Kb5! (see why I gave 21 Ka5 a question mark above? It was a complete waste of time) 22...Rc7 23 Qe4! Rf7 24 Qd4+ Kb8 25 Qd6+ Ka7 26 Kc6 Rb7 27 Qd8 Rh7 28 Qb6+ (or 28 Qa5+ or 28 Qd4+) 28...Ka8 29 Qb1 Re7 (29...Ra7 30 Qb3 Ra6+ 31 Kc7 Ra7+ 32 Kc8 mates soon) 30 Qa2+ Kb8 31 Qb3+ and wins the rook next move.

The reason that my computer didn't like this move (21...Rh7!!) is that it shortens the mate by one move. But it saves the rook for a long time, and we should be more worried about the 50 move rule than we are of an eventual mate.

Philidor's position:

Diagram #3: Let's try something a little easier. This famous and important position (Black moves) is by Philidor, 1777, maybe rotated or reflected: 1...Rh7 (other moves are worse) 2 Qa5+ Kb8 3 Qb4+ (that move is published in several places, but 3 Qe5+! Ka7 4 Qa1+ Kb8 5 Qb1+ is faster) 3...Ka7 4 Qa3+ Kb8 5 Qb3+ Ka7 6 Qa2+ Kb8 7 Qg8+.

If White moves first, then 1 Qd4+ Kb8 2 Qh8+ Ka7 3 Qd8 is the diagram with Black to move.

Diagram #4: Let me pick apart some of Fine's analysis, from this diagram (White moves), as there are some interesting moves here, too: "Best play is" 1 Kb2 Rf4 (1...Kd4 is two moves better) 2 Kc3 Re4 3 Kd3 Rd4+ 4 Ke3 Rd5(A) 5 Qh2+ (5 Qh8 is two moves faster) 5...Kf5? (5...Ke6 is three moves better) 6 Qf4+? (6 Qh5+ is three moves faster) 6...Ke6(B) 7 Ke4 Rd6 (7...Rc5 is two moves better) 8 Qf5+ (or 8 Qf8) 8...Ke7 9 Ke5 Rd7 (9...Rc6! or 9...Rb6! are two moves better) 10 Qf6+ Ke8 11 Qh8+! (11 Ke6?? Rd6+!! is the stalemate idea we saw above) 11...Kf7! 12 Qh7+ Ke8 13 Qg8+ Ke7 14 Qc8! Rd2(C) 15 Qc5+ Kd7! 16 Qb5+ Kc8 17 Ke6! Rc2! 18 Kd6 Rh2! 19 Qe8+? (19 Qc7+ or 19 Qd7+ are four moves faster) 19...Kb7 20 Qe4+ Kb6 21 Qf4 (or 21 Ke7, surprisingly) 21...Rh5 22 Qe3+ Ka5 23 Kc6 (wins the rook) 23...Kb4 24 Qf4+ Ka5 25 Qd2+ and a fork next, R. Fine.

That wasn't too bad, Black only wasted nine moves (and White wasted ten moves). From the above line (Black's move #4), we have this very important variation, which shows the difficulty which White can have in trying to move his/her king past the rook, also by Fine:

A - 4...Rc4! 5 Qh5+(D) Ke6 (or 5...Kd6) 6 Qb5 Rg4! (or 6...Rc1) 7 Qc5 (7 Qe8+ is two moves faster) 7...Rh4 (or 7...Rg1 or 7...Rg6) 8 Kf3 (8 Qc6 or others are two moves faster. Among these faster moves, interesting is 8 Qc8+ Ke2 9 Qc7+ Ke6 10 Qc5 which is the same position with Black to move) and let's look at this diagram:

Diagram #5: 8...Rh1!! [My move. Here Fine went off the deep end by showing 8...Kf6?? (wastes nine moves) 9 Qd5? (9 Qd6+ or 9 Qf8+ are seven moves faster) 9...Kg6?? (9...Rh1!! is nine moves better)] 9 Qc4+ Kd7 10 Qd4+ Ke8! 11 Kg4 Rh7! 12 Qa4+! Rd7! 13 Kf5 Kd8 14 Ke6 Rb7!! 15 Qd4+ Kc7 16 Qd6+ Kc8 17 Qc6+ Kb8 18 Kd6 Ka7 19 Qf3!! (others are almost as good) 19...Kb6 20 Qg2!! Ka6 21 Kc6 Rb6+ 22 Kc7 Rf6, and there are several ways to force a fork, including 23 Qa2+ Kb5 24 Qb2+.

B - 6...Kg6? (loses five moves) 7 Ke4 Rg5 8 Qd6+ Kg7? (the worst possible move, wasting three moves) 9 Kf4! Rg6 10 Qe7+! Kg8 11 Kf5 Rg2 (or 11...Rh6) 12 Qe8+ (12 Qe4 or 12 Qe3 are three moves faster) 12...Kh7 13 Kf6?? (several queen moves are five moves faster, as you will see) Fine's analysis stops here, as he thought he had shown this from another diagram. Continue: 13...Rf2+ 14 Kg5 Rg2+ 15 Kh4 Rh2+ 16 Kg3 Rh6!, which should make White regret move #13.

C - 14...Rd1 (other moves lose quickly) 15 Qc5+ (15 Qe6+ is two moves faster) 15...Kd7? (15...Kd8! is five moves better, and is similar to the above play) 16 Qb5+? (wastes five moves, instead 16 Qf2!! Kd8 17 Ke6 Rb1 18 Qd2 Kc7 19 Qc2+) 16...Kd8 17 Qa5+ (or 17 Qb8+) 17...Kc8 18 Qc3+ Kd7 19 Qb4! Kc7 20 Qc4+ Kd8 21 Ke6 Re1+ 22 Kd6 Rd8+ 23 Kc6 Rd7 24 Qc5 wins the rook with a fork, R. Fine.

D (off note A) - 5 Qh8+ (seems to work more smoothly) 5...Kd5 6 Qd8+ Ke5 7 Qe7+ Kd5 8 Qd7+ Kc5 9 Kd3 Rb4 10 Qc7+ Kb5 11 Kc3 Ka6! (the stalemate idea) 12 Qc8+ Rb7 13 Kc4 Kb6 14 Qc5+ Ka6 15 Qc6+ Ka7 16 Kc5 Rb8 17 Qf3! Kc7 18 Qg2! Ra7 19 Qg7+ Kb8 20 Qe5+ Kb7 21 Kb5 Kc8 22 Kb6 Rb7+ 23 Kc6 Rd7 24 Qe6 wins the rook.

Diagram #6: Not everyone overlooked these strong defensive rook moves. This one (Black moves) is by Max Euwe, 1958: 1...Rf2!! (1...Rf1 wastes two moves) 2 Qd5! (my move. Averbakh and Chekhover give 2 Qe6+ which is slightly inferior) 2...Rb2(A,B) 3 Qd4 Rh2 4 Kf5! Rh5+ (or 4...Re2) 5 Kg4!!! (5 Kg6??? wastes 13 moves! Which move would you make?) 5...Rb5 6 Kf4! Rb3 (or 6...Rh5) 7 Qe5+ Kf8 8 Qf6+ and forks next.

A - 2...Rh2 3 Qf4 Re2+ (or 3...Rb2) 4 Kf5 Kd8 5 Qb8+ Ke7 6 Qb4+ Kd8 7 Kf6! Re8 8 Kf7 (or 8 Qb5) 8...Re2 9 Qd6+ and forks next.

B - 2...Rf7 3 Qc8 Rg7 4 Qc7+ Kf8 5 Qd8+ Kf7 6 Kf5 Rg1 (6...Rh7 is good) 7 Qd5+ Ke8 8 Qa8+ and forks next.

In similar positions, with the pieces moved left or right, the above rook move is not always quite as effective (see diagram #7, below). So, you may have to find your own complicating rook moves.

We need some more examples of these strong rook moves. Here are some that I have discovered (Black moves first in all of these).

Diagram #7: This position can be found in Secrets of Pawnless Endings, by John Nunn. 1...Rd2!! (or 1...Rd1) 2 Qc5 Kd7 3 Qb5+ Kc8 4 Ke6 Rc2! 5 Kd6 Rh2! 6 Qc6+ Kb8 7 Qb6+ Ka8 8 Qb1! (forcing the rook to move) 8...Rf2! 9 Qe4+ Kb8 10 Qb4+ Ka8 11 Kc7 (or 11 Kc6) 11...Rc2+ 12 Kb6 Kb8 13 Qf8+ Rc8 14 Qe7 (or other) and mate soon.

Diagram #8: 1...Rg1!! (or 1...Rg5 or 1...Kf7) 2 Qh4+ Ke6 3 Ke4 Rb1 4 Qh6+ Ke7 (all moves are equally good or bad) 5 Qa6 Rh1 6 Kf4 Rh2 7 Qa7+ Ke6 (or 7...Kd6 or 7...Kd8) 8 Qe3+ Kf6 (or 8...Kf7) 9 Qb6+ Ke7 (or 9...Kf7) 10 Kg5 Rg2+ 11 Kf5 Rc2 12 Qe3+ Kf8! 13 Qa3+ Kg7 14 Qf3! Rc5+ 15 Ke6 Rb5 (or 15...Rc4 or 15...Kg6) 16 Qc3+ Kh6 17 Qd2+ and forks next.

Diagram #9: 1...Ra4!! 2 Qg5+ Rg4 (2...Kh3 or 2...Kf3) 3 Qe3+ Kh4 4 Qh6+ Kg3 5 Ke3 Kg2 6 Qd6 Rg3+ 7 Kf4 Rf3+ 8 Kg4 Rf2 9 Qc6 Kh2 10 Qd5 Rc2! 11 Qe5+ Kg1 12 Qe3+ Kh2 13 Kf3 Rg2 14 Qe1 Philidor's position.

Diagram #10: Here the Black king is stalemated (usually a bad policy for the attacker), but Black cannot draw. 1...Rb4+ 2 Kg3 (or 2 Kh3, but not 2 Kg5?? Rg4+ draw, or 2 Kh5?? Rh5+ draw) 2...Rb3+ 3 Kf2 (or 3 Kh2 or 3 Kg2) 3...Rb2+ 4 Kb1! as there is no check. White can also approach the rook, but that wastes many moves. This is Black's best sequence of moves, as it delays the loss of the rook by many moves. If the rook had started at a8 or f8, then the game is a draw.

Here are some rook moves which are much closer to what Fine was writing about at the top of this article. The rook moves away from the king, and a few moves later is forked (or there is some similar disaster, like mate or Philidor's position).

Diagram #11: 1...Ra7! (better than 1...Rg7+) 2 Qe4+ Kg8 3 Qc4+ Kh7 4 Kf6 Rg7 5 Qh4+ Kg8 6 Qh5 = Philidor's position.

Diagram #12: 1...Rc1! 2 Qd2 (or 2 Qg5) 2...Rb1+ (or 2...Rc7) 3 Kc5 Rg1! 4 Qe3 Ra1 (or 4...Rg7) 5 Qe7+ (or 5 Qe4+) 5...Kc8 6 Qf8+ and fork next.

Diagram #13: 1...Rh2! 2 Qd5+ Kf6 3 Kg4 (or 3 Qf3) 3...Rh7 4 Qf5 Kg7 5 Kg5 (or 5 Qe4) 5...Kg8! 6 Qe4 Rf7 7 Kg6 Rg7+ 7 Kh6 and the rook is lost.

Diagram #14: 1...Ra4! (or 1...Rh5) 2 Qd6+ Kh5 3 Qd5+ Kh4 4 Qd8+ Kg3 5 Qd6+ Kh4 6 Kf3 Kg5 7 Kc5+ Kh4 8 Qe7+ and fork next.

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