Dennis M's Chess Site

This is a blog for chess fans by a chess fan. I enjoy winning as much as anyone else, and I've had a reasonable amount of success as a competitor, but what keeps me coming back to the game is its beauty. And that, primarily, is what this site will be about! All material copyrighted.

Thursday, March 10, 2005

(Not) All Rook Endings are Drawn

Two of my chess students played in a local scholastic event this past weekend, and in the last round one of them had a chance for second place. Unfortunately, some inaccuracies in the late stages of the opening cost him a pawn, and many moves later he (playing Black) was still a pawn down in the following position:

White is winning handily: the Black's king is cut off and he has no prospects of counterplay. Unless White is generous and contributes material to the cause, the win will be in the bag. Which means, of course, that White played

1.b6? Blundering a pawn! Ironically, this move wins quickly and efficiently, but White, reeling from the recognition of his unintentionally giving up the pawn fails to seize his chance. [1.Rc6+ Kd5 (1...Ke5 2.b6 is even easier.) 2.Rxf6 Re4+ 3.Kc3 Re3+ 4.Kd2 Re7 5.b6 axb6 6.Rxb6 Ke4 7.a6 Ra7 8.Ke2 Kf4 9.Kf2 Rc7 10.g3+ Ke4 11.Rb4+ Ke5 12.Rb2 Ke4 13.Ra2 Ra7 14.Ra4+ wins - the White king moves up the board, heading either east or west, depending on what the Black king does, either winning the rook for the a-pawn or breaking through on the kingside.] 1...Rb1+ 2.Kc4? Natural - but bad; it's only this move that throws away the win. [Instead, 2.Ka3! wins elegantly, using the bridge-building technique all players should recognize from the Lucena position. Black's king is close enough to stop the White a-pawn after the trade of rooks, but in the long run Black's kingside weakness will cost him the game: 2...axb6 3.a6 Ra1+ (3...Re1 4.a7 Re8 5.Rd2+ Kc5 6.Re2 Ra8 7.Re7 b5 8.Rxf7 h6 9.Kb3 Rd8 10.Rc7+ Kb6 11.Rh7 Rd3+ 12.Kb4 Rd4+ 13.Kc3 Ra4 14.Rxh6 Rxa7 15.g5 Kc5 16.gxf6 Ra3+ 17.Kd2 Ra2+ 18.Ke3 Kd6 19.g4 Ke6 20.g5+-) 4.Ra2 Rxa2+ 5.Kxa2 Kc6 6.Kb3 b5 7.a7 Kb7 8.Kb4 Kxa7 9.Kxb5 Kb7 10.Kc5 Kc7 11.Kd5 Kd7 12.Ke4 Ke6 13.Kf4 Kd6 14.Kf5 Ke7 15.g3 h6 16.h4 Ke8 17.Kxf6 Kf8 18.h5 Kg8 19.g5 hxg5 20.Kxg5 Kg7 21.g4 Kh7 22.Kf6 Kg8 23.g5 Kf8 24.g6 fxg6 25.hxg6 Kg8 26.g7 Kh7 27.Kf7+-] 2...axb6 3.a6 This too is dubious, and exhibits a common psychological failing of players who have blown a win and know they've blown it. Instead of acquiescing in the position as it is, they play as if they are still winning. The consequence is often a continued slide down the hill, and that's what happens here, too. [3.Rd2+ Kc7 4.axb6+ Rxb6 5.Rd5 Rb2 6.Rh5 Rxg2 7.Rxh7 Kd6 8.Kd4 Ke6 ought to be drawn, but White can pretend to bother Black for a while.] 3...b5+! [3...Ra1 may be playable too, as 4.Kb5 goes nowhere due to 4...Rb1+ Even so, 3...b5+ is better, driving the king back.] 4.Kd4 Rb4+! 5.Kd3 Ra4 At this point I was getting excited: White has lost a pawn and a good deal of space, too, since our starting position; add to this his time trouble (he had less than a minute and a half, albeit with the execrable late-20th century invention of time delay as a safety net), and a miracle for Black was starting to look possible! Objectively, the position is still thoroughly drawn, but the trends are going in the right direction. 6.Rb2 [6.Rf2 Ke6 7.Rf5 b4 8.Kc4 Rxa6 9.Kxb4 Ra2 10.Rh5 Rxg2 11.Kc4 and the position is a dead draw.]

6...Kc6?? OH NO!!!!!!!!!!! Black is right to protect the b-pawn, and his thought must have been that it's better to bring the king into the square of the pawn. But the latter is unnecessary - the rook is going to capture the a-pawn, so it's better to place the king on a more active square. Thus with [6...Kc5! Black gets to direct things, and now it's White who must play accurately to draw. 7.Rc2+ Kd5 8.Rb2 (8.Rc7 is best, going active. Indeed, if there's one rule for rook endings, whether for the strong side or the weak side, it's to play actively! Now the position will quickly resolve itself as a draw after an MPM (mutual pawn massacre). 8...Rxa6 9.Rxf7 Ra3+ 10.Kc2 Rg3 11.Rxh7 Rxg2+ 12.Kb3 f5 13.Rh5 Ke4= 14.Rxf5 (14.gxf5 Rf2 15.Kb4 Rxf5 16.Rxf5 Kxf5 17.Kxb5 Kg5 18.Kc4 Kh4 19.Kd3 Kxh3) 14...Rg3+ 15.Kb4 Rxh3 16.Kxb5 Rg3 17.Rg5 Kf4 18.Rg8 Rxg4 19.Rxg4+ Kxg4) 8...Ra3+ 9.Kd2 Kc5 10.Rc2+ Kb6 Had this position occurred, as I think was entirely possible, I think Black would have had excellent chances to win in White's time pressure. Nevertheless, White should still draw after 11.Kc1 Rxa6 12.Kb2 when Black is in a sort of zugzwang: if the rook moves, 13.Rf2 wins the f6 pawn; if the king moves, then the White rook gets in via c5 or c7. (Pawn moves change nothing - White will play 13.Kb3 in reply and Black's dilemma recurs.) 12...Ka5 (12...Ra7 13.Rf2=) 13.Rc7 Re6 14.Rxf7 Kb4 15.Rxh7 Re2+ 16.Kb1 Rxg2 17.Rf7 Kb3 18.Kc1 Rg3 19.Rxf6 Rxh3=] So, even 6...Kc5 is only a draw. But what's so bad about 6...Kc6? Here's the answer: 7.Rf2! Sadly, the king on c6 prevents Black from defending the f6 pawn with ...Rxa6. White keeps the a-pawn (unless Black captures it, allowing tranposition to a lost pawn ending, as in the game) and devours too many Black pawns too quickly. A pity, but it just goes to show you: not all rook endings are drawn! And yet, resistance was still possible, had Black continued actively, even here. 7...Ra3+? [7...Kd5!

(Going active!) makes things much, much more difficult for White. In fact, I'm not even 100% sure that White is objectively winning here; I think he is, but there are many drawing lines. This is the best I've come up with so far: 8.Rxf6 b4! (8...Ke5 wins the a-pawn straight away, but the loss of time is too significant, and White wins after 9.Rxf7 Ra3+ 10.Ke2 Rxa6 11.Rxh7 Rb6 12.Kd3 Kf4 13.Kc3 Re6 14.Kb4 Re2 15.Kxb5 Rxg2 , when according to the tablebases White has a forced mate in 49 (actually less - see below). Here are the moves - the end is trivial, but it's useful to see how White advances the pawns through what seems like somewhat of a blockade. 16.Rh5 Re2 17.Kc6 Ra2 18.g5 Ra6+ 19.Kb5 Re6 20.h4 Ke5 21.Rh7 Kf5 22.Kc5 Re5+ 23.Kc6 Kg6 24.Rh6+ Kg7 25.Rd6 Re4 26.h5 Rh4 27.Rg6+ Kh7 28.Rh6+ Kg7 29.Kd6 Rg4 30.Rg6+ Kf7 31.Rf6+ Kg7 32.Rf5 Rd4+ 33.Rd5 Rh4 34.g6 Rh1 35.Ke6 Re1+ 36.Kf5 Rf1+ 37.Ke4 Re1+ 38.Kf3 Kh6 39.Rd8 Rg1 40.Rh8+ Kg7 41.Rh7+ Kf6 42.Kf4 Rf1+ 43.Kg4 Rg1+ 44.Kh3 Rg5 45.Rf7+ Ke6 46.Kh4 Rg1 47.Rf3 Ke7 48.Rg3 Rh1+ 49.Kg5 Kf8 50.Rf3+ Ke7 51.Kh6 Ke6 52.g7 Rg1 53.Re3+ Kf7 54.Rf3+ Ke6 55.Kh7 Ke5 56.h6 Ke4 57.Rf7 Ke5 58.Re7+ Kf6 59.Rc7 Rg2 60.Kh8 Ke5 61.g8Q (61.h7 is slower, but it's the "official" tablebase move. The reason, I believe, is that KQRPkr isn't in the tablebase, so that possibility just gets ignored. 61.h7 is an example of what we might call Chinese Room Chess, which is to say, not chess at all. 61...Kd6 62.Rc4 Kd7 63.Rd4+ Kc6 64.g8Q Rxg8+ 65.hxg8Q Kb5 66.Qe6 Kc5 67.Rc4+ Kb5 68.Qc6+ Ka5 69.Ra4#) 61...Rc2 62.Rxc2 Kd6 63.Qg5 Ke6 64.Rc6+ Kd7 65.Qd5+ Ke7 66.Qe6+ Kd8 67.Rc8#) 9.Kc2! (9.Rxf7 looks as natural as the Rockies, but I think Black draws here! 9...Ra3+ 10.Kc2 Rxa6 11.Rxh7 Ra3 12.Rh8 (12.g5 Ra2+ 13.Kb3 Rxg2 14.h4 Rg4 15.Rh8 Kc5= with a draw, as White can't make any progress on the kingside without losing a pawn or getting mated - which would hardly count as progress at all. 16.Rh6 with the idea of crawling forward with g6, h5, Rh7, g7, etc. I'm showing this terrible idea only to show that White doesn't have time for this. 16...Rg3+ 17.Kb2 Rg2+ 18.Kb1 (18.Kb3 Rg3+=) 18...b3 19.g6 Kb4 20.h5?? Kc3 followed by 21...Rg1#) 12...Rc3+ 13.Kd2 Rg3 14.Ke2 Rxg2+ 15.Kf3 Rh2 16.Kg3 Rh1 17.Rb8 Kc4 18.g5 b3 19.Kg2 Rd1 20.h4 Rd2+ 21.Kg3 b2 22.g6 Rd3+ 23.Kf4 Rd4+! (23...Rb3 is the right idea at the wrong time, because after the trade of rooks and mutual promotion, the geometry of the position is such that White can force the trade of queens and win. 24.Rxb3 Kxb3 25.g7 b1Q 26.g8Q+ Kc3 27.Qg7+ Kc4 (27...Kd2 28.Qd4+ and White's next move forces the trade of queens) 28.Qc7+ Kd5 29.Qd7+ Kc4 30.Qe6+ Kc3 (30...Kc5 31.Qf5+) 31.Qe3+ and the trade of queens is inevitable) 24.Kg5 Rd5+ 25.Kh6 Rb5 26.Rxb5 Kxb5 and now, because White can't force the trade of queens, it's a draw! 27.g7 b1Q 28.g8Q Qe4 with a tablebase draw.) 9...Ra3 10.Kb2! (10.g5 Kc4 11.Rf4+ Kb5 12.Rxf7 Kxa6 13.Rxh7 Ra2+ 14.Kb3 Rxg2 15.h4 Rg4 16.Ka4 (16.Rh6+ Kb5 17.g6 Rg3+ 18.Kb2 Rg2+ 19.Kb1 Kc4 and White must abandon the g-pawn to save the draw, as 20.h5?? loses to 20...Kc3 21.Rh8 Rg1+ 22.Ka2 b3+ 23.Ka3 Ra1#) 16...Kb6 again seems to be a draw. White can only push the kingside pawns with the Rh6, g6, h5, Rh7 etc. crawl technique, but Black's queenside counterplay is much too fast. Thus 17.Rh6+ Kc5 18.g6?? Rg3 19.Rh5+ Kc4 20.Ka5 b3 21.Rg5 b2 (21...Rxg5+= 22.hxg5 b2 23.g7 b1Q 24.g8Q+ is a tablebase draw, though Black does need to be careful here.) 22.Rxg3 b1Q and Black wins (tablebase says mate in 33)) 10...Kc4 11.Rf4+ Kd5 12.Rxf7 Rxa6 13.Rxh7 Ra3 14.Rb7 Kc4 15.Rc7+ Kd4 16.Rf7 Rg3 17.Rf4+ Kc5 18.Rf3 Rxg2+ 19.Kb3+- Finally, with the kingside pawns protected and unblockaded, and with Black lacking queenside counterplay - all thanks to the beautifully posted rook on f3 - we can conclude to a White win. But it wasn't easy!] 8.Kd4 Ra4+ 9.Kc3 Ra3+ 10.Kb4 Ra4+ 11.Kb3 Rxa6 12.Rxf6+ Kb7 13.Rxf7+ and now Black should retreat his king to the back rank, but that would only make the game last longer without giving him any real chances to survive. 13...Kb6 14.Rf6+ Ka5 15.Rxa6+ Kxa6 16.g5 Kb6 17.h4 Kc5 18.h5 Kd6 19.g6 hxg6 20.h6! etc. 1-0


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