Endgame Miracle

by admin on October 21, 2008

In my last post I promised to show you the endgame from my last-round game at the Western States Open. It was the last game in the entire tournament to finish, and by winning this game I managed to tie for second place under 2300.

In this endgame miracle, I somehow salvaged a win with rook and bishop versus rook and three pawns. Of course, rook and bishop versus rook is supposed to be a draw, and you would think that the three extra pawns would only help the defender. And it’s true, my opponent should have drawn this game. But it’s nowhere near as automatic as you think!

If you want to do this right, you should start by reading and fully understanding Ernest Hong’s excellent analysis of the Philidor position in his January 7, 2008 blog post. (Sadly, his blog has been somewhat inactive in recent months, but his three “Endgame Obsession” posts are great.)

However, let me be honest with you. I have a pretty low tolerance for theoretical endgame study. Until I actually get to a position in a game, I have trouble motivating myself to really study it. So although I read Ernie’s post, and found it fascinating, I did not memorize the winning technique. I mean, how likely am I to get this position in a game, right? But what I did take away from it was the understanding that the defender in R+B vs. R is in deep trouble if his king is stuck on the back rank. And I had some idea of the correct setup for the stronger side’s pieces — king on a central file on the sixth rank, bishop behind it sheltering the king from checks.

So now let’s get to the game. I’ll start long before we reached the endgame in question, because I think it really helps to see how a position like this could come about, and what choices the two players made before they got there.

White (Jennifer Acon) has just played 45. Re5. It’s clear that Black (yours truly) is in desperate straits, because there is no way to hang onto the pawn. If 45. … Rd6 then 46. Nb7 picks up the a5 pawn. However, Black has one last desperate trick:

45. … Rb6!

[Typo corrected — I originally wrote Rb7, which two commenters pointed out is impossible.]

A stunning move, whose idea is to trap the knight on d8. As the knight has no escape and … Bg7-f8-e7 is threatened, White has no choice but to continue with her plan.

46. Rxd5 Ke7!

Note that 46. … Bf8? would now be too slow, because White could extricate the knight with 47. Rd7 followed by 48. Nb7.

Already a crucial decision for White. Should she try to hold on to the knight, or abandon it to its fate? After the game, Jennifer thought she had made the wrong decision, but in fact she did the right thing! The knight cannot be saved, because Black is threatening … Bf6 and … Ke8. During the game I was worried about 47. b3, but the pawns don’t get there in time. After 47. b3 Bf6 48. c4? bc 49. bc Ke8 White can’t save the knight with 50. c5 because Black has a tempo-gaining check, 50. … Rb2+.

So since the knight cannot be saved, White correctly chooses to get as many pawns as she can for it. And four pawns are quite a lot!

47. Rxf5! Kxd8

Here Fritz says that 47. … Bf6 is more accurate, but White still wins a raft of pawns with 48. Nc6+ Rxc6 49. Rxb5. So I do not think my move was a blunder.

48. Rxg5 Bh6 49. Rxh5 Bh6 50. Rxh5 Bc1

Yet another critical decision. Black is threatening to win the pawn back. I thought that White’s best try here was 50. b4!?, the point being that after 50. … a4 51. Kd3 Bxa3 52. Kc2 Black’s bishop is now trapped! The problem is not that the bishop is in danger, but that it’s out of play. As a result, Black’s rook has to hold the fort alone against White’s rook and three passed pawns. I don’t think it can.

However, Black can save the day by bringing his rook into the fray: 52. … Rf6! 53. Rxb5 Rf2+. And now we see why White was justly afraid of this line — Black’s one passed pawn on a4 is every bit as dangerous as White’s five passed pawns! The computer finds an amazing line where White draws, but for practical, human play it would be ultra-dangerous for White to go into this endgame.

So once again, I think that Jennifer did the right thing by playing 50. a4! Now if 50. … Bxb2 she can play 51. Rxb5! Rxb5 52. ab Bxc3 53. Kd3. With rooks off the board, Black no longer has any winning chances. In fact, I thought I might be losing, although I wasn’t sure. (The computer again says it’s a draw.) So I felt it was essential for me to keep the rooks on the board — even though it meant giving up my last pawns! So I played 50. … ba! 51. Rxa5 and now another critical moment arrives:

51. … Rxb2+!

Here my opponent gave a little jump, as if she was surprised by this move. This is where my familiarity with Ernest Hong’s post about the R+B vs. R endgame started to pay off. I knew that the only way I could possibly win was to imprison my opponent’s king on the back rank. Thus, the automatic 51. … Bxb2? would be a mistake because it allows White’s king to remain free.

52. Kd1 Bd2 53. Rxa4 Bxc3 54. Rc4 Ba5

Up to now, both sides have played quite well in a very difficult endgame. But now my opponent starts to go wrong, and it’s due to a fundamental misconception about the endgame. At this point she should be thinking about how to draw, but she continued to look for a win. She could have drawn effortlessly with 55. Rc2, which springs the White king out of captivity. Instead she played the clever but misguided 55. Ra4? Bc7 56. Ra8+ Kd7 57. Rh8. With her rook maneuver she has managed to keep her three pawns, but she has abandoned her king as a prisoner of war.

She continues to miss some drawing opportunities over the next few moves, but let’s fast forward until the position really becomes critical:

57. … Bd6 58. Kc1 Rg2 59. Kd1 Ke6 60. Rh5 Bb4 61. Kc1 Bc3 62. d5+ Kd6 63. Kb1 Be5

White cannot save the d-pawn, and now there is no obstacle to the continued approach of the Black king … the executioner.

64. Kc1 Kxd5 65. Rh4 Bd4 66. Rh7 Kc4

Here, I believe, is the absolute last chance for White to save a draw, but it would have required her to have a deep understanding of the R+B vs. R endgame. First, she needs to understand that the plausible defense with the rook checking the king from behind does not work, because it leads to the Philidor position, discussed in Ernest Hong’s blog. Next, she needs to know that the way to save the game is to create the option of checking horizontally on the third rank after Black plays … Ke3. If she had realized this, she would realize that the g3 pawn is not helping her but hurting her — it gets in the way of the rook check. And thus she would discover the only saving move: 67. g4!!, clearing the third rank.

As a practical matter, I doubt that she even considered this move. At no point in this endgame did she seem to realize how much danger her king was in. From move 55 on, she has been more interested in preserving her pawns than in saving her king, and she is now about to pay the price.

67. Rc7+? …

Although this is technically the losing move, I can’t bring myself to give it two question marks. From a practical viewpoint, the losing mistakes were earlier.

67. … Kd3

Black has now reached his ideal position, and the threat is mate on the move.

68. Kb1 Rb2+ 69. Kc1 Ra2

Now Jennifer makes her last mistake. I still don’t think that she had any clue that she was losing. The move that puts up the maximum resistance is 70. Kd1! Rxh2 71. Re7. Notice how White needs to switch her rook back and forth, so that it can interpose on either side of the king. Black’s best play now is 71. … Ra2 72. Rc7 Rg2! (Yes, it is important for Black to win the last pawn, because the correct winning method involves a zugzwang. If White still had a pawn left, Black could not put her in zugzwang.) 73. Re7 Rxg3

Position after 73. … Rg3 (analysis).

And now, at long last, we have reached the Philidor position! Now I would have had to prove that I understood the R+B vs. R endgame well enough to win — and ironically, I doubt that I would have been able to do it, because I had not memorized the winning method from Ernie’s blog! What a bitter disappointment that would have been, to play the endgame so impeccably up to this point and then not be able to cash in. You can bet that I’ve memorized the winning method now.

Instead, here is how the game really ended. Here again is the position where she should have played 70. Kd1.

Position after 69. … Ra2 (actual)

70. Rb7? …

The problem with this move is that, unlike in the other line, White can only interpose with her rook on one side of the king. That makes the win much easier for Black.

70. … Rxh2 71. Kb1 …

Another tragic way to lose is 71. Rb3+ Bc3 72. Kb1 Rh1+ 73. Ka2 Ra1 mate. White finally managed to play a horizontal check, but the rook on b3 took away the king’s flight square!

71. … Rh1+ 72. Ka2 Ra1+ 73. resigns

If 73. Kb3 Rb1+, White loses her rook on the skewer.

I think there is a good chance that I will do a ChessLecture about this game at some point. If so, you’ve just gotten a preview.

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{ 5 comments… read them below or add one }

Dan S October 21, 2008 at 10:53 am

45. … Rb7! is indeed a stunning move 🙂 Looks like you meant Rb6.

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Ernest Hong October 21, 2008 at 11:09 am

Isn’t it funny how one interesting (usually won) game can change your whole outlook on chess?

Nice analysis and thanks for the credit. There’s a small typo in the first move; it should be 45…Rb6.

What’s annoying is that even though I may have written that blog post, it still doesn’t mean that I understand it today. I’m glad you were able to recall enough to be helpful to your game.

At the time of my post, you commented: “The consolation is that these endgames are *very* rare in practice. In my entire chess career, I’ve had one game that went to K+Q vs. K+R (I drew with the rook!), one that went to K+B+N vs. K, and I’ve never had a harder one like K+R+B vs. K+R or K+B+B vs. K+N.”

It was good to see you even if but briefly to collect scoresheets of your first round loss and your last round win. Inspired by your example, I think I’m going to come back to chess and chess blogging soon.

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Michael Aigner October 21, 2008 at 11:16 am

Congrats Dana on a solid result. The Luke kid that you chumped in round 2 is not 13 or 14, but 9 or 10! He’s the top rated 9 year old on the October top 100 lists and I saw him beat and draw with FMs in Las Vegas.

I wish I could say that I played well, but I did not. Getting a decent opening vs GM Bhat and then losing within 20 moves. Winning a game in 5.5 hours and finding out that I had a checkmate (or win queen) on move 22. Ignoring my opponent’s move order in round 5 and being worse (with white) by move 10. Blowing an even endgame in the last round, only to have my young opponent offer a repetition of moves with a forced win on the board. Yes, it was a rough weekend.

Keep up the fun blogging!

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admin October 21, 2008 at 11:57 am

Wow, this is some kind of record! I’ve never gotten three comments within the first half hour after posting. Thanks for pointing out the typo, Dan — I’ve fixed it now. Ernie, I was glad to see you, too, and glad that your chess malaise didn’t keep you away from the tournament. Michael, thanks for the info on Luke Harmon-Vellotti. I guess I’m not very good at judging people’s ages! I’m very glad that, after losing to Nicholas Nip when he was 8, I didn’t repeat the embarrassment by losing to Harmon-Vellotti at age 9.

I’m still a long way from understanding the R+B vs. R endgame, too. I was just lucky that in this game the opportunity presented itself to get to a type of position that I had seen before. When I was going over the game on the computer last night (particularly the complicated lines that ensue if White plays 66. g4 or 67. g4) I was really struck by the way that the difference between a drawing move and a losing move for White is sometimes almost invisible. Even Fritz has trouble — its assessment will sometimes be -0.2 pawns for a half minute or a minute, and then whoops! It jumps to -6.0 pawns, a win for Black. So I still need to go over this endgame by hand, without the computer, to make sure I’ve got it right.

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Chessgambiter October 22, 2008 at 12:17 pm

Professional endgame commentarie!

Chessgambiter

http://www.chessgambiter.blogspot.com/

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