The Fourth Endgame of the Apocalypse

by admin on October 29, 2011

The Four Endgames of the Apocalypse are the most notorious “common” endgames in chess, endgames where normal chess concepts go out the window and which lead otherwise sane chess players (??) to pound their heads in frustration. They are:

  1. K+Q versus K+R
  2. K+B+N versus K
  3. K+Q+RP versus K+Q
  4. K+R+B versus K+R

Last weekend in Reno I finally had my first experience with the fourth of these, against International Master Ed Formanek. In this case I was the defender, and I managed to hold on for 50 moves and claim a draw (at 2:30 in the morning!).  The tournament director, Jerry Weikel congratulated me on my defensive technique, but in fact my technique was disastrous … I was just lucky that Formanek’s technique was even worse.

The game is nevertheless instructive because we reached or could have reached several important theoretical positions. If you want to read what other people have to say about this type of endgame, I recommend the following articles:

  1. If you read Russian, Mark Dvoretsky’s Rook and Bishop versus Rook is an excellent article.
  2. If you don’t, check out Irina Zenyuk’s What Many IMs Don’t Know.
  3. Or try Ernie Hong’s Endgame Obsession #3 RBvR. In fact, that’s the article I learned the most from (not #1 and #2 above).

Now, let’s look at Mackenzie-Formanek. Here is the initial position after Black’s 58th move, when he has just captured my bishop on f1 (which had been forced to sacrifice itself for a passed pawn).

Diagram 1. White to move.

This is quite a favorable position for White because his king is in the center of the board.  A quick look at the Nalimov tablebases confirms that it is a draw. (For any readers who aren’t familiar with the Nalimov tablebases, it’s a computer database of all positions with 6 or fewer pieces, which have all been evaluated as won, lost or drawn by a brute force search tree.)

For about 20 moves Black made little progress, but on move 78 I made a critical decision that could and should have backfired.

Diagram 2. White to move.

Here’s where the tablebases are a little bit misleading. The move I played was 78. Rd8?, which I would venture to call a blunder. The move I believe I should have played was 78. Re3. And yet, according to the tablebases, both positions are still drawn.

After this game I came to the conclusion that the defense is easier if you keep your king and rook close to one another. In fact, after 78. Re3 we have an almost-theoretical position. If you take every piece and move it down one rank, so that White’s king and rook are on the second rank, you get what is known as the second-rank defense, which is supposed to be White’s easiest way to draw.

The crazy thing is that I knew this! But somehow I lost my mind, and played according to “standard endgame principles” which say to activate your rook. But highly technical endgames like R+B vs. R have nothing to do with standard endgame principles. They are all about specific, concrete positions.

Does the second-rank defense work on the third rank? Well, as a matter of fact, there is a subtle difference. After 78. Re3(!) Bd5 79. Rd3 Be4 80. Re3 Ra4 we reach a position where White is in zugzwang and has to fall back a rank. However, if we mentally move all the pieces back a rank, it turns out that this does not hurt White. In that position (all pieces moved back a rank) White can play 81. Kd1 Kd3 and now the stalemate defense 82. Rd2+!! holds the draw. However, in the position of the actual game, of course 81. Kd2 Kd4 82. Rd3+?? would just hang a rook.

The moral of the story, according to Dvoretsky, is that “the indicated method of defense is effective only on the second or seventh rank.” The bold-face is his, because he considers it important. However, I respectfully disagree. If you try to play the second-rank defense on the third rank, your opponent can push you back a rank if he plays well. But even so, it merely puts you in a position where you can use the actual second-rank defense. And if he doesn’t play well, you don’t even need to worry! The bottom line is, keep your king and rook close to each other as long as you can.

Another chess authority, GM Nicholas Pert, says in his DVD Killer Endgames II, “As soon as you start moving your rook behind the bishop and king, normally you allow [your opponent] to win.” So from a practical point of view, 78. Rd8 was an error. It enters the land of theoretical positions where White really has to know his stuff to salvage a draw.

But also, by the way, Black really has to know his stuff to pull off a win. That’s what makes this endgame so tense!

After 78. Rd8 Ra3+ 79. Kd2 Bd5 80. Ke2 Kd4 we got to our next theoretical position.

Diagram 3. White to move.

Here, if I had known my stuff, I would have played 81. Kd2! This is again a case where specific positions trump general endgame principles. Ordinarily 81. Kd2 would be a scary move to play because Black can chase me back to the first rank with 81. … Ra2+. But the point is that after 82. Kd1! we get to the Cochrane position, which has been known to be a draw since the 18th century! Black would love to play 82. … Kd3 and threaten mate, but he can’t because that would hang the bishop.

But I didn’t know the Cochrane position, and so I continued running to the kingside with 81. Kf2? Again, if you look at the tablebases they’ll say this isn’t a mistake and that the position is still drawn. But it is a mistake, and White is skating on thinner and thinner ice.

The game continued 81. … Rf3+ 82. Ke2 Rf4 83. Rd6 Rh4 84. Kf2 Rg4 85. Rd8 Rg2+ 86. Kf1 Rh2 87. Kg1 Rd2.

Diagram 4. White to move.

Now we come to another critical moment. Up until now, the tablebases have consistently said that the position is drawn. But after my next move, they say that I am lost. What would you do here?

I played 88. Kf1?! and the tablebases now say it’s mate in 26 for Black. The correct move was 88. Rd6! with the intention, after 88. … Ke3, of swinging the rook over to the a-file for lateral checks with 89. Ra6.

How on earth could a human figure this out? Well, you have to know another concrete position. After 88. Kf1, we are now headed for the Philidor position (to be discussed below), which is a forced win for Black. Basically, once your king is on the back rank and his king is on the sixth rank, you’d better start looking for sideways checks.

But here is another irony. Although the Philidor position is a forced win for the stronger side, it is very tricky. So one might argue that 88. Kf1 was a good move after all–it put the onus on my opponent to find the forced win, and he didn’t manage to do it!

After my so-called mistake, he played 88. … Ke3 89. Kg1.

Diagram 5. Black to move.

Here the computer finds an amazing forced win with 89. … Rd1+ 90. Kh2 Kf4!! This stunning quiet move creates a mating net. White’s only way out is 91. Rf8+ but now after 91. … Kg4! the only thing White can do is play for a stalemate with 92. Rf1! Of course the rook is taboo, but Black wins with 92. … Rd2+ 93. Kg1 Rg2+ 94. Kh1 Rg3+ 95. Kh2 Rh3+ 96. Kg1 (all White’s moves are forced) Kg3 with mate in one or two. Very impressive. But this is exactly the sort of thing that is very hard for humans to find, especially with a limited time. (After move 60 we were in a game/30 time control. Formanek had a little bit more than 30 minutes to start with, but by the time we got to this point he was probably down to 15 or 20 minutes.)

So it’s not surprising that Formanek chose 89. … Rg2+, which is also winning but slower. After 90. Kf1 Rg5 91. Re8+ Be4 92. Re7 Rf5+ (92. … Rh5 was better, but I’ll return to that point later) 93. Ke1 Ra5 94. Rd7 Ra1+ 95. Rd1 Ra2 we have now arrived at Philidor’s position.

Diagram 6. White to move.

Philidor’s position arises when the kings are in opposition, with the defender’s king on the back rank and on a central file (c through f), on the opposite color of the bishop, and with the bishop blocking any checks from behind by the defender’s rook. This is a theoretical win for Black, and I actually knew it was a theoretical win because I had read Ernie’s article. But it’s so tricky that I doubt I would have been able to figure out the winning procedure (or remember it) if I had been in Formanek’s shoes.

In fact, if you are defending this endgame and your king is stuck on the back rank, it might be good practical advice to head for Philidor’s position, even though it’s theoretically lost, because it nevertheless is an optimal defensive setup. One point is that White’s rook is able to defend back-rank checks on both sides (d1 and f1), so Black has to figure out some way to get the rook out of said position.

Formanek started out correctly: 96. Rd8 Rg2! 97. Rf8.

Diagram 7. Black to play and win.

And now we have come to the position that you have to know stone cold. Because over the board, with the clock ticking in a sudden death time control (and these days, you will always be in a sudden death time control by the time you get to this position), you will never be able to figure out the winning maneuver on your own.

The only winning move here is 97. … Bg6! No credit for any other moves, because if you don’t find it now you aren’t going to find it later. There are several points to this ultra-ultra-refined move. First is that the bishop covers e8, so White can’t play a check there. White is actually in zugzwang, although he doesn’t realize it because it looks as if he can simply play 98. Rf6. But the rook is not as well posted on the sixth rank as on the eighth. The next step for Black is to nudge White’s king over to d1 or f1 and then set up a back-rank mate threat that White wants to defend with R to c6 or g6. Except there’s a problem–those squares are controlled by Black’s bishop! That’s why the sixth rank is not as good as the eighth! Got it?

So here is the best play from the diagrammed position:

97. … Bg6 98. Rf6 Bd3! (the same move played in the game, but with the important difference that the rook is on the sixth rank) 99. Re6+ Be4 100. Rf6 (Forced, as on either Kd1 or Kf1 Black goes … Rh2 or … Rb2 with an unstoppable mate threat, as described above) Re2+! (A little nudge to force the king to one of the bad squares) 101. Kf1 (101. Kd1 loses to … Rb2 as before) Rb2 102. Kg1 Rg2+ (Another little nudge back to the bad square. But what is the point? How is Black going to win from here?) 103. Kf1 Rg5!! (Only thusly. The threat is 104. … Bd3+.) 104. Ke1 Bf5! This position deserves another diagram.

Diagram 8. Position after 104. … Bf5 (analysis). Black has proved his mastery of the Fourth Endgame of the Apocalypse.

Black’s amazing bishop move covers the checking square at e6, blocks White’s rook from defending the back-rank mate, and meanwhile threatens a mate-in-three after 105. Kf1 Bd3+ 106. Ke1 Rg1+ 107. Rf1 Rxf1 mate. Notice also that checkmate would have occurred on the 49th move — I would have been one move short of a draw by the 50-move rule! What torture!

Well, the title of Irina Zenyuk’s article, “What Many IMs Don’t Know,” was right on the money. Formanek is an IM, and he didn’t know this maneuver. Instead, in the position of Diagram 7, he tried the same thing with my rook on f8 instead of f6, and it didn’t work:

97. … Bd3 98. Re8+ Kd4?

Tantamount to a draw. I knew it, he knew it.

99. Re7 Ra2 100. Re8 Rh2 101. Re7 Be4 102. Re8 Ke3

Actually the position is now a “tablebase win” again. But even if he could find the winning procedure, which I know he can’t, he wouldn’t have time to win within the 50-move rule.

103. Rf8 Re2+ 104. Kd1 Rb2 105. Rc8 Rb7 106. Rc3+ Bd3 107. Rc8 Rg7 108. Kc1 Rg2 ½-½

Drawn by the 50-move rule. Before we leave this endgame, I want to go back three moves and point out one more thing.

Diagram 9. Position in the game after 105. Rc8.

Here I noticed something interesting in the tablebases that I didn’t see mentioned in any of the aforementioned references — not by Dvoretsky, not by Zenyuk, not by Hong. (I don’t know about Pert.) Consider it your reward for reading this far, if indeed you have.

THIS POSITION IS A DRAW!

Why is this remarkable? Consider the (almost) mirror image position, which could have arisen in the game after 92. … Rh5! 93. Rg7:

Diagram 9½. Position after 93. Rg7 (analysis).

THIS POSITION IS A WIN FOR BLACK!

What’s the difference? The difference is that in Diagram 9, White’s king has one more file to escape on. In Diagram 9½, Black wins as follows: 93. … Rb5 94. Rg3+ Bf3 95. Kg1 Rb1+ 96. Ka2 Rh1 mate. Chess is a cruel, cruel game sometimes. As you can easily see, if there were only a ninth file (an i-file) White could play Ki2 and draw. Also note that playing 94. Kg1 immediately (instead of 94. Rg3+) would not have helped matters, because after the king runs to g3 Black skewers the king and rook with … Rg1+.

In position 9, the equivalent maneuver fails for Black. 105. … Rh2 106. Kc1 Rh1+ 107. Kb2 Rb1+ 108. Ka2 and White’s king runs free.

I think that Diagram 9 is very important because it is a bona fide drawn position with the king on the back rank, which White can aim for if he doesn’t manage to set up the second-rank defense. I said before that if you can’t set up the second-rank defense, you should try the Philidor position and hope your opponent can’t find the win. But an even better rule is to head for Diagram 9. To make matters simpler, head for the corner of the opposite color of the bishop. Notice that if I had obeyed this rule, I also would have avoided the “serendipitous mate” that could have arisen after Diagram 5. That mate was totally dependent on the bishop and rook both controlling the corner square.

We’ve learned a lot of things about this endgame! To sum up, if you are the defender:

  1. If your king is active (i.e., on the third or fourth rank), try to keep your king and rook close to each other. Your king is harder for him to push around if your rook is nearby. Resist the temptation to check his king from behind, as it will only make things worse.
  2. If your king is on the second rank, try to set up the second-rank defense. Keep in mind the stalemate trap.
  3. If this fails, but your opponent’s king has not yet reached the sixth rank, try to reach the Cochrane position.
  4. If your king is on the back rank and his king is on the sixth rank, move your king toward the corner of the opposite color of the bishop (i.e., try to reach Diagram 9).
  5. If this fails, try to reach a position where you can threaten both horizontal checks and vertical checks. (See analysis after Diagram 4.)
  6. If all else fails, head for the Philidor position. It’s lost, but it poses the greatest difficulties for the attacking side.

If you are the attacker, study the Philidor position until you know it by heart. Pay especial attention to the use of the bishop (which will have to move at least once and maybe twice to a square like g6 where it both attacks and defends). Also note the use of zugzwang and the insertion of little checks like … Re2+ that chase the opponent’s king to a “bad” square.

Finally, let me address one more question you may be wondering after this long post: Is it really worth the trouble to learn how to play this endgame? I think that is really up to the individual chess player. You have to accept that this knowledge is highly technical. The ideas are not really transferable to any other endgame position that I know of. And you may play hundreds of games without ever having to play one of these endgames. Those are all really good arguments for not bothering with it.

They are the same arguments for not bothering with climbing Mount Everest. But a certain kind of person just can’t live with knowing that this endgame exists and that you haven’t mastered it yet. You just have to study this endgame … because it’s there. If you are that type of person, you already know it. This post is for you.

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{ 4 comments… read them below or add one }

Ernest Hong November 1, 2011 at 10:04 am

Well, I don’t know if I’d have gotten around to it soon, but the World Cup game between Judit Polgar and Lenier Dominguez Perez prompted me to write down some anaysis. See http://www.chessbase.com/newsdetail.asp?newsid=7514. I used the shredderchess.com online tablebases to figure out where the inefficiencies were. Except for one critical moment, their game stayed in the realm of a win from move 77 to 112.

I like your perspective on the drawing chances. I usually ask how could the stronger side win? It’s more difficult to ask how can the weaker side resist longer?

I try to remember Diagram 7 after the bishop move as the attacker’s target position where the rook and bishop form a kind of awning around the king (g2-g6-e8), I have to test your bishop corner color rule, but I found that the awning “should” be set up on the short side.

I was going to correct you and point out that you won this ending in http://www.danamackenzie.com/blog/?p=315, but there were two pawns that were on the board up to the end.

I always found it a little disheartening that I poured so much analysis and teaching thought into some blog posts and no one commented. Is anyone listening? Do the readers like these endgame obsessions or do they merely tolerate them as rantings of a mind gone off the deep end?

I would much rather face a KBNvK ending than a KNNvKP ending, but maybe the latter is not “common”. I think the KQPvQ is the most painful to understand and not just for rook pawns.

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admin November 1, 2011 at 11:01 am

Hi Ernie,

Good to hear from you — and by the way, thanks for dinner in Reno!

I often have the same questions as you about whether anyone is paying attention, but the little bits of positive feedback like your comment make me think that it’s worth it.

You have a great memory! Yes, my earlier endgame against Jennifer Acon was very much influenced by the fact that I had studied your blog entry. But it technically was R+B vs. R+2P. Ironically, her pawns hurt her because she wasn’t able to use defensive technique 5. (The pawns got in the way of the sideways check.) If she had known this, she could easily have sacrificed a pawn to make the sideways check possible. Also, Jennifer ran her king to the “wrong” corner, so she failed to execute defensive technique 4 as well.

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Ashish November 5, 2011 at 4:12 pm

Your post makes a deep and more general point: in a highly technical or tactical position, the computer-generated evaluation may be unrelated to, or even the opposite of, the result that two humans will usually achieve.

By the same token, preparing for practical OTB play should be very different from learning some theoretical ideal, especially the further we are from Magnus and Vishy.

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Hal Bogner March 27, 2016 at 11:46 am

Bumping up this post to bring it to the attention of folks who watched the penultimate round of the Candidates tournament earlier today. Dana – you have a great way with words: an endgame of the apocalypse, indeed!

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