Monday, January 7, 2008

Endgame Obsession #3 RBvR

The ending of Rook and Bishop versus Rook has shown up at our club two or three times in the past year and now in a top-level GM game. Each time it shows up, people voice the canon that it is theoretically drawn and now verified in the tablebases, but in these anecdotal experiences, the defender tends to crumble and give the full point away. This suggests that studying such an ending might eventually pay dividends, so it has become my next Endgame Obsession. This post will become crazy long because I have to beat this thing into the ground in order to understand it.

Coincidentally, I recently was going over an ending whose solution was lost in cyberspace at Brian Gosling’s Practical Chess Endings. The diagram is given and the author of the study seems to be listed as Philidor, but the solution got deleted or misplaced. So I thought I’d use Fritz to help fill in the solution and help me learn what’s going on.


White has Black's King pinned on the back rank and nearly mated. The bishop’s reach extends to two squares on the eighth rank, b8 and h8, while the White King covers the seventh rank squares. The White Rook would like to execute the back rank mate, sometimes with the help of the bishop by landing on b8 or h8, but the Black Rook is placed the way it should for the defense, ready to interpose Rc8+ with Rd8, maintaining contact with its own King. If White were to start with Rh1, Black plays Rf7, mirroring the start position. The two-sided nature of the position actually favors White, a fact whose antithesis will appear when we move on to the grandmaster game below. First objective: White wants to get control of the seventh rank after which Black's King will be trapped in the narrow band between c8 and g8. 1.Rc8+! Rd8 2.Rc7!


First objective achieved. Now Black must move. If he plays 2...Ra8 or 2...Rb8, White mates starting with 3.Rh7, although the bishop will have to absorb the desperado sac after 3...Ra6+ 4.Bd6 Rxd6+. 2...Rd2! Black's choice of d2 is better than d1 or d3 in order to check the White King from behind. The bishop cannot control e2. (If Black moves his rook sideways 2...Ra8 3.Rh7 Ra6+ 4.Bd6 Rxd6++- ; If Black instead moves his king, 2...Kf8 it's mate in 9 starting with Rh7, eventually going through a weird curlicue Rg7-Rg5-Rh5-Rh8. 3.Rh7 Re8+ 4.Kf6 Kg8 5.Rg7+ Kh8 6.Rg5 Kh7 7.Rh5+ Kg8 8.Kg6 Re6+ 9.Bf6 Rxf6+ 10.Kxf6 Kf8 11.Rh8#; 2...Rd1 3.Bc3 White goes for the Bishop Round Trip (see below) to get the Rook to d3.; 2...Rd3 3.Re7+ White goes for the Rook's Long Detour (see below) to c4. 3...Kd8 4.Rh7) 3.Ra7 White waits a move to get Black to choose A)Rd3 or B)Rd1.

A) 3...Rd3

This loses four moves faster than Rd1. 4.Re7+ Now that the Black Rook is on the third rank, White embarks on a series of rook maneuvers, the Rook’s Long Detour, designed to get the Black King on d8 just before the White Rook moves to c4. Watch as the rook visits e7, h7, and c7 on its way to c4. 4...Kd8 (4...Kf8 5.Rh7 Black loses his rook to delay mate.) 5.Rh7 Kc8 6.Rc7+ Kd8 7.Rc4!


7...Re3 (7...Ke8 8.Bd4 preventing 8...Re3+. Any rook non-capturing move allows 9.Rc8#. 8...Kd8 allows 9.Bf6+ Ke8 10.Rc8+ Rd8 11.Rxd8#.) 8.Rb4+- The Black Rook can only stop 9.Rc8# by sacrificing itself either on e5 or on c3.

B)3...Rd1

This resists four moves longer than Rd3. 4.Rg7! Since Black can interpose his rook at d8, White switches to the kingside, but there's a subtlety. From g7, White can defend a bishop sitting on g3, which is how White will achieve zugzwang after Rf1. (4.Rh7 Rf1 simply transposes to the mirror image of the last position.) 4...Rf1


5.Bg3! The White Bishop goes on a Round Trip from e5 to g3 to d6 to e5 while getting the Black Rook to go from f1 to f3.

(If 5...Kf8

Since the Black King and Rook are both on the f-file, White fast forwards to a Rg4 maneuver coupled with Bh4 which is analogous to the Rg4-Bf4 maneuver at the end of this study. 6.Rg4 Ke8 7.Ra4 Rd1 8.Bh4! Kf8 9.Rg4)

5...Rf3 Notice that Black's rook has been lured to the third rank like the variations after 3...Rd3. 6.Bd6 This now covers the interposing square on f8, but almost begs for the check in the back. 6...Re3+ 7.Be5 Rf3


This position is essentially a mirror of the variation after 3...Rd3. White now uses a Rook Long Detour e7-a7-g7-g4 in order to get to g4 with the Black King on f8. 8.Re7+ White would like Black to commit to f8 where the Black Rook doesn't help interpose. 8...Kf8 9.Ra7 This forces the Black King further toward a false exit at h7. 9...Kg8 10.Rg7+ Psyche! Kh8 allows Rg3+ winning Black's rook. Back to f8. 10...Kf8


11.Rg4!! Ke8 (11...Re3 12.Rh4+- The Black Rook cannot get to g8 because g3 is covered by the White Bishop.) 12.Bf4 This prevents Rf8 and Re3+. If the Black King goes 12...Kf8 to stop Rg8+, the Bishop swoops down 13.Bd6+ Ke8 14.Rg8+ Rf8 15.Rxf8#. 1-0

In the 2007 Russian Superfinal, in which Morozevich won in fine style, there arose an ending between GM Andrey Rychagov 2528 and GM Alexander Grischuk 2715. Rychagov sought refuge in the theoretically drawn Rook and Bishop versus Rook. Grischuk pressed the ending which was a tablebase draw from moves 59 to 90, but Rychagov’s stalwart defense began crumbling at move 90 and eleven moves later, he resigned. What happened between moves 90 and 100 will conclude this Endgame Obsession...at least for now.

Rychagov, Andrei – Grischuk, Alexander, 2007 Russian Superfinal
1.d4 Nf6 2.c4 e6 3.Nf3 d5 4.Bg5 dxc4 5.Nc3 c6 6.e4 b5 7.e5 h6 8.Bh4 g5 9.exf6 gxh4 10.Ne5 Qxf6 11.g3 Nd7 12.Qe2 c5 13.Nc6 Bg7 14.Bg2 cxd4 15.Nd5 Qf5 16.g4 Qg5 17.f4 d3 18.fxg5 dxe2 19.Nc7+ Kf8 20.Nxa8 Bb7 21.Nc7 Nb8 22.Nxb8 Bxg2 23.Kxe2 Ke7 24.Nba6 hxg5 25.Nxb5 Bxb2 26.Rab1 c3 27.Rxb2 cxb2 28.Rb1 f5 29.gxf5 g4 30.Kf2 Bb7 31.Nc5 g3+ 32.Kg1 Bd5 33.Nc3 Bf3 34.Rxb2 exf5 35.Rb4 Kf6 36.Rf4 Ba8 37.Ne2 Re8 38.Nxg3 hxg3 39.hxg3 Re3 40.Nd7+ Kg5 41.Ra4 Bc6 42.Rxa7 Re7 43.g4 f4 44.Ra5+ Kh4 45.Nf6 Kg3 46.Nh5+ Kxg4 47.Nf6+ Kg3 48.Ra3+ f3 49.Nh5+ Kg4 50.Ra5 Re6 51.Kf2 Rh6 52.Rc5 Bb7 53.Rb5 Bc6 54.Rc5 Be8 55.Rc4+ Kxh5 56.Kxf3 Ra6 57.Kf4 Kg6 58.a4 Kf6 59.a5 Rxa5


If White can make it to move 109 without losing his rook, he draws by the 50-move rule. 60.Rb4 Bc6 61.Rc4 Rf5+ 62.Ke3 Re5+ 63.Kd4 Rd5+ 64.Ke3 Bb5 65.Rd4 Rh5 66.Kf4 Ke6 67.Ke4 Bc6+ 68.Kf4 Rf5+ 69.Ke3 Ke5 70.Rd3 Rh5 71.Rc3 Bd5 72.Kd2 Rh2+ 73.Ke3 Rh4 74.Kd3 Rg4 75.Ke3 Bc4 76.Kf3 Rh4 77.Ke3 Re4+ 78.Kf3 Be2+ 79.Kf2 Kf4 80.Rc2 Bd3 81.Rb2 Re3 82.Rb4+ Be4 83.Rb2 Rh3 84.Re2 Bd3 85.Rd2 Rf3+ 86.Kg2 Bf1+ 87.Kg1


I can't comment on the methods between move 60 and 86 to push the Black King to the side because I don’t understand them yet, but the edge is where winning chances start popping up. 87...Ke3 88.Rd5 Bd3 89.Rg5 Be4 90.Kh2 Kf4 Black narrows the gauntlet with this move.


91.Rg8?! Tablebase mate in 52.

(Better was 91.Rg3 Rf1 (offering 91...Rxg3 for stalemate.) 92.Rg4+ Kf5 ( 92...Kxg4 another stalemate.) 93.Rg1=;

Or White could also find 91.Rg7


Now why the heck does Rg7 draw, but Rg8 lose? Applying similar follow-up moves, it appears that Rg7 allows a saving Ra7-Ra3 maneuver which foils White's ideal setup. 91...Rf2+ 92.Kg1! Rc2 93.Ra7! Ke3 94.Ra3+! Bd3=)

91...Rf2+! 92.Kg1


92...Ra2?! Back to tablebase draw.


(92...Rc2! Tablebase mate in 50 moves, but the 50-move draw expires in 18 moves. The next 50 moves in this line are nearly incomprehensible and perhaps will have to wait for another installment of Endgame Obsession.)

93.Rb8?! Tablebase mate in 50.



(93.Rc8! Rg2+ 94.Kf1! Rd2 95.Rc4 Ke3 96.Rc3+! Bd3+ 97.Kg1 Kf3 98.Rc8! Rg2+ 99.Kh1 Ra2 100.Kg1! Tablebase draw)

93...Bd5?! Back to tablebase draw. (93...Rg2+! 94.Kf1 Rd2! 95.Rb4 Ke3! 96.Rb3+ Bd3+ 97.Kg1 Kf3! 98.Rb7 Rg2+ 99.Kh1 Ra2 100.Rb3 Tablebase mate in 43, but too late for move 109. ( 100.Kg1 Bc4! That this move is possible in this position seems to be the reason why 93.Rb8 loses while 93.Rc8! draws. Mate in 29, but again too late for move 109.))

94.Rd8 Kg3 95.Kf1! Bf3


96.Ke1?? This is the crucial error. White's previous inaccuracies could still be remedied by the 50-move rule, but now Black can threaten mate and win the rook around move 100.

(White can draw with 96.Rg8+ Bg4 97.Re8!=; Or 96.Re8=


If you compare this position with the Philidor study above, you'll see that Black has many of the same advantages, but the thing that is lacking is that his rook doesn't have much room to swing over on the king side. The White Rook can interpose a check at e1, but in the study above, the attacking rook had to move to the opposite side of its king. In order for analogous maneuvers to happen here, there would have to be an i2 and a j1 square available. I guess the lesson is that the White King is actually safer at f1 than e1, since Kg1 can prevent Rh1 (after White has forced Bg4 with Rg8+). If you remember nothing else about this post, I think this might be the kernel of what you need to know to draw this ending KEEP THE KING ON THE KNIGHT’S FILE OR THE BISHOP’S FILE WHILE KEEPING THE ROOK IN POSITION TO INTERPOSE OR TO CHECK ON THE KNIGHT’S FILE. If you ask me what to do if the attacking king is on the bishop file, I’ll have to do more research. 96...Rh2 97.Rg8+ Bg4 98.Kg1!=)

Now back to 96.Ke1??


96...Re2+! (96...Ra1+ 97.Kd2 Rd1+ 98.Ke3!= Rxd8 stalemate!) 97.Kf1


97...Re3! This is an important only move for the attacking side. The rook pullback relieves the bishop of its defending duties and stops Rd3. Black now threatens Bg2+ and Re1 mate. (If Black rushes to 97...Re7 White holds with 98.Rd3=) 98.Rg8+ Bg4! 99.Rg7


If White doesn't mark time with his Rook on the g-file, Black will play Bh3+ and Re1 mate. Black still needs to zugzwang the White Rook further out of position. 99...Re8 100.Rg5 (100.Rg6 Rd8!-+) 100...Rh8 0-1 (Black resigned in sight of 100...Rh8 101.Ke1 ( 101.Kg1 Rd8-+) 101...Rd8!-+; 100...Rf8+ also wins. Black is basically making sure that the White Rook has no interposition when his Black Rook goes to d8. 101.Ke1 Rd8-+; To illustrate the danger of incorrect technique, 100...Rd8?? leads to a tablebase draw again. 101.Re5!=)

Now that a super GM has shown that an ordinary GM can fail to hold the draw of Rook against Rook and Bishop, is it “bad manners” to press the stronger side in the hopes your opponent will screw up? I say no, because the burden of proof is on the defense to show that the attacker can't convert. I think I would say so even if I end up on the defending side soon.

3 comments:

ChargingKing said...

wow I feel like a stranger in a strange land after looking through that blog. You are on a completely different level in the endgame Ernie!! That is impressive.

qxpch said...

Great analysis on R+B vs R! I will study this carefully.

Do the tablebases come with ChessBase? (I only have Fritz but not ChessBase, so I'm wondering whether it would be worth it to invest in a copy of ChessBase.)

It seems to me that you have identified one important factor in telling the won positions apart from the drawn positions -- the R+B have better winning chances when the defending king is in the center on the back rank, giving the stronger R two sides to work with. I wonder if a way to further systematize this endgame is to realize that (taking Rychagov-Grischuk as our model) Black's king is only going to be comfortable on a3, c3, e3, or g3. Those are the four black squares on the third rank, which allow Black to set up mating threats while at the same time using the bishop to shield the king from checks from behind. It might be useful to tabulate won positions and winning procedures when Black is on each of those four squares. The Philidor study would apply to e3, and the Rychagov - Grischuk game would apply to g3. Of course, one thing that makes it tricky is that some variations involve "turning the corner," as in the Philidor study.

To "chargingking": I think that *all* chess players feel this way when it comes to pawnless endgames. The usual shortcuts we use to understand chess positions simply break down in some of these positions, and the winning procedures turn into a series of irrational-looking moves. 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.

Soapstone said...

chargingking - Welcome to Wonderland! :) You didn't think that the rabbit hole was it, did you?

qxpch - You've identified some areas that my analysis could be more complete and systematic so that it could lead to easier guidelines for our human tablebases to remember. ChessBase does not come with tablebases as far as I know. I bought the 3-4-5 man tablebases from Convekta (http://store.convekta.com). They don't always work well with Fritz as some significant lines seem missing or misevaluated if you are looking at a single repetition of the position. I highly recommend the free Shredder website (http://www.shredderchess.com/online-chess/online-databases/endgame-database.html) which I think has the 6-man tablebase also.