Endgame Obsession #4 KBNvK

The ending King, Bishop and Knight versus lone King was probably one of my first endgame obsessions. I lived in a small dorm room in the middle of Chicago and owned (still own) one of the early-to-mid generation of chess computers: Radio Shack Chess Champion 2150. I think I paid $130 for it. Contrary to my hope of training with an in-house strong expert, eventual testing showed it to be closer to 1750 rating. Still, it was fun to set up openings and try to outplay the computer. I used to watch what it was thinking because computer chess was so new and I was curious how this machine "thought".

But one day, I found out that bishop and knight versus lone king was not a draw, just a difficult win under the constraints of the 50-move draw. So I started setting up positions on my trusty computerized punching bag and trying to win. I have known generally what to do and had even developed my own final phase beginning with this position:

My winning method involved moving the Bishop to the f1-h3 diagonal and shifting the Knight from e4 to f3, all the while taking care not to stalemate the Black King. The moves are 1.Ke1 Kg1 2.Bh3 Kh2 3.Bf1 Kg1 4.Nd2 Kh2 5.Kf2 Kh1 6.Bg2+ Kh2 7.Nf3#.

Last Sunday, I decided to try some internet chess and reached this position after my 55th move as Black in which I captured White's last pawn Kxe5:

So I had a chance to test myself. Over the years, I would not say that I ever learned this ending cold. And my successful but imperfect technique here pushed me to try to learn more of those subtleties that continue to elude me about this ending. With the help of the Shredder Tablebase website, I went over my game score with a fine-toothed comb and tried to figure out where I wasted moves and what the proper technique should have been.

I want to push the White King to the edge of the board by centralizing all my pieces. White wants to stay away from the light-squared corners because that's where he can be checkmated. Once I get the White King to the corner, I need to organize my pieces a certain way and maneuver to force the White King to the deadly corner.

56.Kd3! I have to execute the mate before my 105th move. Shredder says Mate in 25 which I will hereafter abbreviate like M25. Optimal would be to checkmate on move 80. 56...Nf4+ WASTE+1. 56...Nc5+ was better by one move, but I don't think I can really fault myself for some of these small differences. 57.Kc3! Kd5 58.Kd2 Kd4! 59.Kc2! Ne2?!

This time Shredder tells me I have wasted 2 moves: WASTE+2. Better was 59.Nd3! with the Knight and Bishop eventually taking away c2 and e2. 60. Kb2?! WASTE-1 (White helps Black closer to mate by one tempo). 60.Kd2 resists one move longer. 60...Kc4?! WASTE+1. 60...Kd3 was better by one move.

Notice that the Bishop is on one of the long diagonals pointing into the non-mating corner and dividing the board into two triangular regions. If the White King gets chased by the Black King to the smaller red triangle, then he's that much closer to getting pushed to the mating corner.

61.Kc2! Nd4+ 62.Kb2! Bg6 63.Ka2! Kc3 (This is where the Black King likes to be.) 64.Ka3?! WASTE-5

White does well to choose the corner with 64.Ka1! instead of the game allowing 64...Bf7 65.Ka4 Bb3+! 66.Ka5 (66.Ka3 Nb5#) Kc4 67.Kb6 looks like he's breaking free of the walls, but 67...Ba4 sets up a new wall from a4-e8 that with the Black King's help can contain the White King in the small triangle a5-a8-d8.

But here my stereotyped thinking hurt me a little. I knew of the idea of attacking the corner square with the knight to dig the King out of the spider hole. And then the follow-up is to attack the next square with the bishop. But the knight isn't in place yet, so I confused myself here. More properly following my slightly suboptimal strategy would have been to play 64...Nb3 and if 64.Ka2 Bf5 (biding time) 65.Ka3 and only then 65...Bb1 66.Ka4.

Unfortunately, my confusion lasts for the next seven moves during which time my opponent offered a draw, but I soldiered on until move 72 began to look familiar again. 64...Bb1?! WASTE+2 65.Ka4 Kc4?! WASTE+2 66.Ka3! Kc3! 67.Ka4 Bc2+?! WASTE+2 68.Ka3! Nb3?! WASTE+3 69.Ka2! Nc5?! WASTE+2 70.Ka1 Nd3?! WASTE+2 71.Ka2 Nb4+ 72.Ka1! Bb3! 73.Kb1 M20. After 17 moves, I've only moved five moves closer to mate. But I'm familiar enough with this position to make steady progress from here.

Here begins the maneuver to dig White's King out of the non-mating corner. 73...Nc2! If the Knight arrived here by checking the King on a1, the Bishop can waste time by simply moving along the a2-g8 diagonal. 74.Kc1 Ba2! 75.Kd1 Nd4!

Notice that by centralizing, the knight grabs more squares, particularly the e2 square where it currently stops the White King from taking a shortcut toward the safe h8 corner. e2 is also where the knight may drop in to help herd the White King toward its doom at h1. The Black Knight will make a W pattern from where it began on b4-c2-d4-e2-f4. 76.Kc1 WASTE-3. From the above diagram, White has one of his best chances to break for freedom. Black must know the technique of stopping the fugitive with some well-timed moves. This maneuver is one of the prettiest in the mate and helps illustrate the cooperation of Bishop and Knight. 76.Ke1 Kd3 77.Kf2 starts to see daylight above the first rank. 77...Ne2!

A friend of mine called this the lock position. The Black King guards the green squares at e2, e3, and e4 while the Black Knight guards the seemingly porous red squares at g3 and f4. The White King needs to find a path to h8 via f3-g4 or g2-h3-h4. Luckily for Black, Be6 cuts off all these routes, keeping the fugitive near the deadly h1 square.

Back to the game after 76.Kc1

76...Ne2+ 77.Kd1 Kd3 78.Ke1 Bb3?! WASTE+2.

Here I mixed up the more crucial prophylaxis of 78...Ke3! with the timewasting 78...Bb3. If the White King goes back to d1, the Bishop can check him out of there. 79.Kf2 Bd5! Helping cover f3 ad g2 while the Knight covers g3 and f4. The White King either has to go g1-h2-h3 or back toward e1-d1. 80.Ke1 Ke3! 81.Kd1 Bb3+ 82.Ke1

Black's final tasks involve getting the Bishop to the d1-h5 diagonal and squeezing White down to two squares at h1 and h2. Unfortunately, many of my misconceptions still lead to inefficient moves. 82...Nf4! 83.Kf1 Bd1 84.Ke1 Bg4 85.Kf1

Here I went awry again by trying to post my pieces according to my formation at the top of this post. The game finished with 85...Nd5?! WASTE+6 86.Ke1?! WASTE-4 Nc3 WASTE+4 87.Kf1 Kd2 88.Kf2?! WASTE-1 Ne4+! 89.Kg2 Ke2 (my formation) 90.Kh2?! WASTE-2 Kf2 91.Kh1 Bh3?! WASTE+1 92.Kh2 Bf1?! WASTE+1 93.Kh1 Nd2 94.Kh2 Nf3+ 95.Kh1 Bg2# I mated with ten moves to spare and a net wastage of fifteen moves. But my opponent chose continuations totaling about 16 moves where he helped me toward mate. Without those, I might have overstepped the 50-move draw.

The most efficient path I know now from the above diagram is: 85...Be2+! It's okay and actually desirable to check the king here. The Knight hiding at the Black King's shoulder is in the right spot to deliver checkmate if the White King chooses 86.Ke1 Nd3#. 86.Kg1 Kf3 The King takes a drunken path to g3. 87.Kh2 Kf2 88.Kh1 Kg3 89.Kg1 Nh3+ 90.Kh1 Bf3#

Although the bishop check is a little harder to remember, the aesthetics of this final position and the fact that it is fastest persuades me to memorize this final method as the way to go.

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.

Endgame Obsession #2 RaPvB

I became interested in this ending while watching the last game to finish from the 2005 Western States Open. Then-IM (now GM) Jesse Kraai was pressing against GM Alexander Stripunsky. A large crowd of about a hundred players were watching the game, aided by a demo board. I whispered to a 2300 player sitting near me, "Is there a win?" He nodded without elaborating. IM John Donaldson walked by and I heard him say, "It doesn't look like he knows the method." The way he said "method" got me hooked. There's a METHOD? What METHOD? The game ended with Kraai being unable to find the method over the board, running out of time, and conceding a draw. Eventually, I investigated this myself and found a complicated ending equal to my tendency to obsess. White must not advance the Pawn too quickly because Black can successfully blockade it at a6 under many circumstances. The White King ends up having to use a vacant a5 square in the winning method. Also note that if the pawn were gone, Black's King is in the proper corner to stalemate itself in a Rook versus Bishop drawn endgame.

(16) Kraai,J (2497) - Stripunsky,A (2629) [D13]

Western States Open Reno, NV (6.4), 16.10.2005

1.Nf3 d5 2.c4 c6 3.cxd5 cxd5 4.d4 Nc6 5.Nc3 Nf6 6.Bf4 Nh5 7.Bd2 g6 8.Qb3 e6 9.e3 Bg7 10.Be2 0-0 11.0-0 b6 12.Rfc1 Bb7 13.a4 Rb8 14.Rc2 Nf6 15.Rac1 Ne4 16.Be1 Nd6 17.Nb5 Rc8 18.Ne5 Nxe5 19.Nxd6 Qxd6 20.Bb4 Qb8 21.Bxf8 Rxf8 22.dxe5 Bxe5 23.h3 Rd8 24.Bb5 d4 25.exd4 Bxd4 26.Bc6 Bxc6 27.Rxc6 Qf4 28.Qf3 Qxf3 29.gxf3 Bxb2 30.Rc8 Rxc8 31.Rxc8+ Kg7 32.Rc7 a5 33.f4 Ba3 34.Kg2 Bd6 35.Rb7 Bc5 36.Kg3 h6 37.h4 Kf6 38.Kf3 Bd4 39.Rd7 e5 40.fxe5+ Bxe5 41.Ke4 h5 42.Rb7 Bc3 43.Rxb6+ Ke7 44.f4 Kf8 45.f5 Kg7 46.Ra6 f6 47.Ra7+ Kh6 48.Rf7 Be5 49.Rf8 Kg7 50.Ra8 Bc3 51.Rb8 Be1 52.Rb5 Kh6 53.Kf3 gxf5 54.Ke2 Bb4 55.Rxf5 Kg6 56.Rf1 Be7 57.Kd3 f5 58.Rh1 Bc5 59.Rc1 Bf2 60.Rc6+ Kf7 61.Ra6 Bxh4 62.Rxa5 Ke6 63.Ra6+ Kd7 64.Rh6 Kc7 65.Rxh5 Bg3 66.Rxf5+- Kb7 67.Rf6 Ka8 68.Rf7 I chose to deviate here from the game continuation in order to place the Bishop on its best diagonal, g1-a7. 68...Bh2 [ The actual game continued 68...Be5 69.Kc4 Bd6 70.Kb5 Be5 71.Ka6 Bg3 72.Ra7+ ( 72.a5 See method 2B below 72...Kb8 ( 72...Be5 73.Rf8+ Bb8 74.Kb5 Kb7 75.a6+ Ka8 76.Rg8 Ka7 77.Rg7+ Ka8 78.Kb6 Be5 79.Rd7 Bf4 80.a7 Be3+ 81.Ka6 Bb6 82.Re7 Bd8 83.Rg7 Bc7 84.Rg8+ Bb8 85.Rxb8#) 73.Kb6) 72...Kb8 73.Rg7 Bf2 74.Rg8+ Kc7 75.Rg2 Bd4 76.Rg4 Be3 77.Rb4 Kc8 78.Rb5 Kc7 79.Rb1 Kc8 80.Rb7 Bf2 81.Rb5 Kc7 82.Rb1 Be3 83.Rb2 Kc8 84.Rb3 Bf2 85.Rb5 Kc7 Draw eventually agreed after a time scramble.] 69.Kc4 Bg1 Black's best defense involves keeping his king out of checkmate threats, e.g. when White has his king on the a-file, his own king is on the c-file and vice versa. The Bishop is best placed on the g1-a7 diagonal to prevent White's usage of Kb6 and eventually to stop an advancing Pa7. SETUP: White aims for Ka6 and then Rb7+ to force Black to choose his last stand at a8 or c8.70.Kb5 Bd4 71.Ka6 Kb8 72.Rb7+ Setup complete. Black's main resource in this ending is that the a-pawn can either be blocked by the Black King or the White King. When the White King goes to a6, the Black King's best defense is to go to c8. When the White King crosses to the c-file, the Black King does well to cross over to the a-file. If Black allows White to press the vertical opposition mate threats will appear. White's strategy consists of three plans: OPERATION CROSS OVER: moving the White King from the a-file to the c-file without allowing the Black King to cross over to the a-file. This typically involves a maneuver such as Ka6-a5-b4. OPERATION CUT OFF: pushing the Black King to the d-file and cutting him off with the White Rook on the c-file, perhaps with lateral opposition from the White King on the a-file. This usually happens when the Black King moves to c6. And OPERATION PUSH PAWN: If the Black Bishop can be prevented from getting onto the g1-a7 diagonal for a while, White uses both the Rook and the King to escort the pawn to a7. This typically happens when the Bishop goes to the edge of the board. When the pawn reaches a7, the Bishop must not be allowed to sacrifice itself for stalemate.

PLAN B [ 72...Ka8 PLAN B, PHASE 1: White's job is a little easier in this variation. The overall plan is to advance the a-pawn to a7 while threatening mate on the back rank, ultimately winning a pinned bishop at b8. The position of the kings facing each other in the corner and the pawn on the 4th are important to MEMORIZE with the rook anywhere safe on the seventh and the bishop anywhere on the g1-a7 diagonal. This is the moment for PHASE 1: Advance The Pawn to the 5th. 73.a5! Bf2 PLAN B, PHASE 2: Force the bishop to b8. 74.Rf7 Bc5! This move offers a bit more resistance because Rc7 is a little too close to the King to carry through all the mate threats. Nevertheless, wherever the bishop goes, the rook travels laterally to hit it and threaten checkmate. The goal is to pin the bishop at b8 from a kingside square e8-h8. ( 74...Bg3 75.Kb6 Bh2 76.Rg7 Be5 77.Ra7+ Kb8 78.Rd7) 75.Rc7 Bd6 This is the only move that prevents mate. Notice that from d6, the Bishop does not have enough checking distance to deter a White King at b6. 76.Rg7 This square and the e7 square are good spots for the White Rook because they are far away from the Black King and they threatens to move to eighth rank squares which cannot be controlled by the Black Bishop. 76...Bb8 ( 76...Kb8 77.Kb6!; 76...Be5 77.Rg8+ Bb8 78.Kb5!) 77.Re7 The Rook MUST arrive on the eighth rank with check. 77...Bd6 78.Re8+ Bb8 79.Kb5! This stalemate-avoiding move is one that White must remember. Again Black has two paths, but they soon converge. PLAN B, PHASE 3: Use waiting moves (Re8 or Rg8) to get the Black King to come out on the 7th, check it back with the rook (Re7+ or Rg7+) and then advance Pa6. Use a similar maneuver to get the King on b6. Beware of stalemate always. 79...Kb7 ( 79...Ka7 80.Re7+ Ka8 81.a6 transposes to the 79...Kb7 line.) 80.Re7+ ( 80.a6+ also works. 80...Ka8 81.Rg8 Ka7 82.Rg7+ Ka8 83.Kb6) 80...Ka8 ( 80...Kc8 81.a6 Kd8 82.a7+-) 81.a6 Ba7 82.Re8+ Bb8 83.Rg8 Ka7 84.Rg7+ Ka8 85.Kb6 Be5 86.Rd7 guarding against Bishop check from d4. 86...Bg3 87.a7 Bf2+ 88.Ka6 Bb6 Watch out for stalemate! 89.Rg7 Bd8 Watch out for stalemate! The Rook MUST arrive on the eighth with check. 90.Rg6 Bf6 Watch out for stalemate! 91.Rg8+ Bd8 92.Rxd8#]

PLAN A: 72...Kc8 The tablebase shows that not only does this resist six moves longer, but it is also quite a bit more complicated than Ka8. PLAN A, PHASE 1: Set up OPERATION CROSS OVER: getting the White King to the c-file without allowing the Black King to get back to the a-file. 73.Rb5 With the Black King on c8, White starts by setting up Operation Cross Over with two paths. If Black commits to a Bishop move, White tries for the two branches of the Cross Over beginning with Ka5. If Black plays Kc7, then the Rook has to play to Rb3 to set up a king feint at Ka5-b4-c4.73...Kc7 This resists more stubbornly than Bishop moves. PLAN A, PHASE 2: If the Black King comes to c7, place the White Rook at g3, hitting the Bishop first if it's on f2. With the Black King cutting off one of the Cross Over pathways through b6, White has to do some dancing with the Rook against the Bishop. [ 73...Be3 74.Ka5 Bd2+ ( If Black doesn't prevent Operation Cross Over, then the win becomes fairly easy. 74...Kc7 75.Kb4 Bb6 76.a5 Ba7 77.a6 Bb6 Even if Black establishes the blockade of b6, as long as the White Rook stays on the b-file, the Black King cannot make it back to the a-file. 78.Kc4 Kc6 79.Rb1 Kc7 ( 79...Be3 80.Rb7 Bb6 81.Rh7 Be3 82.a7+-) 80.Kd5 Black would have a draw if his king were on a7 right now. 80...Be3 81.Rb7+ Kc8 82.Kc6 Bd4 83.a7+-) 75.Kb6 Kb8 76.Re5 guarding against Be3+ while threatening Re8#. 76...Kc8 77.a5 ( 77.Re8+ Kd7 78.Re4 Bg5 79.Rc4 Bd8+ 80.Kb5) 77...Bf4] 74.Rb3 If the Bishop is on d4, e3, or g1, put the rook on b3. If the Bishop is on f2, flush it to another square by moving Rb2 before moving Rb3. 74...Bf2 [ 74...Kc6? Black shouldn't volunteer for horizontal opposition because White then can start Operation Cut Off. The Rook chases the Bishop in order to quickly get to the c-file. 75.Rd3 Bf6 76.Rd2 Kc7 ( 76...Kc5 77.a5 Kb4 78.Rd5 should be an easy win.) 77.Ka7 Kc6 78.Rc2+ should be an easy win.; 74...Kc8] 75.Ka5 Here, the path diverges in several directions. If the Bishop goes to a7 or g1, White responds with Rb5 and tunneling his King through b4. If the Black King comes forward again, White plays Rb5. 75...Be1+ This causes a fumbled Operation Cross Over where Black's King jumps back to the opposite side. However, the Bishop becomes trapped in a sense such that it cannot get back to the g1-a7 diagonal for the next eight moves. [ 75...Bg1?! 76.Rb5 Be3 77.Kb4 achieves Operation Cross Over.; 75...Bd4?! 76.Kb4 Kb6?? 77.Kc4+ This discovery wins the Bishop.; 75...Kc8 76.Rb5 Ba7 ( 76...Be1+ 77.Kb6 Kb8 78.Rf5 guarding against the check on f2. 78...Kc8 79.Rf8+ Kd7 80.a5 Bb4 81.Rb8 Bd6 82.Rb7+ Ke6 83.a6+-) ; 75...Ba7 76.Rb5 Bd4 77.Kb4 achieves Operation Cross Over.; 75...Kc6 76.Rb5 This looks like White is just repeating moves, but now that Black has come forward, he is vulnerable to Operation Cut Off. 76...Bc5 Stops Kb4, Operation Cross Over. However, the Black King is stuck at c6 for a couple moves, allowing White to switch to Operation Cut Off. a) 76...Be1+ 77.Ka6 Kc7 78.Rb7+! While the Bishop is on the lame e1-a5 diagonal, White can make maneuvers such as Ka6-b6-c6. 78...Kc6 (a) 78...Kc8 79.Kb6! Ba5+ 80.Kc6 achieves Operation Cross Over.) 79.Rb1 Bd2 80.Rb2 Be1 81.Rc2+ achieves Operation Cut Off.; b) 76...Kc7 77.Kb4; 77.Ka6 taking the lateral opposition. 77...Be3 78.Rb3 Bd4 ( 78...Bd2 79.Rb2 Be1 80.Rc2+ achieves Operation Cut Off.) 79.Rd3 Bg7 ( 79...Bf6 80.Rd2 Kc7 81.Ka7!) 80.Rd2 Kc7 81.Ka7 Kc6 82.Rc2+ achieves Operation Cut Off.] 76.Kb5 Kb7 77.Rf3! The Rook at f3 controls so many squares that the Black Bishop requires at least four moves to get back to the g1-a7 diagonal. Meanwhile, White will try to push the a-pawn to a7.77...Bd2 78.a5 Bh6 79.a6+ Here the path diverges when Black chooses a8 or b8. If Ka8, then the next move is Kb6. If Bg7, then the response is Rh3. After either line, White's plan is basically Rd3, Rd7, Kb6, and a7. 79...Kb8! This route has a couple devious stalemate traps. White basically moves over to h3 to tag the Bishop before returning to the route Rd3-Rd7. [ 79...Ka8 White basically moves Kb6, followed by Rd3-d7 80.Kb6 Bg7 81.Rd3! denying the Bishop its d4 destination for at least another three moves. 81...Bf6 ( 81...Be5 82.Rd7) 82.Rd7 Bg5 83.a7 Be3+ 84.Ka6 Bb6 85.Re7 Bd8 86.Rg7 Bc7 87.Rg8+ Bb8 88.Rxb8#] 80.Rh3 Bg7 [ 80...Bc1 81.Kb6 Bb2 82.Rd3 Kc8 ( 82...Bf6 83.a7+ Ka8 84.Rd7 Bd4+ 85.Ka6!+- (85.Rxd4?? stalemate)) 83.Kc6 ( 83.a7 Bd4+ 84.Ka6 Bxa7 85.Kxa7+-) 83...Kb8 84.Rb3+ Ka7 85.Rxb2+-] 81.Rd3 denying the Bishop its d4 outpost for another three moves. [ 81.Rh7? Bd4= White can no longer put his King and Rook in contact with h7.] 81...Bf6 82.Rd7 Kc8 83.Rf7 Bd4 84.a7 Bxa7 85.Rxa7+-

Endgame Obsession #1 RdPvB

Since Wahrheit, who comprises half my audience asked for it, here is the game that started my Endgame Obsession. It was about three years ago, a week before 10th World Champion Boris Spassky made his first appearance at the Western States Open. I was playing a tournament game against a friend who knows quite a bit about the endgame. The game itself was quite interesting through the opening and middlegame, but the endgame turned into a complex struggle down to the last four pieces. I ended up with a Rook versus Bishop draw, and the postgame analysis seemed to indicate that I had nothing more than a draw, but of course Fritz had other things to say. I had recently discovered endgame tablebases and had purchased the 5-man Nalimov tablebase DVD along with Comprehensive Chess Endings from Convekta. My research below would never have been possible without the tablebases. The tablebase software doesn’t always work perfectly with Fritz because Fritz occasionally cuts out good lines because they involve a single repetition of a position. Since then, I have discovered that the web-based Shredder tablebase is one of the best ones around since it has fast response and includes the 6-man tablebases. Basically, my method for understanding this ending and other ones like it involve going up and down the variations in the tablebase to understand why some moves get closer to mate and why some don’t. Incidentally, about ten months later, I ended up on the worse side of a Bishop versus Rook ending and I could have tested my opponent’s knowledge of this, but I didn’t realize what I had before me, so I lost.

By popular demand, here is Rook and King Pawn versus Bishop. Apologies for the extreme length and complexity, but how else can I show you the depth of my insanity? If you actually like this stuff, email me and I can send the ChessBase file so that you can run through the tangled web of variations on your own computer. If you actually enjoy this over watching paint dry, please holler, and I can provide two more installments of Rook and Pawn versus Bishop before moving on to Queen versus Rook and others.

(14) Fleming,G (1754) - Hong,E (1929) [B06]

Spassky Six (6), October 7, 2004

1.e4 g6 2.d4 Bg7 3.Nc3 d6 4.Be3 a6 5.Qd2 Nc6 6.d5 Ne5 7.h3 c5 8.f4 Nd7 9.Nf3 b5 10.e5!? Qc7?! 11.e6?! fxe6 12.Ng5 Nf8 13.dxe6 Bxe6 14.Nxe6 Nxe6 15.Qd5?! Qc8!? 16.f5?! gxf5?! 17.Bd3?! Nf6 18.Qxf5 Nd4 19.Qg5 Qe6 20.0-0 Rg8 21.Rae1 Qe5 22.Rf5? Nxf5 23.Bf2 Bh6?! 24.Qxf5 Qxf5 25.Bxf5 Bf4? 26.Ne4 Be5 27.Nxc5 Bg3?! 28.Ne4 Nxe4 29.Bxe4 Bxf2+ 30.Kxf2 Ra7?! 31.Bxh7 Rg7 32.Bd3 e5 33.g4 Raf7+ 34.Ke3 Rf4 35.Rf1 Rgf7 36.Rxf4 Rxf4 37.g5? Ke7?! 38.a3 Ke6 39.Be4?! Rh4?! 40.Bb7 Rxh3+ 41.Kd2 Rh2+ 42.Kc3 a5 43.Bc8+ Kd5?! 44.g6 Kc5 45.b4+ axb4+ 46.axb4+ Kc6 47.Be6 Rg2 48.Bf7 d5 49.Kd3 Kd6 50.c3 Rg3+ 51.Kd2 d4 52.cxd4 exd4 53.Be8 Ke5 54.Bxb5 Rxg6 55.Be8 Rb6?! 56.b5 Kd5 57.Kd3 Kc5 58.Bc6 Rb8 59.Bd7 Rd8 60.Bc6 Rd6 61.Be8 Re6 62.Bd7 Re3+ 63.Kd2 Ra3 64.Bc6? This puts the Bishop where it can't check the Black King off c4.

64.Be8! [ 64.Bc6? This puts the Bishop where it can't check the Black King off c4. 64...Rb3?! ( 64...Kc4! A straightforward win that I overlooked because I was worried about the b-pawn. The White Bishop can't even hassle my King. 65.b6 ( 65.Be8 Ra2+ 66.Ke1 Kc3) 65...Ra2+ 66.Ke1 Rb2 67.b7 d3 68.Bf3 Kc3 69.Bc6 d2+ 70.Ke2 Kc2 71.Ba4+ Kc1 72.Kd3 Rxb7 73.Ke2 Rb4 74.Bd1 Re4+ 75.Kd3 Kxd1 76.Kxe4 Ke2) 65.Bd7 Rb4 66.Kd3 Rb3+ 67.Kd2 d3? This at last throws away the win. ( 67...Ra3 68.Be8 Kc4 69.Bf7+ Kxb5 transposing back to the variation under White's 64th move) 68.Be6 Ra3 69.b6 Kxb6 70.Bc4 Kc5 71.Bxd3 Kd4 72.Bg6 Ra2+ 73.Kc1 White knows that a1 is the safe corner, one in which he can stalemate himself, meaning the king in the corner with the bishop pinned right next to him. The other corner, h1, allows a winning zugzwang. 73...Kc3 74.Kb1 ( 74.Bf5?? Rf2 75.Bh3 Rh2 76.Bf1 Rh1) 74...Rg2 75.Bf5 Rf2 76.Bg6 Kb3 77.Ka1 Rf1+ 78.Bb1 If this were the lower right corner, White's light-squared bishop would be on f1 and the White king would have room to move between g1 and h1. The rook would just make lateral moves until the king went to h1 and then pounce on the bishop for checkmate. 78...Kc3 79.Ka2 Draw agreed] 64...Kc4 65.Bf7+! If White doesn't push the Black King back, his King will soon find itself staring at mate. [ 65.b6? Ra2+ 66.Kd1 Rb2 and Black will eat White's cake and keep his own.] 65...Kxb5 This ending is deceptively difficult. The Rook is already well-placed, but it must often abandon its good position to help the King. The PRIMARY OBJECTIVE is to push the pawn to d3 without losing it. In order to do that, Black must first get his King to c4 or e4 without the Bishop checking him back. We'll call Ke4 or Kc4 the SECONDARY OBJECTIVE. As the current position stands, the Bishop is well placed to snipe at the King from behind. Also, White's King is as well placed as it can be. If he moves to one side or the other, a Bishop check can no longer keep the Black King from getting to c3 or e3. The winning method involves slowly taking the backfield squares - namely a4, b5, c6, d7, e8, f7, g6, h5 - away from the Bishop. We will start with this TERTIARY OBJECTIVE. This takes a lot of fancy maneuvering where Black doesn't look like he's making progress.66.Bg6 Kc5 Step 1: King to e5. Mate in 34.67.Be8 Kd5 Notice that right now the Black King covers c6. The bishop can only check from the kingside for now. 68.Bf7+ Ke5 69.Be8 Step 1A: Stop Be8-c6, if necessary. When the King gets to e5, if the Bishop is on e8, move the Rook to c3. If the Bishop is elsewhere, start on Step 2.69...Rc3!! Step 2: Stop Bc6 and Bg6. Place the King at d5 and the Rook at g3 so that the Bishop cannot use the c6 and g6 pivot points. Mate in 31.70.Bh5 If the bishop goes kingside (f7, g6, or h5), then first secure g6 with Rg3, and then secure c6 with Kd5. If the bishop goes queenside (d7, b5, or a4), then first Kd5, followed by Rg3. 70...Rg3! 71.Be8 [ 71.Bf7? This move would stop Kd5, but allows 71...Ke4! skipping to the Secondary Objective. Note that the Bishop lacks a useful check.] 71...Kd5 72.Bb5! Bb5 and Bd7 are most testing.

Here we'll digress to take care of everything but Bb5 and later come back to the position after 72.Bb5 [ 72.Bf7+? Ke4 Black achieves the Secondary Objective; 72.Ba4? Kc4! Secondary Objective. In many of the winning positions of the Secondary Objective, the Black King has a two-square opposition toward the White Bishop, either lateral opposition or vertical opposition.; 72.Bh5? Ke4! Secondary Objective; 72.Bd7!? White begins the bishop chase right away. 72...Rg7 From this position, d7, c6, e6, and g4, are immediately unsafe for the Bishop. Bh3 and Bc8 allow Ke4 while Be8 and Ba4 allow Kc4, the Secondary Objective. Only Bf5 and Bb5 prevent Black from achieving the Secondary Objective. 73.Bf5 ( 73.Bb5 is a mirror image of the Bf5 lines. 73...Rb7 74.Be2 Rb2+ 75.Kd3 Rb3+ 76.Kd2 ( 76.Kc2 Whenever the White King chases the Rook, the usual best policy is to laterally dodge one square. 76...Ra3) 76...Ke4) 73...Rf7 74.Bc2 a) 74.Bb1 Rf2+ 75.Kd3 Kc5 76.Bc2 Rf3+ 77.Kd2 (a) 77.Ke2 Rg3) 77...Kc4 Secondary Objective. Note the Black King's opposition to the White Bishop.; b) 74.Bg6 Rf2+ 75.Kd3 Rf3+ 76.Kd2 (b) 76.Ke2 Rg3!) 76...Kc4 Secondary Objective; 74...Rf2+ 75.Kd3 Rf3+ 76.Kd2 ( 76.Ke2 Rg3) 76...Kc4 Secondary Objective]

Now back to the position after 72.Bb5! Step 3: Once the King and Rook are on their destination squares (Kd5, Rg3), if the Bishop is on b5, then prepare the bishop chase with a slight rook adjustment. 72...Rh3!! 73.Be8 Step 4: Chase the bishop toward its king at the front of the pawn. [ 73.Bd7?! Rh7 74.Bb5 Rb7 and ( 74.Bf5 Rb7) as in the lines above after 72.Bd7.; 73.Ba4? Kc4!] 73...Rh8 74.Bf7+ Ke5 If the King gets checked off d5 and he can't safely get to c4 or e4, then e5 is usually the best place to be. 75.Bg6 Rg8 76.Bc2 Step 5: Use checks to get the Rook back to the 6th rank and then prepare the King to get in opposition to the bishop. [ 76.Bf7? Rg2+ 77.Kd3 Rg3+ 78.Kd2 Ke4 79.Be8 Rg2+; 76.Bb1!? Step 5A: If the Bishop retreats to b1, then check the position of the Black King. If he's already at d5, then use the maneuver 76...Rg2+ 77.Kd3 Kc5. If the Black King is still at e5, the method of Rg2+, Kd5 fails to Ba2+!! and the Bishop is immune because Rxa2 is stalemate. Kf4 is the short unorthodox way to achieve the primary objective. The Rook will chase the bishop to b1 and sacrifice for the Bishop, leaving Black with a winning pawn ending. 76...Rg2+ 77.Kd3 Rg3+ ( 77...Kd5?! 78.Ba2+!! Ke5 ( 78...Rxa2?? stalemate) ) 78.Kd2 78...Kf4!! 79.Bh7 Rg7 80.Bb1 Rg2+ 81.Kd3 Rb2!! 82.Bc2 Rxc2 83.Kxc2 Ke3! 84.Kd1 Kd3! 85.Ke1 Kc2-+] 76...Rg2+ 77.Kd3 Rg3+ 78.Kd2 Kd5 79.Bf5 Step 6: If the Bishop moves to f5, use Rg7 to make it go back. This is one more tricky zugzwang that is hard to find. 79...Rg7!! Now the ending branches into one nearly trivial variation (80.Bh3 Ke4 Secondary Objective) and three major variations. Variation A) 80.Bb1 Step 6A: If the Bishop goes behind its King, check the King forward and use its blockage of the Bishop's mobility for a zugzwang that forces the bishop forward so that your king can reach opposition to it. 80...Rg2+ 81.Kd3 Kc5 82.Bc2 Rg3+ 83.Kd2 Kc4 Secondary Objective

Variation B) 80.Bc2 Step 6B: Use checks to get the Rook back to the sixth rank and move your King into vertical opposition to the Bishop.80...Rg2+ 81.Kd3 Rg3+ 82.Kd2 Kc4 Secondary Objective

Variation C) 80.Kd3 Step 6C: If the White King comes forward, you may need one last zugzwang move. 80...Ke5! 81.Bc8 81...Ra7!! 82.Bg4 [82.Kd2 Ke4! 83.Be6 d3 84.Bc4 Ra3 Primary Objective 82...Ra3+ 83.Kd2 Ke4 Secondary Objective

Now back to the moves we actually played.64...Rb3?! [ 64...Kc4! A straightforward win that I overlooked because I was worried about the b-pawn. The White Bishop can't even hassle my King. 65.b6 ( 65.Be8 Ra2+ 66.Ke1 Kc3) 65...Ra2+ 66.Ke1 Rb2 67.b7 d3 68.Bf3 Kc3 69.Bc6 d2+ 70.Ke2 Kc2 71.Ba4+ Kc1 72.Kd3 Rxb7 73.Ke2 Rb4 74.Bd1 Re4+ 75.Kd3 Kxd1 76.Kxe4 Ke2] 65.Bd7 Rb4 66.Kd3 Rb3+ 67.Kd2 d3? This at last throws away the win. [ 67...Ra3 68.Be8 Kc4 69.Bf7+ Kxb5 transposing back to the variation under White's 64th move] 68.Be6 Ra3 69.b6 Kxb6 70.Bc4 Kc5 71.Bxd3 Kd4 72.Bg6 Ra2+ 73.Kc1 White knows that a1 is the safe corner, one in which he can stalemate himself, meaning the king in the corner with the bishop pinned right next to him. The other corner, h1, allows a winning zugzwang. 73...Kc3 74.Kb1 [ 74.Bf5?? Rf2 75.Bh3 Rh2 76.Bf1 Rh1] 74...Rg2 75.Bf5 Rf2 76.Bg6 Kb3 77.Ka1 Rf1+ 78.Bb1 If this were the lower right corner, White's light-squared bishop would be on f1 and the White king would have room to move between g1 and h1. The rook would just make lateral moves until the king went to h1 and then pounce on the bishop for checkmate. 78...Kc3 79.Ka2 Draw agreed 1/2-1/2