Saturday, November 3, 2007

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

1 comment:

Wahrheit said...

Thanks, that was very useful and instructive--I spent just a little time and now feel like I know what to aim for. Whether I'll exactly remember the 79. ...Rg7!! maneuver or not, I don't know, but it was really interesting to see the big picture.