Wednesday, June 17, 2015

Endgame Caveat #7: Two Rules Don't Substitute for Actual Calculation

I have had a lot of good luck lately. I played two three-game matches against average rating 2112 players and beat each player by a convincing score of 2.5-0.5 for a 6-game performance rating of 2379. My second-to-last tournament game was a peculiar one, especially the ending. Both of us thought that I had won and I accepted his resignation with relief. But when I went home and had Stockfish show me the unseen, it revealed that my opponent resigned in a drawn position.

My opponent had been close to winning at several points in the game. Disappointment when his expectation changed from win to a draw contributed to the downward trend and helped cause him to misevaluate. Also, my 58th move was probably surprising enough to be a psychological blow. Ultimately, laziness on both our parts caused us to misapply the endgame rules of thumb and blind us to the truth of the position. As I stated in the first Endgame Caveat, this series is not meant to teach dogmatic rules, but mostly show how caveats, or exceptions, make these rules hazardous.

After 56...h4-h3

Having sacced my own rook for one of White's passers at c7, I have been trying to for the last 6 moves to create enough trouble with my f- and h-pawns to at least draw. To that end, my Black King has been trying to muscle the White King away from blockading a pawn by staying toward the center on the f-file. Now I have two pawns on the 6th rank. The endgame after the rook sacrifices for the h-pawn and the White King captures the f-pawn seems to be drawn unless White can capture the f-pawn and get a 4-step lead on the Black King. Two rules of thumb are coming into play. #1) It is often said that "Two connected pawns on the sixth rank beat a lone rook." I am hoping that with my king's help, two disconnected pawns on the sixth or seventh can beat the rook. #2) The Rule of the Square, which is probably the first endgame rule taught to beginners, seems to indicate that the f-pawn is currently outside the White King's range of stoppability. White played 57.Re8. After the game, my opponent thought that 57.Re4+ was a better try for a win, but concrete evaluation says no: 57...Kg3 58.Ke3! f2 59.Rf4! h2! 60.Rf8! h1=Q 61.Rg8+! Kh2 62.Rh8+ Kg1 63.Rxh1+ Kxh1 64.Kxf2=.

After 57.Re1-e8

During the game, I thought that 57.Re7 would have been better for White, but checking distance again becomes crucial, so the attempt to gain an advantage with Rxa7 loses because of insufficient checking distance in the main variations below. I am still trying not to let the White King into the blockade, so I felt that 57...h2! was the right move and it is. 57...f2 looks like it might be a viable alternative, but f2 actually loses to 58.Rf8+! Kg3 59.Ke3 h2 60.Rg8+ Kh3 61.Kxf2 and whether Black promotes to queen or knight, White's Rook will triumph. Allowing the White King to get closer to the f-pawn is anathema.

After 57...h2

Even though White has committed to checking from the back, guarding the queening squares is still a drawing option. e.g. 58.Re1 f2 59.Rf1 Kf3 60.Kd3! Kg2 61.Ke2 h1=Q 62.Rxh1 Kxh1 63.Kxf2=. His next move was 58.Rf8+.

Instead of making an automatic Kg3 move, I stopped to examine my options. My opponent was probably counting on 58...Kg3 59.Ke3 h1=Q 60.Rg8+ Kh2 61.Rh8+ Kg1 62.Rxh1+ Kxh1 63.Kxf3 which is a drawn endgame. Once I knew that, I felt that as long as it wasn't losing, 58...Kg5! was going to be my move.

After 58...Kg5!

I'm adding the exclam to Kg5 because of its psychological shock value. The move is neither singularly necessary to maintain the evaluation, nor is it winning in an objective sense, but for intangibles, it was enough of a bluff to help me tremendously. The Rook can kill the f-pawn now, but the h-pawn safely queens. It looks as if two advanced pawns DO beat a rook. 59.Rg8+

White's last move was actually necessary to save the draw. It looks as if it is helping Black get his King to attack the White Rook, but the reason Rg8+ was necessary was to put the Black King on a skewerable square and indirectly defend against a queening f-pawn. Notice that if White had moved his Rook to e7 on move 57, this crucial skewer possibility would be gone and White would be lost. Continuing the idea of not being skewered against the h-pawn, I played 59...Kf6. At some point here or in previous moves, I had grabbed my captured Black Queen from his side of the board, ready to queen my pawn. This also may have added to the psychological pressure.

Here my opponent offered his hand and resigned??? Out of sheer stubbornness and not giving up, he might have just played on and then the additional moves may have revealed his drawing path. The exclams show all moves are necessary for both sides to draw: 60.Rh8! f2! 61.Ke3! Kg7! 62.Kxf2! Kxh8! 63.Kg2! and the game is drawn. If Black queens either pawn, the Rook can kill the new queen where it stands and be in position to blockade the other pawn, meaning White wins. White had to let his Rook die on h8 to buy time for his King to catch both pawns. In contradiction to the two Rules, the White King should have caught the f-pawn even though it was outside the square and two pawns shouldn't have beaten the rook even though they might have both gotten to the seventh rank. Here are diagrams of the drawing variation:

After 60.Rh8!

60...f2! 61.Ke3!


62.Kxf2! Kxh8! 63.Kg2!

So the game ended in a study-like draw, but my opponent resigned in a drawable position. I'm pretty sure I haven't gotten an extra half point before from someone resigning a drawn position. I have resigned before in a drawn position, so maybe this is the karmic payback. Luck has a bizarre way of distributing points and leading us on strange left turns.

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