Monday, June 15, 2015

Practical Rook Endgames 04: The Corner Draw and the Exceptional Win

Continuing with the endgame of the previous two Practical Rook Endgames, analysis showed two interesting turns that might have been. When the basic RPvR endgame first showed on the board, my opponent had a draw with best play, but it was extremely hard for a human to find. One one hand, the practicality of this lesson could be questioned, but the underlying subtleties are valuable for a complete understanding of this deceptively difficult endgame.

After 56.Rxa3

56...Rd6!= Not knowing the Rule of Five, I felt that cutting off the king as far away from my pawn seemed correct.

After 56...Rd6, White to find one move and draw

If White offers a rook trade so that the White King can blockade the pawn, one can calculate that Black wins. 57.Rd3?

57...Rxd3 58.Kxd3

58...Kf6! 59.Ke4 Kg5! 60.Kf3 Kf5 and with the opposition, Black can queen his pawn in for the win.

After 56...Rd6, White to find one move and draw

So how can White draw? Shredder tablebases are invaluable for finding hidden gems in these endgames. The title of this post gives the answer away. 57.Ra1!! draws. Why should this be? Checking distance is critical for frontal draws, which is the correct defense to fight the king and pawn. Since the rook trade loses, White might as well get checking distance. It turns out that in a way similar to zugzwang, Black cannot improve his position because. 57...f5 58.Rd1 draws! 58...Rxd1 59.Kxd1 Kf6 60.Ke2 Kg5 61.Kf3 and White gains the opposition. Black can also try tricking White with 57...Rd8. Now 58.Rd1? loses to 58...Rxd1 59.Kxd1 just like the variation above when Black walks his king in front of his pawn to win the opposition. Only waiting moves like Kc3, Rb1, Re1, Rf1, Rg1, and Rh1 hold the draw using the frontal check defense. The White Rook stays at f1 and checks the Black King whenever it is on the g- or e-file, back to threaten the pawn when the king goes to the h-file. If Black tries to stabilize the pawn using the spread offense or the screen pass, White needs to know that his king belongs between c3 and c4, as this fake rush is crucial to defeating both strategies. 58.Rf1 Ke6 59.Re1+! Kf6 60.Kc3!=.

In the actual game, my opponent played 57.Re3+

...leading to tablebase wins. Surprisingly, Black can play a version of the spread offense with his pawn on the third rank. This time, the pawn seems like a quarterback with almost no pass pressure, and the rook and the king are downfield receivers. 57...Kf6! 58.Rf3+ Kg6! In the actual game, we continued 59.Rf1 f5 60.Kc3 Kg5 61.Rg1+ Kh4 to arrive at the starting position for Practical Rook Endgames 02 and 03. But here I want to explore the mysteries of 59.Rg3+ Kh5 60.Rf3 f6

After 60...f6

According to the Rule of Five, Black does not have the conditions to win this endgame (pawn on 3rd + 2 cutoff files = 5 which is not greater than 5). However, the tablebases beg to differ. Black gets his checking distance 61.Rf1 Kg4 62.Rg1+ Kf3! 63.Rf1+ Ke2 64.Rf5 Ke3 65.Rf1 Rd2+ 66.Kc3 Rf2

Black should win since he controls all the queening squares and can establish the Lucena in short order. It's probably time to discard the Rule of Five as a useful endgame rule.

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