Wednesday, April 10, 2019

An Amazing Endgame Position: A Tale of Zugzwangs

This position came up in the recent world championship match, with black to move:

White:  King on g6, Pawns on f5 and h5, Bishop on c4
Black:   King on f8, pawn on f6, Bishop on g5, Knight on d4

What makes this position so amazing is that, despite its seeming simplicity, none of the top players of the world were able to figure out the wining move!  And, what's even more amazing is that even after being shown the winning move, found by a computer, none of the top players in the world could see why the move won!!

Before delving into the wining continuation, I would offer some observations about the position.

1)  World champion Magnus Carlsen, playing white, has sacrificed a piece in an effort to relieve the pressure he was facing.  Carlsen candidly admitted after the game that he didn't know if this was the best move, but he just didn't know what else to do. Hence, white is now playing for a draw, and black for a win.

2)  It is apparent that white must keep his bishop on the a2-g8 diagonal, in order to prevent the black king from getting to the h8 corner. If black's king does get to the h8 corner, then his knight will check the white king from a dark square, forcing the king to f7, after which the black king leisurely walks up the h-file to capture the white pawn on h5.

3)  White's passed pawn on h5 seems like a threat, but black can stop it.  For example, if it was white to move in the starting position, play could go 1 h6 Nf3 2 h7 Ne5+ 3 Kh5 Kg7 and the black king stops the pawn.

4)  What the foregoing line illustrates is the advantage knights have in close positions like this. There is a common belief that bishops are better than knights, but when the pawns are all on one side of the board in an endgame, especially when some are locked up and therefore immobile as here, the knight is hugely better.

An analogy could be made to the rule of thumb that a knife is better than a gun when the adversaries are within 21 feet of each other, as illustrated in a memorable "Criminal Minds" episode called "The Tribe", in which the BAU team visits a Native American reservation in New Mexico.

Based on the foregoing, it might be supposed that the position is a draw. Indeed, that is what happened in the actual game, which continued 1...Nf3 2 Kh7! Ne5 3 Bb3 Ng4 4 Bc4 Ne3 5 Bd3 Ng4 6 Bc4 Nh6 7 Kg6 Ke7 8 Bb3 Kd6 9 Bc2 Ke5 10 Bd3 Kf4 11 Bc2 Ng4 12 Bb3 Ne3 13 h6 Bxh6 Drawn

But the computer came up with a move so totally counter-intuitive that no human ever considered it. (I will highlight the winning line.) The winning move is 1...Bh4!! All the top players, match participants and spectators alike, thought white could hold the draw by responding 2 Bd5. However, what the computer has seen is that black can win by playing his knight to e2, instead of to f3. Hence, black makes a waiting move, forcing the white bishop to unguard the e2 square.

After 1...Bh4 2 Bd5, play continues 2...Ne2!, and now 3 Bf3 loses to the amazing Ng1!!, another move which no human would ever even consider playing, as it seemingly traps his knight on g1. After 4 Bg4 Kg8 the win becomes obvious, as white will soon run out of moves and have to free the knight, which can then head to e5, freeing the black king.

The top human players thought 4 Bd5 would still hold (instead of Bg4), but this falls to 4...Bg5! 5 Kh7! (Avoiding 5 h6 Ne2 6 h7 Nf4mate) Ne2! 6 Bf3 Ng3 7 Bg4 (Not 7 Kg6 Kg8) Kf7 8 Kh8! 

And now it looks like white can draw by simply moving his king between h7 and h8. However, black has a diabolically clever plan to reposition his bishop to f8, creating a mating net in the h8 corner.

Bd2! 9 Kh7 Bb4! 10 Kh8 Bf8! 11 Kh7 Ne4! and white is soon mated!  Black has the classical bishop + knight mate against a bare king, as white's pawns and bishop are relegated to irrelevancy.

You might suppose that white could try 10 h6 to thwart black's mating net, the idea being that white can now drive the black king away from f7 by delivering a bishop check on h5 whenever white moves his knight to e4.  However, black plays 10...Bf8, putting white in zugzwang. If white moves his king, he loses the pawn on h6; and if he moves his bishop to any square but h3, he loses his pawn on f5. Consequently, play continues 11 Bh3 Ne4 11 Bg4 Ng5+ 12 Kh8 Bxh6 13 Bh5+ Kf8 followed by 14...Bg7mate. Black's domination of the dark squares at the end is a wonder to behold!