Monday, August 28, 2006

Remarkable endgame from CTS

Today I failed a problem on CTS and as a result spent some time analyzing an endgame. At first I was convinced that my move, while not as crushing as the actual solution, was easily winning. While trying to win the position against a computer program I nearly convinced myself it was a draw until I found a rather neat resource. Since I don't want to forget the position, I'm posting it here where there will be a record of it.

Here is the starting postition, white to play:

Now that your 3 seconds are over, the real solution is 1. Bd6! There are two important motifs here, the pinned rook on e7 and the mating attack if Rxd6.

The move I played was 1. Nh7+. This leads to 1. ... Ke8 (Kg8 Rxe7) 2. Rxe7+ Kxe7 3. Bf6+ Kd7 4. Bxd8 Kxd8 (D)

In my few seconds of thinking time during a CTS problem I was sure that this was winning. However, when I tried to play it out against the computer, I didn't manage more than a draw.

I kept hunting for the right way to play this and eventually found a cute resource for white. One of the main problems for white is that black can try to trade off the kingside pawns and leave white with no mating material. Black tries to bring the king to e6 and play f6 and g5. For example, if White starts out trying to reactivate his knight with 5. Nf6 Black will play 5. ... a5 and now the king is too far away so the knight must chase down the pawn and play might go like this: 6. Nd5 a4 7. Kf3 a3 8. Nc3 Kd7 and black will play f6 next. (Note that it doesn't help white to play 7. f5 trying to get his king over quicker.)

Another way for white to fail to win this position is to leave the knight on h7 to prevent the f6 push: 5. Kf3 a5 6. Ke3 a4 7. Kd4 Ke7 8. Kc4 Ke6 and now the black king penetrates to f5 and takes the f4 pawn.

So far we have learned that (a) if we use the knight to stop the a-pawn, the king will be too slow to prevent the black king from supporting the f6 push and (b) if we use the king to stop the a-pawn, the knight can not be contented to stop the f6 push sitting on h7 because the king will come to f5 and take the f4 pawn. But it turns out the knight can defend the kingside all by itself! So here is the solution:

5. Kf3 a5 6. Ke3 a4 7. Kd4 Ke7 8. Nf6! Ke6 9. Ng4!! a3 10. Kc3 Kf5 11. Nh6+ Kxf4 12. Nxf7 (D)

The white knight now remarkably holds the g-pawn. If the black king tries to drive the white knight away, the knight will simply move to h6 causing a long trip for the black king to get back to the g-pawn. In the meanwhile, the white king is free to mop up the a-pawns before coming back to help on the kingside.

I doubt this endgame study will ever help me win a game, but at least it was entertaining!

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