Monday, October 29, 2018

An Exciting Endgame Adventure

About a month ago I came across a wonderful column in the Spring, 2007 issue of Chess Horizons.  The column was entitled "Half-point Theft", written by Derek Meredith.  The author gives the reader an endgame position and then analyzes it from the points of view of seven classes of players, from Class E clear up to Master.

The key position of interest is this: white has K on f5, R on h2, P's on a4, b3 and c4; black has K on a2, B on b2, and P's on a5 and c5.  The author opined that in this position black could block off the white rook with his bishop, and start capturing the white pawns. Consequently, he had varied earlier in order to avoid getting to this position.

However, I realized immediately that after 61 Rh3 Ka3 62 Ke4 Kb4 63 Kd5, black's attempt to "build a bridge" with 63...Bc3, loses easily to 64 RxB! KxR 65 KxP KxP 66 Kb5. 

The author correctly points out that in the key position 61 b4!! wins. However, this is a move which only a computer would find; it is doubtful that any human would ever find it.  More realistic is to try to find a white win even if black avoids the blunder 63...Bc3??

My first try in this regard, playing as white against the Stockfish computer, went as follows:  61 Rh3 Ka3 62 Ke4 Kb4 63 Kd5 Bc1 64 Rh8 Kxb3 65 Kxc5 Kxa4 66 Rb8 Bf4 67 Rb1 Be5 68 Kd5 Bh2 69 c5 Ka3 70 c6 a4 71 Ke6 Bc7 72 Kd7 Bh2 73 c7 BxP 74 KxB Drawn

The problem here is that 74...Ka2 75 Rb7 a3 76 Kc6 Ra1 77 Kc5 a2 78 Kc4 is stalemate.  The salient point is that the white rook by itself cannot win against the black king plus a-pawn; rather, the white king needs to be close enough to help out.

What is amazing is that it only needs to be one move closer!  Say the white king was on c4 instead of c5, after 77...a2. Play could then continue 78 Kb3 (giving the black king a move) Kb1 79 Rh7! And now, black cannot promote to a queen because of the mate on h1. Consequently, he must promote to a knight. Play continues 79...a1(N)ch 80 Kc3 Ka2.

Now we have a position that I spent a fair amount of time looking at to find a win. Knight vs. Rook is normally a draw, but I felt sure that in this position, with the knight trapped in the corner, there had to be a win. I'm embarrassed to say that I had to finally give the position to a computer, and the winning move turns out to be the waiting move 81 Rb7!  This simple move puts black into zugzwang, as any move allows white to either mate or capture the  knight.  White's 81 Rb7 represents a martial arts type of concept, using your opponent's aggression against him. The "aggression" in this case is the fact that the rules require black to move. If he could pass, white would have no win, as black would simply shuffle his king back and forth between a2 and b1.

Armed with this knowledge, I sought a line in which white's king didn't stray so far from the a1 corner. The solution was simple:  use the rook to shepherd the c-pawn down the board, rather than the king. Using this approach, I was able to beat Stockfish rather easily.

But then I wondered about a different black move 63. Instead of 63...Bc1, what if black played 63...Bd4, guarding the c-pawn? Play could then continue 64 Kc6 Bg1 65 Rh7 Kxb3 66 Kb5!, and white should win from here.

All in all, I had the key position set up on the desk in my den for three solid weeks, and kept coming back to the position, searching for the truth in the position. And a very satisfying three weeks it was!

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