Umesh P. Narendran

An Interesting Endgame study of Reciprocal Zugzwangs

Endgame studies are one of the most entertaining things for a chess enthusiast. These puzzles are carefully crafted with each unit serving a purpose. Like chess problems, they have unique solutions and aesthetically pleasing themes, but at the same time, are closer to actual play and in fact may help the reader improve his game.

A zugzwang occurs when a player finds that having the move is a disadvantage. In a reciprocal zugzwang, both the players are in zugzwang. Solving such studies involves getting the opponent into zugzwang without oneself not getting into one. Here is one of them, showing the theme of reciprocal zugzwang. This was composed by Liss Karllson in 1946.

With some careful analysis, some endgame studies are pure joy.

The task is White to play and win.

None of the units except the two Kings has any moves. The White King has three moves: Kg1, Kg2 and Kh2. One of them wins and the other two only draw.

The solution of the problem is not straightforward. In addition to the diagrammed position, there are 14 reciprocal zugzwang positions, marked C through Q, with “White to move draws, Black to move loses” theme.

Let us start with ideas of how White can win.

Two crucial squares for White are c4 and f6. If the White King reaches one of these squares, White wins.

In positions A and B, White wins irrespective of whose move it is. In A, Black loses the crucial pawn on b4 with move. With White to move, 1. Kc5! forces Black to give up the pawn. In B, Black loses the crucial pawn on e6 with move. With White to move, 1. Kf7! wins the pawn.

The rest of the strategy involves reaching (or not allowing to reach) position A or B. Table 1 shows each square the White King can occupy and the safe squares for the Black King not allowing the White King to reach c4 or f6 directly.

Distance to c4	Distance to f6	WK at	Black’s safe squares (Equal)	Black safe squares (Closer)
1	4	d3	b5 c5
2	3	e3	c6
2	4	e2	b6	b5 c6 c5
2	5		a6 a5
3	2	f4	d7
3	3	f3	c7	c6 d7
3	4	f2	b7	b6 b5 c7 c6 c5 d7
3	5	d1 e1 f1	a7	a6 a5 b7 b6 b5 c7 c6 c5 d7
4	1	g5	e7
4	2	g4	d8 e8	d7 e7
4	3	g3	c8	c7 c6 d8 d7 e8 e7
4	4	g2	b8	b7 b6 b5 c8 c7 c6 d8 d7 e8 e7
4	5	g1	a8	a7 a6 a5 b8 b7 b6 b5 c8 c7 c6 c5 d8 d7 e8 e7
5	1		f7	e7
5	2	h4	f8	d8 d7 e8 e7 f7
5	3	h3		c8 c7 c6 d8 d7 e8 e7 f8 f7
5	4	h2		b8 b7 b6 b5 c8 c7 c6 c5 d8 d7 e8 e7 f8 f7
5	5	h1		a8 a7 a6 a5 b8 b7 b6 b5 c8 c7 c6 c5 d8 d7 e8 e7 f8 f7

But being in one of the safe squares is not good enough for Black: It just prevents a direct race to c4 or f6. Among these positions, there are many zugzwangs. In fact, this problem has as many as fifteen reciprocal zugzwangs. Positions C to Q show these reciprocal zugzwangs. With the move, White only draws, but Black loses.

C) Black to move loses: 1... Kb5 2. Kd4! Ka5 (2... Kb6 3. Kc4! Ka5 4. Kc5! +-) 3. Kc4 +-. For any other Black move, White plays 2. Kc4 and wins.

With White to move, it is a draw: 1. Ke3 Kc6! reaches F. 1. Ke2 Kb6! reaches G. With White to move, both these positions are draws.

D) Black to move loses. He has no square that is within 4 squares to c4 and 1 square to f6.

With move, White only draws: 1. Kf4 Kd7! reaches E. 1. Kg4 Kd8! reaches K. 1. Kh4 Kd7! also draws.

White's strategy to win this ending is to get the King to c4 (A) or f6 (B), or to reach C or D with Black to move. It turns out that it is always possible with precise play.

E) From Table 1, Black doesn't have any squares from d7 to keep a safe distance from f4. 1… Kc6 2. Kg5! Kd7 3. Kf6! +- or 1... Ke7 2. Ke3! Kd7 3. Kd3! Kc6 4. Kc4! +-.

With the move, White only draws: 1. Kg5 Ke7!, reaching D. 1. Ke3 Kc6!, reaching F.

F) From Table 1, Black doesn't have any squares from c6 to keep a safe distance from e3. 1… Kd7 2. Kd3! Kc6 3. Kc4! +- or 1... Kb6 2. Kf4! Kc6 3. Kg5! Kd7 4. Kf6! +-.

With the move, White only draws: 1. Kf4 Kd7!, reaching E. 1. Kd3 Kc5!, reaching C. 1. Ke2 Kb6!, reaching G.

G) From Table 1, only safe squares are c6, c5 and b5. However, 1... Kc6 2. Ke3! reaches F. After 1... Kb5, White can play 2. Kf3, and the only safe square c6 for Black leads to F after 2. Ke3. After 1... Kc5 2. Kd3, reaches C. Hence any Black move from G loses.

With the move, White only draws: 1. Ke3 Kc6!, reaching F. 1. Kd3 Kc5!, reaching C. 1. Kf2 Kb7!, reaching I. 1. Kf1 Ka7 (1... Kc7 also draws, but not 1... Kc5? 2. Kf2! wins for White. See R), reaching J.

H) From Table 1, the only safe squares are c6 and d7. However, 1... Kc6 2. Ke3! reaches F, and 1... Kd7 2. Kf4! reaches E.

With the move, White only draws: 1. Kf4 Kd7!, reaching E. 1. Kd3 Kc5!, reaching C. 1. Ke2 Kb6!, reaching G.

I) From Table 1, the only safe squares are b6, c6 and c7. However, 1... Kc6 2. Ke3! reaches F. 1... Kc7 2. Kf3! reaches H. 1... Kb6 2. Ke2! reaches G. So, any Black move loses.

With the move, White only draws: 1. Kf3 Kc7!, reaching H. 1. Kd3 Kc5!, reaching C. 1. Ke3 Kc6!, reaching F. 1. Ke2 Kb6!, reaching G, or 1. Kg3 Kc8!, reaching L.

J) From Table 1, the only safe squares from a7 are a6, b7 and b6. However, 1... Kb7 2. Kf2! leads to I, while 1... Kb6 2. Ke2! reaches G. In the case of 1... Ka6 2. Kg2!, Black is forced to reach G by 1... Kb6 2. Ke2! or I after 1... Kb7 2. Kf2!. So, any Black move loses.

With the move, White only draws: 1. Kf2 Kb7!, reaching I. 1. Ke2 Kb6!, reaching G, or 1. Kg3 Kc8!, reaching L.

K) From Table 1, the only safe squares from d8 are e8, d7 and e7. 1... Kd7 2. Kf4 reaches E. 1... Ke7 2. Kg5 reaches D. After 1... Ke8 2. Kf3 Kd7 (Only safe square) 3. Kf4 reaches E.

With move, White only draws. 1. Kf4 Kd7! reaches E. 1. Kf3 Kc7! reaches H. 1. Kg3 Kc8! reaches L. 1. Kh4 Kd7! reaches O. 1. Kg5 Ke7! reaches D.

L) From Table 1, the only safe squares from c8 are c7, d8 and d7. 1... Kc7 2. Kf3 reaches H. 1... Kd8 2. Kg4 reaches K. After 1... Kd7 2. Kf4 reaches E.

With move, White only draws. 1. Kf4 Kd7! reaches E. 1. Kf3 Kc7! reaches H. 1. Kg4 Kd8! reaches K. 1. Kh4 Kd7! reaches O. 1. Kg2 Kb8! reaches M. 1. Kh3 Kc7! reaches P.

M) From Table 1, the only safe squares from b8 are b7, c8 and c7. 1... Kb7 2. Kf2 reaches I. 1... Kc8 2. Kg3 reaches L. After 1... Kc7 2. Kf3 reaches F.

With move, White only draws. 1. Kf4 Kd7! reaches E. 1. Kf2 Kb7! reaches I. 1. Kf3 Kc7! reaches H. 1. Kg3 Kc8! reaches L.

N) From Table 1, all the three squares accessible from a8 are safe. 1... Kb7 2. Kf2 reaches I. 1... Kb8 2. Kg2 reaches M. 1... Ka7 2. Kf1 reaches J.

With move, White only draws. 1. Kf1 Ka7! reaches J. 1. Kf2 Kb7! reaches I. 1. Kg2 Kb8! reaches M. 1. Kh2 Kb7! also draws.

O) From Table 1, the only safe squares from d7 are d8, e8 and e7. 1... Kd8 2. Kg4 reaches K. 1... Ke8 2. Kg2 reaches M.

With the move, White only draws. 1. Kg5 Ke7! reaches D. 1. Kg4 Kd8! reaches K. 1. Kg3 Kc8! reaches L.

P) From Table 1, c8, c6, d8 and d7 are safe squares. 1... Kd8 2. Kg4 reaches K. 1... Kc8 2. Kg3 reaches L. 1... Kd8 2. Kg4 reaches K. 1... Kd7 2. Kh4 reaches O.

For, 1... Kc6, any of 2. Kg4, 2. Kg3 or 2. Kg2 wins, because their drawing squares (d8, c8 and b8, respectively) are far from c6 and White reaches the winning squares wherever Black moves to.

With the move, White only draws. 1. Kg5 Ke7! reaches D. 1. Kg4 Kd8! reaches K. 1. Kg3 Kc8! reaches L.

White's winning strategy is detailed in Figure 1.

White plays 1. Kg1!! to reach N, then follows the acyclic directed graph given in the figure. Unsafe squares as per Table 1 are not explicitly listed.

Postscript:

In the puzzle diagram, with move, Black draws by either 1... Kb7 (White cannot reach f2) or 1... Ka7 (White cannot reach f1) but loses with 1... Kb8? 2. Kg2!.