Endgame Lab: The Spirit of Sam Loyd
By GM Pal Benko   
October 1, 2007
The “Puzzle King” created few artistic endgames, but his ideas have had a fruitful impact on endgame studies. Here are some examples.

Sam Loyd 1856

White to play and mate in 14 moves

The white king must lose a tempo to take on h4, but the light squares are a minefield. The only possible approach is through a8, the lone safe light square. Only 15 when he composed this, it is a classic example of his ingenuity. With some alteration, this would also work as an endgame.

1. Kc5 Bg1 2. Kb6 Bh2 3. Ka7 Bg1 4. Ka8 Bh2 5. Kb8 Bg1 6. Kc7 Bh2 7. Kd8 

7. Kd6 is an alternative.

7. ... Bg1 8. Ke7 Bh2 9. Kf8 Bg1 10. Kg7 Bh2 11. Kh6 Bg1 12. Kg5 Bh2 13. Kxh4 Bg1 14. Rxg3 mate.

The great author and endgame composer Troitzky readily admitted that he derived ideas from Loyd, writing, “The exhaustive study of this theme has been inspired by a 14-move problem of Loyd in which White’s king takes 13 moves to lose “the move.”

Troitzky Example
A. A. Troitzky 1931

White to play and win

The author wrote that if Black is to move, then Black loses at once. 1. ... Ka4 2. Ra8 a5 3. Rb8; 1. ... Ka6 2. Kb4 or 1. ... a6 2. Ra8 when it is “possible to return to the initial square in an odd number of moves by the following route: [moves] 1-9: Kc2, d1, e1, f2, g3, f4, e5, d4, c3, or reverse.”

This work was recommended to A. Havasi, the leading columnist of Magyar Sakkvilag, who wrote, “[Troitzky] presents an excellent idea that no one has succeeded with before. The king can make it [to the correct square] by wandering in both directions, but no one can call it a ‘side solution’ since both ways are [essentially] the same.”

Yet, if we can reach the same objective via two methods, that is called a “dual” and that is a flaw. My friend Dr. F. Gorgenyi asked me whether I could make an improvement.

So I have taken a thorough look and I made an astonishing find. The white king can only walk the route in one way! Let’s examine the proofs.

The solution 1. Kc2? given by Troitzky leads only to a draw! 1. Kc2? Ka4 2. Kd1 Ka5 3. Ke1 Ka4 4. Kf2 Ka5 5. Kg3 Ka4! 6. Kf4 Bxg5+! assures at least draw for Black after 7. Kxg5 Qxh5+ 8. Kxh5 Bxc4 9. Rb7 a5 10. Rxc7 Bxa2 11. Rxg7 Be6! 12. Rf7 Bxf7 13. gxf7 a2 14. f8=Q a1=Q.

So now, let’s take a look at the other direction!

1. Kd4! Ka6 2. Ke5 Ka5 3. Kf4 Ka4!

Now 3. ... Bxg5+ 4. Kxg5 Qxh5+ 5. Kxh5 Bxc4 6. Rb1! Ka4 (6. ... Bxa2 7. Ra1! wins) 7. Ra1 Kb4 8. Kg5 Bg8 9. h5 Kc3 10. h6 gxh6+ 11. Kxh6 Kb2 12. Rd1 Kxa2 13. Rd8 Be6 14. Rb8! Ka1 15. Kg5 wins.

4. Kg3 Ka5 5. Kf2 Ka4 6. Ke1 Ka5 7. Kd1 Ka4 8. Kc2 Ka5 9. Kc3

Black must move, therefore White wins. So there is a great difference if the king stands on a4 or a5 on move five.

A. A. Troitzky  1931
Version by P. Benko


White to play and win

After having invested so much time in the previous work, I thought it worthwhile to further scrutinize the position and see if it was possible to further develop that great idea. Here we go!

1. Ka1!!

If 1. Kc2? Bh7! 2. Rxh8 Bxg6+ 3. Kb3 Bxh5 and Black wins or 1. g4? Bxc4! 2. Rxh8 Bd3+ 3. Ka1 Bd2 and mates.

1. ... Ka4 2. g4

This is the only solution.

2. ... Ka5 3. g5 Ka4 4. Kb1 Ka5 5. Kc2 Ka4 6. Kc3 Ka5 7. Kd4! etc.

The rest has already been shown in the previous example.

I find it interesting that Troitzky used Loyd’s idea after 75 years and I could correct and improve it after yet another 75 years.

Queen sacrifices
Sam Loyd 1848
Version by P. Benko


White to play and mate in four moves

1. Qa8 Rg4 2. Qh1+! Kxh1 3. Nxg4 Bh2 4. Nxf2 mate.

The original by Loyd was a solid mate- in-three (queen on c6, rook on g4), but its value was degraded because it started with a check. Loyd himself later called it  an “old style” problem. I could not resist  eliminating that. Now it starts with a “silent” move and the queen sacrifice is better hidden. I believe that it is more impressive this way.

More inspiration from Loyd
A.A. Troitzky 1896

Troitzky’s next famous piece I also believe was also inspired by Loyd’s work in the previous example.

White to play and win

1. Bc6! Rb1+ 2. Ke2 Rxh1 3. Bg2+! Kxg2 4. Nf4+ Kg1 5. Ke1 g2 6. Ne2 mate!

The passive queen sacrifice is enriched by the bishop sacrifice. The knight then mates after Zugzwang, just like in Loyd’s work.

“Castling the pawn”
Sam Loyd 1878

White to play

White could have won by 1. f8=R instead of:

1. f8=Q?  Rf4+ 2. Qxf4 Stalemate.

The point was: “Did you ever hear of queening the pawn? Apply the same construction to castling the pawn.”

It seems that World Champion Emanuel Lasker liked that idea, so he modified the position to give more play by placing the c6 pawn on a5 and moving the rook from a4 to g4.

But in my humble opinion the solution is too evident. It could have been better hidden with a short introduction.

Emanuel Lasker 1892
Version (A) by P. Benko


White to play and win

1. f7 Rg2+ 2. Kf1 Rg4! 3. f8=R! Ra4 4. Ra8 Kg4 5. Ke2 Kf5 6. a6 Kg6 7. Kd3 Kf7 8. Kc3 Kg7 9. Kb3 Ra5 10. Kb4 Ra1 11. Kb5 Rb1+ 12. Kc6 Ra1 13. Kb7 Rb1+ 14. Ka7 Kf7 15. Rb8 wins.

Version (B)

Placing the rook on e2 instead of h2 in the starting position enriches Black’s drawing motifs.

1. f7 Re1+!

1. ... Rg2+? now is misleading.

2. Kf2 Re4! 3. f8=R!? Kg4 4. a6 Re7 5. Ra8 Kf4 6. a7 Ke4 7. Ke2 Kd4+ 8. Kd2 Rd7 9. Kc2 Rc7+ 10. Kb3 Kc5, Draw. 

Thus, as you can see, the ideas found in the problem world can often be borrowed for endgame composition. .

View Chess Life’s online section at uschess.org to download this month’s games in a .pgn file.

Benko’s Bafflers

Most of the time these studies resemble positions that could actually occur over-the-board. You must simply reach a theoretically won or drawn position for White.

Solutions can be found on the Solutions page.

Please e-mail submissions for Benko’s Bafflers to: pbenko@uschess.org

Problem I
Sam Loyd,

White to play and mate in eight moves

Show Solution

Problem II
Sam Loyd,

White to play and draw

Show Solution