Lesson 2 by Lifemaster Igor Epshteyn

UMBC, room ECS 023, 2-17-99

Notes by David Joyner. (No claim to completeness.)

Theme: The principle of two weaknesses and the triangulation manuever.

The pawn endgame is the easiest way to convert a positional advantage to a win. Therefore, it it is important to know it well. We shall study in this lesson “triangulation” and the “principle of two weaknesses”.

Position 2.1:
This position is very similar to the first basic endgame position in lesson 1, except there is are extra pawns (but no extra tempi since they are fixed). Note black has two weaknesses: the pawn fixed on the 6th rank at a6 and the passed white pawn which the black king is forced to defend against.

Principle of two weaknesses: If your opponent has two weaknesses, try to choose a move which exploits both.

White wishes to gain access to b6 to win the a6 pawn, thus exploiting both of black’s weaknesses. To do this, he must try to lose a tempo. The classical triangulation manuever accomplishes this.

In Forsyth notation:




White to move and win.


Note that (with white to move) when

  1. the white king is at c5 the black king should defend at c7,
  2. the white king is at c4 the black king should defend at c8,
  3. the white king is at d4 the black king should defend at d8 (long opposition),
  4. the white king is at d6 the black king should defend at d8 (short opposition),
  5. the white king is at b4 the black king should defend at b8.

More briefly, we simply say that the following pairs define coordinating squares in this position: c5-c7, c4-c8, d4-d8, d6-d8, b4-b8.

1. Kd5 Kc8 (1 … Kd8 2. Kd6 Kc8 3. c7 Kb7 and white’s pawn promotes). Now we reach the following position.

White to win.


With white to move, the white king must first triangulate to lose a tempo. White’s king must gain access to the square d6 (or b6), after which it is relatively easy to win. The above list of coordinating squares indicates that white should now move to c4.

1. Kc4! Kd8 (if 1 … Kc6 then 2. Kc5 gains access to d6 or b6) 2. Kd4 Kc8 3. Kd5. Now we are in the original position but with black to move. 3. … Kc7 (if 3 … Kd8 then 4. Kd6 Kc8 5. c7 and white’s pawn promotes) 4. Kc5 Kb8 5. Kb6 and white wins black’s a6 pawn.

Position 2.2: The position below occurred in the game Dvoretsky-Nikitin, Moscow, 1970.

In Forsyth notation:




What if … Kxf4?


We will examine the position after black plays 42 … Kxf4, which was in fact not played in the actual game. This allows White to play the tactic 43 Rxc6 bxc6 44. Bc7 Ke4 45 Bxe5 Kxe5. The following moves of black are forced: 46 Ke3 c5 47 Kd3 Kf5 48 Kc3 Ke5 49 b4 cxb4 50 Kxd4 Kd4! 51 Kb3 Ke5. Is the resulting endgame a win for white?



White to move and win.


One can either triangulate, 1. Kb3 Ke5 2. Ka4 Ke4 3. Ka3 Ke5 4. Kb3 to lose a tempo (computing the coordinating squares confirms this). Not 1. Kb3 Ke5 2. c5? since then black can draw with 2 … Kd5 3 Kb4 Ke6! 3 Kc4 Kd5. After 1. Kb3 Ke5 (which is Position 2.3) white obtains a position like that of position 2.1 which is a win for white, as we have seen.

Position 2.4: Study of Hrashek, 1928.

In Forsyth notation:



White to play and win.


1. Kc6 Ke5! 2. Kc7! Kd5 3. Kd7! Ke5 4. Kc6! and wins.

Position 2.5: Study of Grigor’ev, 1933.

In Forsyth notation:



White to play and win.


1. Kd1. Now black has several alternatives to choose from.

  1. 1 … Kxc3?? then 2. b5 wins.
  2. 1 … d5 2. Kc2 d4 3. cxd4 and white wins by playing the king over to the a-file, as in the third basic endgame position in lesson 1
  3. 1 … Kb5 2. Kc2 Kc4
    (1st triangulation; also note black cannot allow 3. Kd3) 3. Kd2 d6 4. Kd1 Kb5 5. Kc2 Kc4 6. Kd2 (2nd triangulation) d5 and white wins as in item 2 above.


Solve the following problems.

  1. Gruber-Sharkozi, Budapest, 1926.In Forsyth notation:


White to play and draw.


solution below

  • Alekhine-Yates, Gamburg, 1910.In Forsyth notation:




White to play and win.


solution below

  • Educational example.In Forsyth notation:


    White to win.


    Solution below

    Homework solutions:

    1. Very similar to the fourth basic endgame position in lesson 1, except there is an extra pawn and and extra tempo. Since either player may use the tempo, it is called a reserve tempi. As a general rule, the defending side should not use the tempo unless the draw is clear. By the way, a mollificient tempo is a tempo move that is to your disadvantage.

    Black wants to force white to push the pawn, leading to a position similar to
    the previous study but with colors reversed.

    With white to move: 1. Kd1! Kd3 2. Kc1 c2 3. a3 draw. (Not 1. Kc1? Kd3 2. Kd1 c2+ 3. Kc1 Kc3 4. a3 (the mollificient tempo) Kb3 and black wins.)

    With black to move: 1. … Kc4 2. Kd1. Now either 2 … a3 or 2 … Kb4 3. Kc1 Ka3 4. Kc2 draw. The only other choice is 2 … Kd4 3. Kc2 and we are back in the original position or 2 … Kd3 3. Kc1 c2 4. a3 draw.

    • 1. Kd3 Kd7 (1 … Ke6 then 2 Kd4) 2. e4 f4 3. Ke2 Ke6 4. Kf2! and white wins.
    • (given in class): If white can get his king to d6 with the opposition then white will win. With black to move this is relatively easy (see move 3 in the solution below). With white to move, the white king must first perform a triangulation manuever to lose a tempo.


    1. Kd4 Kc6 2. Kc4 Kd7 3. Kd5.

    Now we are in the same position but it is black’s move. 3 … Kd8 (if 3 … Kc8 then 4. Ke6) 4. Kd6. This is the desired position. Now the win is relatively easy but white must be careful not to push the c-pawn too early: 4 … Kc8 5. Ke7 Kb8 6. Kd7 Ka8 7. c6 (finally!) bxc6 8. Kxc6. This is very similar to that examined in the first basic endgame position in lesson 1, a win for white.