Exercise 9.1Find the move
White to move
White to move and win.
9
Calculation in Chess · Yatish Chandra Shukla
Pawn Races and Counting in the Endgame
In this lesson you will learn
- Why endgame calculation is mostly counting
- The rule of the square: can the king catch the pawn?
- How to count a pawn race correctly
- The opposition and the pawn breakthrough
Every board on this page is live. Move the pieces by tapping or dragging, click any move in the lines to see that position, and press ↺ to start again.
9.1 When Calculation Becomes Counting
With few pieces left on the board, calculation changes character. There are fewer tactics, but every tempo — every single move — can decide the game. A king that arrives one move late is simply too late. That is why endgame calculation is mostly counting: how many moves does my pawn need to promote? How many does the enemy king need to stop it?
The good news is that counting is exact. In many pawn endings you can calculate the result with certainty before you make your move — if you count carefully.
NoteWhen counting, always ask: whose move is it? The same position can be a win with one side to move and a draw with the other.
9.2 The Rule of the Square
Can a king catch a passed pawn? You could count moves one by one, but there is a quicker way. Imagine a square drawn from the pawn to its promotion square and then sideways towards the enemy king. If the king can step into that square on its move, it catches the pawn. If not, the pawn promotes.
Diagram 9.1White to move
Example 9.1
White's b-pawn needs four moves to promote. Its square runs from b4 to f4, f8 and b8. The black king on g5 stands just outside it.
White to move: 1.b5! The square shrinks to b5–e5–e8–b8, and the king on g5 cannot step into it.
1...♔f4 2.b6 ♔e5 3.b7 ♔d6 4.b8=♕+ and White wins. Black to move: 1...♔f5! (or 1...♔f4) steps into the square, and the king catches the pawn in time. Draw.
LessonDraw the square in your head before you start counting. It answers the question "can the king catch the pawn?" in a single glance.
9.3 Pawn Races
When both sides have a passed pawn, there is a race. Counting a race needs three questions:
1. How many moves does each pawn need to promote?
2. Who moves first?
3. When the first pawn promotes, can the new queen stop the other pawn — or does the second pawn promote with check?
Diagram 9.2White to move
Example 9.2
White to move. Both sides have one pawn. Who wins the race?
White's g-pawn needs four moves (g5, g6, g7, g8). Black's a-pawn needs five (a5, a4, a3, a2, a1). With White to move, White promotes first: 1.g5! ♔b2 2.g6 a5 3.g7 a4 4.g8=♕ a3 and the new queen catches the a-pawn, for example by checking the king and then taking the pawn. White wins.
But if White wastes one move, the count changes: 1.♔g2? a5 2.g5 a4 3.g6 ♔b2 4.g7 a3 and Black's pawn arrives in time. The game is drawn. One tempo decides everything.
LessonIn a race, count moves, not squares, and remember who is to move. Then look at the position when the first pawn promotes: can the new queen stop the other pawn?
9.4 The Opposition
When two kings stand facing each other with one square between them, the player who does not have to move is said to have the opposition. The other king must give way, and that often decides whether a pawn can promote.
Diagram 9.3Black to move
Example 9.3
Black to move. The kings face each other on the e-file. Does it matter whose move it is?
With Black to move, White has the opposition. Black's king must step aside, and White's king advances: for example 1...♔d7 2.♔f6! and the king escorts the pawn to e8. White wins. With White to move in the same position, Black has the opposition, and White cannot make progress: after 1.♔d5 ♔d7 or 1.♔f5 ♔f7 the black king keeps facing the white king, and the game is a draw.
TipThe opposition is a counting idea too: you count which king will run out of useful moves first.
9.5 The Breakthrough
Diagram 9.4White to move
Example 9.4
White to move. Three pawns against three, and both kings are far away. Can White create a passed pawn?
1.b6! — a pawn sacrifice. If 1...axb6 2.c6! bxc6 3.a6 the a-pawn runs through to promote. If 1...cxb6 2.a6!
bxa6 3.c6 the c-pawn promotes instead. Either way, one white pawn breaks through, and the black king is too far away to stop it.
LessonIn a breakthrough you count after the sacrifices. Two pawns are given away, but the third reaches the eighth rank before the enemy king can arrive.
9.6 Worked Examples
In each example, count before you read the solution: how many moves does each side need?
Diagram 9.5White to move
Example 9.5
White to move and win.
Find the key move.
Solution. 1.h5 ♔d6 2.h6 ♔c5 3.♔f4 ♔c4 4.h7 and White wins. The natural 1.♔g4? only draws: 1.♔g4 ♔d8 2.♔g5 ♔e8.
Diagram 9.6White to move
Example 9.6
White to move and win.
Find the key move.
Solution. 1.c6 ♔d5 2.c7 ♔e4 3.♔e7 ♔f4 4.c8=♕ and White wins. The natural 1.♔g7? only draws: 1.♔g7 ♔xc5 2.♔g6 ♔d6.
Diagram 9.7White to move
Example 9.7
White to move and win.
Find the key move.
Solution. 1.♔g5 ♔d5 2.♔g6 ♔c4 3.f5 ♔d5 4.f6 and White wins. The natural 1.f5? only draws: 1.f5 ♔xf5 2.♔g7 ♔e4.
Diagram 9.8Black to move
Example 9.8
Black to move. Find the only move that saves the game.
Find the key move.
Solution. 1...♔a3 2.♔d7 ♔b4 3.♔c6 ♔c3 4.♔b5 ♔xc2 and the game is drawn. The natural 1...♔b1? loses:
1...♔b1 2.c4 ♔c2 3.c5.
Diagram 9.9White to move
Example 9.9
White to move and win.
Find the key move.
Solution. 1.♔c6 ♔e5 2.♔c5 ♔e6 3.d4 ♔d7 4.♔d5 and White wins. The natural 1.♔c7? only draws: 1.♔c7 ♔e5 2.♔c6 ♔d4.
Diagram 9.10White to move
Example 9.10
White to move and win.
Find the key move.
Solution. 1.♔g7 ♔e4 2.h5 ♔d3 3.h6 ♔d4 4.h7 and White wins. The natural 1.♔e7? only draws: 1.♔e7 ♔f5 2.♔d7 ♔g4.
Diagram 9.11Black to move
Example 9.11
Black to move. Find the only move that saves the game.
Find the key move.
Solution. 1...♔d4 2.h5 ♔e5 3.♔g3 ♔f6 4.♔f4 ♔g7 and the game is drawn. The natural 1...♔c4? loses:
1...♔c4 2.h5 ♔d5 3.h6.
Diagram 9.12White to move
Example 9.12
White to move and win.
Find the key move.
Solution. 1.a4 ♔f7 2.a5 ♔g6 3.♔d2 ♔f5 4.♔e3 and White wins. The natural 1.♔c2? only draws: 1.♔c2 ♔f7 2.♔b3 ♔e6.
LessonIn pawn endings one tempo decides everything. Before every move, count the race again — for both sides.
Remember
- In the endgame, every tempo counts. Calculation becomes exact counting.
- Use the rule of the square to see at once whether a king catches a pawn.
- In a race, count moves for both pawns, note who is to move, and check what happens after the first promotion.
- The king that does not have to move — the one with the opposition — often wins the fight for key squares.
- A breakthrough sacrifice works when, after counting, your last pawn arrives first.
Exercises · Lesson 9
Every puzzle is a king and pawn ending. Count before you move: the question says whether you are playing to win or to save the game.
Exercise 9.2Find the move
Black to move
Black to move. Find the only move that saves the game.
Exercise 9.3Find the move
White to move
White to move and win.
Exercise 9.4Find the move
White to move
White to move and win.
Exercise 9.5Find the move
Black to move
Black to move. Find the only move that saves the game.
Exercise 9.6Find the move
White to move
White to move and win.
Exercise 9.7Find the move
White to move
White to move and win.
Exercise 9.8Find the move
Black to move
Black to move. Find the only move that saves the game.
Exercise 9.9Find the move
White to move
White to move and win.
Exercise 9.10Find the move
White to move
White to move and win.
Exercise 9.11Find the move
Black to move
Black to move. Find the only move that saves the game.
Exercise 9.12Find the move
White to move
White to move and win.
Exercise 9.13Find the move
White to move
White to move and win.
Exercise 9.14Find the move
Black to move
Black to move. Find the only move that saves the game.
Exercise 9.15Find the move
White to move
White to move and win.
Exercise 9.16Find the move
White to move
White to move and win.
Exercise 9.17Find the move
Black to move
Black to move. Find the only move that saves the game.
Exercise 9.18Find the move
White to move
White to move and win.
Exercise 9.19Find the move
White to move
White to move and win.
Exercise 9.20Find the move
Black to move
Black to move. Find the only move that saves the game.
Exercise 9.21Find the move
White to move
White to move and win.
Exercise 9.22Find the move
White to move
White to move and win.
Exercise 9.23Find the move
Black to move
Black to move. Find the only move that saves the game.
Exercise 9.24Find the move
White to move
White to move and win.
Exercise 9.25Find the move
White to move
White to move and win.
Exercise 9.26Find the move
Black to move
Black to move. Find the only move that saves the game.
Exercise 9.27Find the move
White to move
White to move and win.
Exercise 9.28Find the move
White to move
White to move and win.
Exercise 9.29Find the move
Black to move
Black to move. Find the only move that saves the game.
Exercise 9.30Find the move
White to move
White to move and win.
Exercise 9.31Find the move
White to move
White to move and win.
Exercise 9.32Find the move
Black to move
Black to move. Find the only move that saves the game.
Exercise 9.33Find the move
White to move
White to move and win.
Exercise 9.34Find the move
White to move
White to move and win.
Exercise 9.35Find the move
Black to move
Black to move. Find the only move that saves the game.
Exercise 9.36Find the move
White to move
White to move and win.
Exercise 9.37Find the move
White to move
White to move and win.
Exercise 9.38Find the move
Black to move
Black to move. Find the only move that saves the game.
Exercise 9.39Find the move
White to move
White to move and win.
Exercise 9.40Find the move
White to move
White to move and win.