Exercise 4.1Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
4
Calculation in Chess · Yatish Chandra Shukla
Counting Exchanges
In this lesson you will learn
- How to count a chain of captures to the end
- Why the order of captures matters
- Defenders that do not really defend: pinned and overloaded pieces
- How an in-between move can change the whole count
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.
4.1 The Score Card
In Chapter 1 we met the basic rule: count the attackers and the defenders of a square. In this chapter we make that rule reliable. The key is to keep a small score card in your head while you play through the captures:
1. Write down the captures in the order they would be played — yours, then your opponent's, then yours again.
2. After each capture, note what has been won and what has been lost.
3. Remember that either side can stop capturing at any moment. Each player will stop at the point that is best for them.
4. The real result is the score at the moment when the side who is behind decides to stop.
Point 3 is the one beginners forget. They calculate the whole chain to the very end, but in a real game the opponent will simply not continue a series of captures that is bad for them.
NoteUse the piece values from Chapter 1: pawn 1, knight 3, bishop 3, rook 5, queen 9. The king can capture too — but only on a square that is not attacked.
4.2 Cheapest Piece First
Diagram 4.1White to move
Example 4.1
Black's knight on d5 is attacked twice (by the knight on c3 and the queen on d1) and defended twice (by the e6 pawn and the queen on d8). What should White do?
Two against two: the count is equal, so White cannot win the knight. But look at what happens with different capture orders.
| Line | Score card | Verdict |
|---|---|---|
| 1.♘xd5 exd5 | White gives a knight, gets a knight. Even. | EQUAL |
| 1.♘xd5 exd5 2.♕xd5?? ♕xd5 | White continues: after the knight trade, White gives the queen (9) for a pawn (1). | LOSES |
| 1.♕xd5?? exd5 | White starts with the most valuable piece: queen (9) for a knight (3). | LOSES |
The lesson is simple: capture with your cheapest piece first, and stop when the next capture would cost more than it wins. Here the sensible choice is 1.♘xd5 followed by quiet development — or no capture at all.
LessonIn a fight for one square, the side that captures last usually wins. The side that captures with expensive pieces first usually loses. Count the value, not just the number of pieces.
4.3 Defenders That Don't Defend
Sometimes a piece seems to defend a square, but in reality it cannot capture there. The two most common reasons are the pin and the overload.
A pinned piece stands between an attacker and a more valuable piece behind it, usually the king. If the pinned piece moves, the piece behind it is exposed. When the king is behind, the pinned piece is not even allowed to move.
Diagram 4.2White to move
Example 4.2
The pawn on e5 is attacked by the knight on f3 and seems to be defended by the knight on c6. Is it?
Look along the diagonal from b5 to e8. The knight on c6 stands between White's bishop and Black's king, so it is pinned and cannot move. That means it does not really defend e5. 1.♘xe5! wins a pawn for free:
1...♘xe5?? is illegal.
Black's best is to unpin with 1...♗d7, but after 2.♗xc6 ♗xc6 3.♘xc6 bxc6 White is still a clean pawn up.
LessonWhen you count defenders, check each one: is it pinned? A pinned defender counts as zero.
An overloaded piece has too many jobs at once — for example, it must defend a piece and guard against mate. If you force it to carry out one job, it can no longer do the other. When you count defenders, ask of each one: "Is this piece already busy defending something else?"
4.4 The In-Between Move
Counting assumes that both sides simply take turns capturing on one square. But at any point a player can interrupt the sequence with a more forcing move — usually a check — and then return to the captures later. This is called an in-between move (chess players also use the German word Zwischenzug).
You saw one in Exercise 2.8: instead of recapturing a rook at once, White first moved the attacked queen with check, and only then recaptured. Because the check had to be answered, Black never had time to take the queen.
TipBefore you finish counting an exchange, run the CCT scan once more at every step — for both sides. Is there a check, or a bigger threat, that interrupts the sequence?
4.5 Worked Examples
Study each example as if it were a puzzle: cover the solution, calculate, and only then read on.
Diagram 4.3White to move
Example 4.3
White to move. Keep a score card of the captures and find the move that wins material.
Find the key move.
Solution. 1.♔xh2 axb3 2.♗f3 a4 3.♖xg7 — the rook on h2 was not defended. White wins a rook and keeps a winning position.
Black's other defences do not help:
1.♔xh2 ♔b5 2.bxa4+ ♔xa4 — White is winning.
1.♔xh2 ♔c5 2.bxa4 ♔b4 — White is winning.
Compare a natural alternative, 1.bxa4?: after 1.bxa4 ♖h5 2.♖b1+ White is clearly better. That is far less than the key move achieves.
LessonA piece without a defender is the easiest target on the board. Before every move, ask which pieces are loose — yours and your opponent's.
Diagram 4.4Black to move
Example 4.4
Black to move. Keep a score card of the captures and find the move that wins material.
Find the key move.
Solution. 1...♗xd5 2.♖xg2 ♖xf7 3.♖g4 ♖c7 Black wins a rook and a bishop for a pawn.
White's other defences do not help:
1...♗xd5 2.♘f4 ♖xf7 3.♖xg2 — Black is winning.
1...♗xd5 2.♗g6 ♘xg1 3.♘xg1 — Black is winning.
Compare a natural alternative, 1...♕c7?: after 1...♕c7 2.♕xf3 ♗xd5 the position is about equal. That is far less than the key move achieves.
LessonKeep a score card of every capture, and stop the count only when the captures run out.
Diagram 4.5Black to move
Example 4.5
Black to move. Keep a score card of the captures and find the move that wins material.
Find the key move.
Solution. 1...hxg3+ 2.♔xg3 gxf4+ 3.♔h2 ♖e2 Black wins the queen.
White's other defences do not help:
1...hxg3+ 2.♖xg3 gxf4 3.♖f3 — Black is winning.
1...hxg3+ 2.♔g1 ♖g6 3.fxg5 — Black is winning.
Compare a natural alternative, 1...g4?: after 1...g4 2.♕xh4 gxf3 the position is about equal. That is far less than the key move achieves.
LessonChecks come first in the CCT scan because they leave the opponent the fewest replies.
Diagram 4.6Black to move
Example 4.6
Black to move. Keep a score card of the captures and find the move that wins material.
Find the key move.
Solution. 1...♗xb3 2.axb3 g4 3.hxg4 ♘xg4 Black wins the queen for a bishop.
White's other defences do not help:
1...♗xb3 2.♗b5 ♗xc2 3.♖cxd6+ — Black is winning.
1...♗xb3 2.♘xg5 ♗xa2 3.♖a6 — Black is winning.
Compare a natural alternative, 1...♗d5?: after 1...♗d5 2.♕b5 ♗xc6 the position is about equal. That is far less than the key move achieves.
LessonKeep a score card of every capture, and stop the count only when the captures run out.
Diagram 4.7Black to move
Example 4.7
Black to move. Keep a score card of the captures and find the move that wins material.
Find the key move.
Solution. 1...♕xe5 2.♕xe4 fxe4 3.♘xh5 b5 — the bishop on e5 was not defended. Black wins the queen and a bishop for a rook and a knight and keeps a winning position.
White's other defences do not help:
1...♕xe5 2.♕e2 ♖xh4 3.g3 — Black is winning.
1...♕xe5 2.♘xd5 exd5 3.♕e2 — Black is winning.
Compare a natural alternative, 1...dxc4?: after 1...dxc4 2.♗xg7 ♖xg5 the position is about equal. That is far less than the key move achieves.
LessonA piece without a defender is the easiest target on the board. Before every move, ask which pieces are loose — yours and your opponent's.
Diagram 4.8Black to move
Example 4.8
Black to move. Keep a score card of the captures and find the move that wins material.
Find the key move.
Solution. 1...♗xa3 2.♔h1 ♘xd4 3.cxd4 ♗b4 Black wins a knight.
White's other defences do not help:
1...♗xa3 2.♔f1 ♘xd4 3.cxd4 — Black is clearly better.
1...♗xa3 2.♖d1 ♗c5 3.♔h1 — Black is clearly better.
Compare a natural alternative, 1...♘xd4?: after 1...♘xd4 2.cxd4 ♕xd4+ Black is a little better. That is far less than the key move achieves.
LessonKeep a score card of every capture, and stop the count only when the captures run out.
Diagram 4.9White to move
Example 4.9
White to move. Keep a score card of the captures and find the move that wins material.
Find the key move.
Solution. 1.gxf5 O-O-O 2.fxe4 ♘xe4 3.♗g2 — the bishop on f5 was not defended. White wins a bishop.
Black's other defences do not help:
1.gxf5 g6 2.♘e3 O-O-O — White is clearly better.
1.gxf5 ♖d8 2.fxe4 ♘xe4 — White is clearly better.
Compare a natural alternative, 1.h4?: after 1.h4 ♗d7 2.g5 the position is about equal. That is far less than the key move achieves.
LessonA piece without a defender is the easiest target on the board. Before every move, ask which pieces are loose — yours and your opponent's.
Diagram 4.10White to move
Example 4.10
White to move. Keep a score card of the captures and find the move that wins material.
Find the key move.
Solution. 1.♘xc6 ♕xe3+ 2.fxe3 bxc6 3.♗a4 White wins the queen for a bishop.
Black's other defences do not help:
1.♘xc6 ♕xc6 2.♗xc6+ bxc6 — White is winning.
1.♘xc6 bxc6 2.♗xb6 cxb5 — White is winning.
Compare a natural alternative, 1.O-O?: after 1.O-O ♕c7 2.♗e2 White is a little better. That is far less than the key move achieves.
LessonKeep a score card of every capture, and stop the count only when the captures run out.
Diagram 4.11Black to move
Example 4.11
Black to move. Keep a score card of the captures and find the move that wins material.
Find the key move.
Solution. 1...♖xh3 2.♕d6 ♖xe3 — the rook attacks the queen and the knight at the same time. Black wins a knight and a pawn.
White's other defences do not help:
1...♖xh3 2.♕f4 g5 3.♕f2 — Black is a little better.
1...♖xh3 2.♕xh3 ♗xh3+ 3.♖xh3 — Black is clearly better.
Compare a natural alternative, 1...♗b7?: after 1...♗b7 2.♕f4 ♘h6 the position is about equal. That is far less than the key move achieves.
LessonMaterial can be given away when the result has been calculated to the end. Count at the end of the line, not after the first move.
Diagram 4.12White to move
Example 4.12
White to move. Keep a score card of the captures and find the move that wins material.
Find the key move.
Solution. 1.♖xe4 dxc2 2.♕xc2 White wins a knight.
Black's other defences do not help:
1.♖xe4 fxe4 2.♘xh2 ♕xa4 — White is winning.
1.♖xe4 ♕xe4 2.cxd3 ♕e7 — White is winning.
Compare a natural alternative, 1.gxf5?: after 1.gxf5 ♘xf2+ 2.♔xh2 White is a little better. That is far less than the key move achieves.
LessonMaterial can be given away when the result has been calculated to the end. Count at the end of the line, not after the first move.
Remember
- Keep a score card: after each capture, note what has been won and lost.
- Either side can stop capturing at any time. Each side stops where it suits them best.
- Capture with your cheapest piece first.
- A pinned or overloaded defender does not really defend.
- Look for in-between moves — checks and bigger threats can interrupt any exchange.
Exercises · Lesson 4
Each puzzle is about a fight for one or more squares. Keep a score card of every capture, and remember that your opponent can stop capturing whenever it suits them.
Exercise 4.2Find the move
Black to move
Black to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.3Find the move
Black to move
Black to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.4Find the move
Black to move
Black to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.5Find the move
Black to move
Black to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.6Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.7Find the move
Black to move
Black to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.8Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.9Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.10Find the move
Black to move
Black to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.11Find the move
Black to move
Black to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.12Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.13Find the move
Black to move
Black to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.14Find the move
Black to move
Black to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.15Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.16Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.17Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.18Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.19Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.20Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.21Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.22Find the move
Black to move
Black to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.23Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.24Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.25Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.26Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.27Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.28Find the move
Black to move
Black to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.29Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.
Exercise 4.30Find the move
White to move
White to move. Keep a score card of the captures and find the move that wins material.