Part I · First steps Chapter 8 of 40
Piece values and trades
Tartakower won a knight and resigned two moves later. We learn to count material, spot what is hanging and trade at a profit, then see when the count misleads.
What to know first: 5 · Check, checkmate and stalemate
What you will learn
- count material in a position and notice pieces that are hanging
- compare attackers and defenders before a capture and capture with the cheapest piece
- decide when to trade, and see when the exchange or a pawn is worth more than the count says
Vienna, 1910. Savielly Tartakower, playing Black, took White's knight on e4 with his own knight on move eight, and he was a whole piece up. After two more White moves he resigned: there was no escape from mate.
We recorded this game of Richard Réti against Tartakower move by move in the chapter on notation, and in its last section a question was left: why did Tartakower lose, when he had counted correctly? The answer "material is not everything" is true, but it helps little until you can count the material itself. So we start there.
You know the piece values from the second chapter: a pawn is 1, a knight and a bishop 3 each, a rook 5, a queen 9. There we saw where they come from. Now we put them to work: we count who is ahead, find what is lying loose, decide when to trade, and work out how to count several captures on one square. At the end we give up a rook ourselves, in a position where the count says to keep it.
Who is ahead
Everything a side has left on the board except the king is called its material. At the start of the game each side has 39 points: eight pawns, two knights, two bishops, two rooks and a queen. Adding it all up every time takes too long, so chess players count differently. In their heads they cross out equal pairs: queen against queen, rook against rook, pawn against pawn. What is left is what has no pair.
Try it on Tartakower's position. White has made eight moves, Black has too, and 8… Nxe4 has just been played.
The position after 8… Nxe4. Who is ahead in material, and by how much?
Cross out the pairs: queen against queen, two rooks against two, two bishops against two, six pawns against six. Black's knight is left without a pair: Black has an extra piece, three points. Add everything up and you get the same: 34 for White, 37 for Black. How Réti won by giving up his queen you saw in chapter 7. Why the count misled here will be clear by the end of this chapter.
Pairs can be unequal too. A queen against two rooks, a rook against a bishop and two pawns: such pairs are compared by value, and the differences are added up afterwards. Count this one yourself.
Who is ahead in material, and by how much?
A bishop against a knight is a pair, so cross it out. A queen against two rooks is 9 against 10, a point to Black. Pawns: four against five, another point to Black. So Black is ahead by two. The full count, 16 against 18, says the same.
Count the material after every capture, yours and your opponent's. After a few trades it is easy to forget who gave up which pawn, and the count is the only way not to fool yourself.
What is hanging
The simplest way to win material is to take what your opponent has left undefended. A piece that the opponent can capture for nothing, or at a profit, is called a hanging piece: we say it "hangs". Before every move it helps to ask two questions. What is hanging in my opponent's camp? What will be left hanging in mine after my move?
A hanging piece is easy to find when there is only one. It is harder when there are several captures and all of them look tempting. Then, for each target, check who defends it.
White to move. The queen on e4 can take the knight on e7, the rook on a8 or the pawn on h7. Which capture costs nothing?
Qxe7: nobody defends the knight, and White wins three points for nothing. The rook is worth more, but the rook on f8 defends it: after Qxa8 Rxa8 White would have given the queen (9) for a rook (5). The king defends the pawn on h7: Qxh7+ Kxh7, and the queen is lost for a pawn.
The second question, what will be left hanging in my camp, is asked less often, and wrongly so. A piece that leaves its square stops defending what it defended, or stops blocking the line it blocked. The knight went off to attack, and the bishop it defended is left under attack. Before you move, remember whom this piece defends right now.
That is how Tartakower lost too. His knight left f6 for e4 to win material, and the diagonal g5–d8 to the black king opened: along it, two moves later, came the check from the bishop.
White to move. The pawn on f5 hangs: the knight on d4 can take it for nothing. What will be left hanging after Nxf5?
Nxf5? Rxb5: White took a pawn and gave up a bishop, two points down. Before you capture, ask whom the capturing piece defends.
A defended piece can hang too. A defence promises only one thing: if the piece is captured, you capture back. When the attacker is of the same value or higher, that is enough: at worst it comes to an equal trade. But when the attacker is cheaper, the recapture does not save you.
White to move. The pawn on e5 attacks the knight on d4. The pawn on c3 defends the knight. Can the knight stay where it is?
A pawn is cheaper than a knight, and to a pawn even a defended knight hangs: exd4 cxd4, and White is two points down. The knight has to move, for example to b5 or f5. The rule is simple: a piece attacked by a cheaper piece is in danger, defended or not.
Finding hanging pieces has to become automatic, and that can be trained. The trainer sets up the pieces and you find the one that can be taken for nothing. At the second level, defended pieces appear among the targets, and capturing them does not pay.
Trades
In a game, trades happen more often than hanging pieces. A trade is a capture that the opponent answers with a capture. A knight for a knight, a rook for a rook, a bishop for a knight are equal trades: the difference in the count is the same afterwards. A rook for a knight is unequal: someone gave more than they got.
If an equal trade does not change the difference, why make one? Something else changes: how that difference works. Suppose you have an extra knight. While all the pieces are on the board, that is 3 points out of 39, and your opponent has enough force to attack. Trade queens and rooks, and your knight is left against pawns alone. Hence the main rule: when you are ahead in material, trade. And if you are behind, do the opposite: keep the pieces on the board. With them you have more chances to attack, and even to save the game with a stalemate swindle.
Trade pieces, not pawns. Without pawns an extra knight does nothing: a king and a knight cannot mate a lone king, it is a draw, as you saw in the third chapter.
You are a knight up, and the rest of the material is level. What is it in your interest to trade?
Every trade of pieces makes the extra knight weigh more, and you need the pawns so that you have something to push to promotion.
A trade does not always happen by itself. Often one side offers it: it puts a piece opposite an enemy piece, so that each attacks the other and each is defended. The opponent decides whether to capture or move away. If you are ahead, make such offers yourself. If you are behind, step aside while there is somewhere to go.
How do you answer the offer of a trade?
After Qxd5 exd5 White has a knight and five pawns against six pawns, and Black has no pieces left to make threats.
This is what the side with an extra knight aims for: queens off, and enough pawns.
There are other reasons to trade besides the count. It is worth trading off an active enemy piece that is bothering you for one of yours that has nothing to do. If you are being squeezed and your pieces lack room, a trade lets them breathe. But the first question is always the same: who is ahead?
You are a rook down. Your opponent offers to trade queens. What do you do?
The side that is behind needs pieces: with them it creates threats and catches the opponent's mistakes. The side that is ahead, on the contrary, looks for trades.
A queue on one square
The most common place for a mistake is a square that several pieces of both sides attack at once. In the chapter on line pieces you already won a knight with two rooks against one: there were more attackers, and the last capture was yours. Now we count such a queue in full.
Notice two things. First, either side can stop: Black does not have to capture on d5 if it is bad for them, and White does not have to go on. Second, a king can stand in the queue too, but only last. As you remember from the first chapter, it will not step onto a square that an enemy piece attacks, even to capture. So the king recaptures only when the attackers have nobody left in reserve.
While the pieces in the queue are of the same value, a simple count is enough: more attackers than defenders, and the pawn is yours. But the queue holds different pieces, and every capture is a small trade. So capture with the cheapest piece, and the defender also answers with the cheapest. Let us give Black one more pawn and count again.
White to move. Black now has a pawn on e6. Is it worth capturing on d5 now?
Black will answer with the cheapest piece, the pawn: Nxd5 exd5, and White has already given a knight (3) for a pawn (1). Black can answer with the knight instead, and the result is the same: the pawn on e6 captures last. Going on is worse: Bxd5 Nxd5, and the bishop is gone after the knight. There are as many defenders as attackers, so do not capture.
A complicated queue is counted like this. Line up the attackers in your head from the cheapest piece to the dearest, and the defenders too. Play the captures through one by one, and after each reply look at the total. If after any one of the recaptures you are behind and cannot win it back, do not capture.
The count works the other way too. If the target is worth more than your piece, you can capture it even when it is defended: the recapture gets back less than your opponent lost. A pawn that takes a defended knight wins; a queen that takes a defended pawn loses. So a great deal depends on which piece captures.
White to move. The knight on f3 and the queen on c3 attack the knight on e5, and the rook on e8 defends it. Take the knight so that you come out ahead.
Nxe5: knight takes knight, and if the rook on e8 recaptures, the queen takes the rook. Black will not recapture: White has won a knight for nothing, and instead of one point down is now two up. But Qxe5 would lose: Rxe5 Nxe5, and White has given the queen (9) for a knight and a rook (8). The cheapest piece goes first in the queue.
Most often people overlook a defender that stands far away: a bishop in the corner of the board, a rook at the other end of a file. Here you need the habit from the second chapter too: trace every ray from the square. Let us ask the engine about a move that beginners make all the time.
Qxd5: at first glance nobody defends the pawn on d5. But the bishop on b7 attacks d5 along the diagonal b7–c6–d5.The exchange
The knight and the bishop are called minor pieces, the rook and the queen major pieces. A rook is worth two points more than a minor piece, and that difference has a name of its own: the exchange. Whoever takes a rook and gives a knight or a bishop for it has won the exchange. Whoever gives a rook for a minor piece has given up the exchange. You met the phrase in the second and third chapters, and now it has a definition.
You can win the exchange even when the rook is defended: a minor piece takes it, the opponent's rook recaptures, and you are two points up.
White to move. Win the exchange.
Bxa8: the bishop goes along the diagonal d5–c6–b7–a8 and takes the rook. The rook on f8 takes the bishop, and White gives 3 and gets 5. Before the trade the material was level, and after it White is ahead by the exchange. Bxf7+ is not worth it: the pawn on f7 is defended by both the king and the rook.
The exchange is worth about two pawns. So when one side wins the exchange and the other takes pawns in return, you have to count who is ahead in the end.
Before this, the material was level. White won the exchange, and in return Black took two pawns. Who is ahead on the count now?
Plus two for the exchange, minus two for the pawns: the count is level. This is called "the exchange for two pawns". Who stands better in such a position is decided no longer by points but by how the pieces stand, for example how far the pawns have advanced.
The exchange is also given up on purpose. In the Opera Game, Paul Morphy made his first move of the finale a rook for a knight, 13. Rxd7: that was the exchange given up. In return his pieces landed so well that four moves later he mated. For an attack on the king, for a pawn that will break through and promote, for the removal of a strong enemy piece, even the strongest players pay it. But give it up only when you can see what you get in return.
The bishop pair
On the count, two bishops are worth the same as a bishop and a knight or two knights: six points. But a pair of bishops has a property that neither bishop has alone. As you remember from the second chapter, a bishop stays on squares of one colour all game and attacks only half the board. A light-squared and a dark-squared bishop together attack squares of both colours.
Such a pair is called the bishop pair, or "the two bishops". It is strongest in an open position, where the bishops have free diagonals, and in the endgame. Experienced players value the pair a little above six points, and do not trade one of the bishops for a knight without need. The engine of this course thinks the same: for the bishop pair it adds to its evaluation less than a quarter of a pawn in the middlegame and more than half a pawn in the endgame, and the fewer pieces there are on the board, the bigger the bonus.
In a closed position, where pawns block the diagonals, the strength of the pair melts away. There a knight, which jumps over pawns, is as good as a bishop, and sometimes better. The chapter "Bishop against knight" tells more about this old argument.
White has two bishops, Black has a bishop and a knight. White can trade the light-squared bishop for the knight. What changes?
In points, a bishop for a knight is an equal trade. But White is left with one dark-squared bishop, and all the light squares of the board are out of its reach. That is exactly the property you lose when you give up one bishop of a pair.
When the count misleads
The values 1-3-3-5-9 are averages. In every position a piece is worth a little more or a little less, as we said as far back as the second chapter. A bishop shut in by its own pawns is often worse than a knight. A rook in the endgame, when the files are open, is stronger than at the start of the game. The king, which is given no value at all, walks into the fight itself towards the end.
A piece that takes no part in the game is worth less than its price too: a rook shut in the corner by its own king, a knight on the rim that is two moves from the centre. Until they come into play, your opponent has an extra piece in the fight, though on the count all is level. How the engine weighs this is told in chapter 27.
And sometimes the difference is huge. A pawn one step from promotion is worth far more than one point: it is about to become a queen. The piece that guards it in such a position is worth more than any rook. And Tartakower's game is the same case: he counted the knight correctly but did not ask the second question, and mate ends a game whatever the count.
Now the last problem. In it the count says one thing and the board another.
White to move. On the count Black is ahead: a rook and a knight against a rook. But the white pawn on b7 is one step from the promotion square b8, and that square is guarded by a single black piece. Find the move.
Rxc6! The rook gives itself up for the knight, the only guard of b8: White gives up the exchange. After dxc6 the pawn promotes with check, b8=Q+ (the way to write a promotion is in the chapter on the pawn), and White has a queen against a rook. If Black does not take the rook, it goes to c8 next to the pawn, and Black will have to give up their own rook for the pawn. Promoting at once, b8=Q+, is weaker: after Nxb8 Rc8+ Kh7 Rxb8 White wins the knight back, but the pawn is gone, and on the count White stays behind.
Count the result: White gave a rook for a knight, minus two, and the pawn became a queen, plus eight. The count made no mistake: it simply stopped one move too early.
What's next
Now you can count material, see what is hanging and work through a queue of captures on one square. But a strong opponent does not leave pieces hanging, and in a game material is won another way: with one move you attack two targets at once, and you cannot defend both. That is the fork, and the second part of the course begins with it, chapter 11.
Before that, there is one wall that the rule "ahead, so trade" runs into. You have traded everything, and you are left with a king and a queen or a rook against a lone king. That material wins only if you can deliver mate and avoid stalemate. How to do it by a plan, against any defence, is taught by chapter 9, "First checkmates".