Chess piece values: the 1-3-3-5-9 table and when it fails

Chess piece values are measured in pawns: a pawn is worth 1, a knight 3, a bishop 3, a rook 5 and a queen 9. The king has no number, because it can never be traded. The table tells you at a glance whether a trade suits you, but it is a guide rather than a law: the same piece is worth more or less depending on the position, and knowing when that happens is what separates someone who counts from someone who plays.

The 1-3-3-5-9 table

The classical scale, the one you will find in almost every textbook, is this:

• Pawn: 1 point.
• Knight: 3 points.
• Bishop: 3 points.
• Rook: 5 points.
• Queen: 9 points.
• King: no point value.

The numbers are not arbitrary. They reflect how many squares each piece controls in a typical position and how hard it is for the opponent to deal with it. The queen, which moves like a rook and a bishop at the same time, is worth roughly a rook plus a bishop plus a pawn. The rook dominates whole files and ranks but takes a long time to get into play, which is why it barely matters in the opening and rules the endgame.

When you add up the material on the board, count every piece except the king: in the starting position each side has 39 points (eight pawns, two knights, two bishops, two rooks and a queen).

What counting material is for

The table answers the most common question in any game: does this trade suit me? A few examples that come up all the time:

• Bishop for knight: 3 for 3, an even trade. Whether it is good depends on the position, not the count.
• Rook for bishop: 5 for 3. You are two points up, which is called winning the exchange.
• Two minor pieces for rook and pawn: 6 against 6. Even on paper; in the middlegame the two pieces are usually better.
• Queen for rook and bishop: 9 against 8. Almost even, and two coordinated pieces are often more annoying than a lone queen.
• Minor piece for three pawns: 3 against 3. In the middlegame the piece is nearly always preferable; in the endgame the three pawns can be more dangerous.

If you are just starting, this count will save you from the most expensive mistakes: giving up a rook for a knight with nothing in return, or grabbing a poisoned pawn and losing a bishop. The typical beginner mistakes almost always start with not counting.

Bishop versus knight: which is worth more?

The table says they are equal, and on average that is true. Larry Kaufman, who studied hundreds of thousands of games between strong players in an article published in Chess Life in 1999, found that a single bishop and a knight are worth practically the same. What changes is where each one performs:

• The bishop wants open positions. With clear diagonals and pawns on both wings, it crosses the board in one move. In an endgame with pawns on both sides, a good bishop usually beats a knight.
• The knight wants closed positions. When pawn chains block the diagonals, the bishop becomes "bad", shut in behind its own pawns, and the knight jumps over everything.
• The knight needs an outpost. A square in the centre or in the enemy camp where no enemy pawn can chase it away makes it as strong as a far more active piece.

The useful question is not "which is worth more?" but "is this position going to open up or stay closed?". If it is going to open, keep the bishop; if it is going to close, the knight.

The bishop pair

Here is the most important exception to the table. Two bishops together cover each other's weaknesses: one controls the light squares and the other the dark ones, so there is no colour where the opponent can hide. Kaufman's same study estimated that the bishop pair is worth about half a pawn on its own, and that it grows more valuable as pawns come off the board and the position opens.

That is why giving up the pair needs a reason. In the Exchange Variation of the Ruy Lopez, White does it on purpose:

White trades the bishop for the knight and hands Black the two bishops. In return, Black is left with doubled pawns on the c-file: if the central pawns are exchanged and the game reaches a pawn ending, White's four-against-three kingside majority can create a passed pawn, while Black's queenside majority, with its doubled pawn, cannot. It is a trade of advantages: two bishops against structure. Neither shows up when you add points.

The exchange and unequal trades

The exchange is the difference between a rook and a minor piece, about two points. Winning it is a serious advantage: with everything else equal, it is usually enough to win most endgames.

But the exchange is also sacrificed, and not only for tactics. There are positions where a rook has no open files and a knight on a strong outpost does more, or where removing a defending piece wrecks the opponent's structure and leaves an attack that cannot be stopped. That is the territory of positional sacrifice, and the course The Art of Sacrifice: Pawns, Pieces, and the Exchange is entirely about recognising when the compensation justifies giving up material.

Other imbalances are worth knowing by name:

• Two minor pieces against rook and pawn. In the middlegame the two pieces are usually better: they hit more squares and coordinate against the king. In the endgame the rook gains value, and so do the pawns.
• Queen against two rooks. On paper 9 against 10. In practice it depends on king safety: if the king on the side with the rooks is exposed, the queen gives endless checks; if the rooks can double against a target, they win.
• Three minor pieces against a queen. 9 against 9. The three pieces usually prevail if they are coordinated and protect each other; the queen wins if it finds loose pieces.

The course Master Chess: Attack, Openings and Endgames has a lesson on unequal piece trades, precisely to learn how to assess these positions without stopping at the sum.

When material is not everything

The table counts what is on the board, not what it does. Three things can be worth more than a pawn, or even a piece:

Activity and the attack on the king

A classic sacrifice for learning this is the Fried Liver Attack in the Italian Game:

White has given a knight for a pawn: by the table, two points down. But the black king is stuck in the middle of the board on e6, and White has the initiative. Black can defend with precise moves, but in practice it is a very hard position to hold. Here time and king safety are worth more than the knight.

Passed pawns

A pawn is worth 1 on the table, but a passed pawn on the seventh rank is worth almost a queen, because it forces the opponent to tie a whole piece to stopping it. In endgames the question is not how many pawns you have, but which ones can promote.

Draws the count cannot see

Sometimes an extra piece is not enough to win. The best-known case is the "wrong" bishop with a rook's pawn:

White is a bishop and a pawn up and still cannot win: the pawn queens on a8, a light square the bishop will never control, and the black king just sits there. In the same way, a lone knight or a lone bishop is not enough to give mate. The guide to the endgames you must know covers the most useful ones.

How to use piece values in your games

A simple routine that works from your first game to your first tournament:

1. Before every trade, count. What you give, what you get, in points. If you lose material, there has to be a concrete reason you can name.
2. If the count is even, look at the position. Is it opening or closing? Who keeps the bishop pair? What pawn structure is left?
3. If you are ahead on material, trade pieces, not pawns. With fewer pieces on the board, a material edge weighs more.
4. If you are behind on material, look for complications. Avoid trades and keep your pieces active: simple endgames favour the side with more.
5. If your opponent gives up material, ask what they want. They almost never give anything away: time, an open file or an attack on the king are the most common forms of compensation.

When you are not sure whether an unequal trade was right, that is the kind of question you settle by analysing the game afterwards. If you want someone strong to explain it, Ask the GM lets you ask about a specific move. And for the next step, the guide on how to think in the middlegame shows how the material count fits into a plan.