In-depth take on Chess Theoretical value (Made easy!)

Chess hosts a unique set of 6 different pieces with their own strengths and abilities. Each of these pieces has a value different from one another, hence is used to make proper trades.

The universally accepted Reinfeld evaluations give a pawn’s worth as 1 point, the knight and bishop as three points, the rook being 5, and the queen as nine points. The king is said to have infinite value more than any combination of all other pieces.

Why do chess pieces have assigned values?

The objective of any chess game is to strike the opposing player with a checkmate. A Checkmate is a condition that gets the opposing king unstoppably be captured the next turn. It can be done through different checkmate patterns that usually cannot be fully executed.

The opponent after all has the opportunity to prevent the said threat. Unless a checkmate cannot be absolutely prevented. Then there should be better things to accomplish with our turns.

I’m not saying you shouldn’t try to deliver a checkmate. It’s just doing so especially in a competitive sphere (where the opponent can easily spot the threat) will lose time. So we have to resort to a better strategy!

Instead of assembling pieces for an all-out attack that becomes churn and burn. It’s better to accumulate our forces in a way better than our opponents. That includes having better pieces not just by quantity but also by quality.

Chess pieces have different inherent values to offer. Of course there are several factors to consider when determining which piece is better.

But generally, the likelihood of making better exchanges can be increased by following the theoretical value.

Theoretical value in chess

Every chess game would experience some kind of trades at some point. A pawn capturing pawn, only to be captured back immediately for example is a trade. It is an exchange that hopes to gives a piece for another to gain some kind of advantage.

Making key trades to ensure you’re getting a good bargain is an essential skill. It is in fact should be one of the things to learn as a beginner.

The theoretical value is essentially a guideline to which pieces are more valuable than the other. There are many versions that have been created over time. Here’s the universally accepted and most popular one:

Standard Valuations (Reinfeld values and its alternatives)

The table below shows all the pieces in chess and their respective value (Reinfeld values) :

Chess PieceTheoretical Value

The pawn having a one point is less valuable than a Knight with three points. The Knight with three points is more valuable than a rook that has five points.

The higher the number, the more valuable a piece is considered. So trading a bishop for a queen is a good exchange. Since the bishop is worth less than the queen.

Then you are essentially trading all our lower-valued pieces for a high valued one. This is also a good concept when it comes to determining the value of a combination of multiple pieces.

Related: Are Two Bishops Better Than a Rook? (A Comparison!)

Using reinfeld values in piece combinations

Trading multiple pieces could be quite complicated. It’s hard to know whether a bishop with a knight is worth a rook. Or whether the bishop pair can be traded knight with a knight. Or is it really?

Let’s bring out the table again with the Reinfeld values:

Chess PieceTheoretical value

Here, we know whether to trade a piece when it has a lower number. A rook can be traded for a queen because it has a lower number. But can we trade two knights for a queen?

The way we go about this would be instead of just comparing one piece values with another. We actually have to add both pieces that were going to trade for another one. The two knights for example total an amount of 6.

Each knight is worth 3 points, so 3+3 equals six. We add the value of the combined piece and compare it to the piece we’re about the trade. The queen is worth 9 points.

So if we’re going to take the initial principle of trading lower pieces for higher pieces. Then it is okay to trade two Knights for a queen. Since 6 is lower than 9. I hope you’re starting to see my point.

But even this model is not absolute. In fact, the whole theoretical value model is out for the entire debate. One of the reasons is the murky side of the knight and bishop’s actual value.

The Knight Bishop issue

Seeing the Reinfeld values, we are led to believe that the bishop and the knight hold the same priority. This couldn’t be further from the truth. It’s actually quite complicated.

To summarize, the bishop is stronger of a piece in a variety of positions. Leading a lot of players to speculate it to be slightly higher than the Knight. This leads us to some other forms of this theoretical value.

Alternatives to the reinfeld values

The following table was presented by former world champion Bobby Fisher:

Chess PieceTheoretical value

As you can see, it is quite similar to our original system. The only difference is that the bishop is slightly more powerful. This would lead us to believe the trading knight for a bishop may not be so equal as we think.

A bishop is usually slightly more powerful than a knight, but not always – it depends on the position.

(Evans 1967)

This is only one of the many samples. Some of which are specifically created to address the knight bishop issue. Some books actually give the value of the bishop as 3.5.

Meaning the bishop pair are almost 1 point (like a pawn) above the Knight pair. But even this is not entirely accurate. There is one thing that ignores all of this which is the most important.

Positional factor of the theoretical value

Chess is a positional game. One cannot say to always trade the rook for a queen. All exchanges should play under the context of the position. Maybe you can’t capture the queen because you’re getting mated.

Or maybe you could capture the queen but you’re giving off a rook and two pieces via a tactic. There is just so much to consider in a positional context that ignores all the theoretical guidelines.

It is difficult to compare the relative value of different pieces, as so much depends on the peculiarities of the position.

Edward Lasker

There are even cases where it is ideal to sacrifice an exchange just to hold a position. Sacrificing an exchange means trading a higher value piece for a lower value one. Which is something we said we need to avoid.

But if necessary to prevent a checkmate for example, should be done.

Related: Which Bishop is Better, Light-squared or Dark-squared?

Engine evaluation can alter the value of the pieces

Looking at an engine, the thing gives a number during chess evaluations. This is based on the theoretical guidelines. It can give a +1 for a position. Meaning the position is good enough to be almost as if the player is up a pawn.

And It could actually be that the player is not up by an actual pawn. It’s just that the position is bad enough to be treated almost as if. This is a really good way to get a hang of making good trades.

Playing in for example will constantly give you the theoretical advantage while playing the game.

So it’s a very good way to practice since the engine would be doing most of the calculation than just being on your own.

Value does not mean power. Another issue I haven’t addressed yet is the King. We keep spilling out that it has an infinite value. But does that mean that it is more powerful than any other piece? It has more value after all.

Of course not! The stronger the piece is, the likely it has to be of more value. That is true for all other pieces. But not for the King!

It is considered even weaker than an individual Knight and Bishop in the early game. It’s just more valuable since the player can’t really afford to lose the King.

In the endgame, where there is usually little danger of checkmate, the fighting value of the king is about four points.

Emanuel Lasker

The king however becomes a little bit more powerful later in the game. Since there are actually few pieces to threaten a checkmate (The King being captured). The king is then used to escort pawns and maybe other pieces.

Related: Is a Queen Better than a Rook and Bishop? (Analyzed!)

Let’s see some examples!

Now you already have a rough idea of the theoretical value. It’s time to implement the thing in real game examples

Here’s that table again just for reference:

Chess PieceTheoretical value

Should you trade a Knight for a Rook?

In this example, white is to move and has the opportunity to exchange a knight for a rook:

Should white do it? Is it favorable? Of course it is! A Knight is worth three points, and therefore trading it for a 5 point rook is quite a good exchange.

Should the Bishop capture the Knight?

What about this sample:

As you can see, the bishop can capture the Knight. But should white do it? The Reinfeld value after all states that they are equal. Of course not! Well, professional players can, since they break principles left and right anyway.

But you as a beginner should not do this. The Bishop is just stronger than the knight in a lot of positions. Hence why most players put it at .5 or .025 higher than the Knight.

It specifically addresses this one trade saying “don’t make this exchange” What about piece combinations?

Piece combinations

This section contains theoretical values samples dealing with multiple pieces.

Should you trade a Rook for a Knight and pawn?

Look at this one:

White is able to capture the knight and the pawn with the rook and queen.

Which you can see here:

White just traded a rook for a knight and pawn. These are two pieces for one (well a pawn is not called a piece but you get the point). But that doesn’t really matter since we’re following the theoretical guideline.

So is this a good trade? What do you think? Heck no! The knight and the pawn collectively equals an amount of four points (3+1). The rook that is about 5 points, is higher valued than this.

White just traded a higher valued piece higher than the combination of its exchanged parts. This is therefore a bad trade.

Should you trade Queen for three pieces?

Take a peek into this diagram:

The queen has the option to capture the knight for three pieces.

Since after Queen captures and Bishop recaptures, the rook can take the other bishop due to the check on the side:

Essentially the question being is this a reasonable trade? Doing the math, two bishops and a knight is equal to 9. The queen is valued at 9. So is this exchange possible?

Of course! but things are not that clear yet. This is the kind of position where the player has to make a choice It’s not a wrong move to do something like this, it’s just that some players prefer the queen more than 3 pieces.

Related: 1 Queen vs. 3 Minor Pieces: Which is Better? (Truth!)

I personally think that those three can easily outplay a queen. But this is up for argument. This is just another demonstration of how the theoretical guideline can only tell us what’s possible, not guide us.

Positional Factor

The theoretical values are good, but not absolute. Remember when I told you that the position dictates all? Even the value of pieces in specific situations? These are the samples.

Giving up the queen for a rook.

It’s white’s turn to move here:

The rook is attacking the queen. The queen has to move right? Since it is equal to 9 and rook only has 5. You can’t afford to trade a higher piece for a lower one. You can’t right?

Wrong! In this example it is best to give up the queen. The King after all is caged on the back rank.

After queen captures rook and bishop recaptures, rook capture the bishop:

And that is checkmate! After the rook reaches the last rank, the king has nowhere to go. White won. This is an example of how a positional condition changes the value of pieces.

It is correct to give up a nine-point piece here since it will deliver a checkmate.

An active Knight and Bishop for a rook and pawn

See this:

This is a common position in chess. Black can choose to give up the knight and bishop for a rook and pawn. Using the guidelines, The knight and bishop are equal to 6 (3+3).

Or even 6.025 (3+3.025).

But let’s just say it to be six (since 0.25 is really just the ability of the bishop to be more powerful
in open positions). The .25 is really just in place to make it slightly stronger than the knight.

Let’s say black chooses to do this:

Black gives up the knight and bishop for rook and pawn. A rook equals 5 points and a pawn amounts to 1 point. Five plus one is equal to six. That is equal to the amount of a knight and bishop.

So is this trade good? What do you think? It is not! It can be in other positions but not this one. The bishop and the knight in this case are what we called active pieces.

They are the pieces that have already been moved or developed. Meaning they are useful! Plus you’ve already used turns to activate them! And you’re exchanging it for this lonely rook.

This is a very passive piece that got a pawn in its way. And you just trade two active pieces for that. It would be better if the value is at least not close to equal (6/6).

But since they are, this is considered a bad exchange.

Final thoughts

Achieving a checkmate can happen in multiple ways. Sometimes it will be very straightforward, which is easy and awesome!

But most of the time, mounting stronger pieces than your opponent’s until you deliver one can
be the right choice. This is what the theoretical value is for.

The guide beginners need to understand when applying this concept. Have fun and play chess!