How much is a rook worth?

Are rooks worth 4.5 or 5 points? Classically, rooks have been considered to be worth 5 points, but modern European chess theory considers the rook worth only 4.5 points. Which is correct?

More importantly, rooks are worth less in the beginning of the game (so many pieces clutter the board limiting movement) and in general rooks become worth a little more every time pawns are traded off the board.

The standard values (such as 5 for a rook) are more like the typical endgame potential... in other words a typical active rook in an endgame is worth 5. It could be worth a lot more if it's checkmating, or a lot less if it's stuck defending, but in most endgames it will beat a minor piece, and lose to a queen. That's the basic idea.

So when you're not in a technical endgame, instead of thinking in terms of "this rook is 5, this bishop is 3" it's better to think in terms of which pieces are active (activity being some combination of general mobility and being in contact with weaknesses like pawns or kings). So it's more like this rook is a 5 if the game lasts a long time, so I can either wait it out, or in the short term I might sacrifice it because right now it's more like a 2 and their knight is a 6

I have a saying; "Take their rook and break their back, take their queen and break their heart".

If it's not an intended sacrifice or trade, opponent's tend to resign when either of these occur early in a match. At least from my experience playing at the novice level (@800 matches on chess.com - two accounts).

It’s a good question because I always hesitate trading my dragon bishop for the rook in the corner. The dragon bishop is such an important piece because it has influence on a long diagonal and protects my king.

Weakening my king safety for +2 material advantage doesn’t always translate to a win.

Could be worth a pawn

Depends how much they bid on Ebay

lmao

agreed, depends on the position.

The problem is that the answer, like almost all answers in chess, is positional. 

Rooks are the only pieces that start the game hanging, but they're so useless in the opening that no one cares or notices. As the pieces come off the board and the files start opening up, though, they become more and more valuable. 

R = 5.63 P
See table 6
https://arxiv.org/pdf/2009.04374.pdf 

too muich

the value of a piece changes over the course of the game

Interesting resource, thanks for the link.

Agreed and subtle details can make all the difference. I'd say Rook being worth 5 points is a good estimate, but this isn't an absolute value. In positions where the Rooks can't get open files, they can be easily outperformed by a minor piece (Typically, it is safe to say I'd rather keep an outposted Knight on the 6th rank than capture an inactive Rook on the 8th rank for instance). Similarly, connected passed pawns in the endgame can sometimes rival a Rook's defensive efforts.

With this said, give the Rooks an open file to infiltrate or the coveted 7th rank and the Rook can easily command the attack and compete with even a Queen.

It isn't a good mindset to get too attached to arbitrary piece values; this might make you hesitant for good moves like an exchange sacrifice that would otherwise be calling out to be played.

If it just a plastic piece from a cheap set then not much.. If it is part of a historical significant set or sapphire encrusted precious metals from a priceless set then quite a bit..

Just stick with 5. In a game you don't want to be like: I'm up an exchange. It is risky to sacrifice a pawn? Let's see 4.5 - 3.15... and end up with useless decimals

What most chess players do not realize is  the value of each piece changes after every move or half move of the game.

Also in the opening position knights and bishops are worth quite a bit more than 3 points.  Also the bishop starts out worth more than a knight. 

If people realize this--this discussion would change.

5 is right. A rook and a pawn is worth a knight and a bishop.

knight and bishop is worth more in the early and middlegame compared to a rook and a pawn