Values of pieces

Hello Chess.com team. The only noteworthy issue I can think of right now is the (mathematical) value of the pieces, even though I'm perfectly aware this is directly dependent on the situation, e.g. a rook will do much more for you in the endgame than does a bishop and therefore win the game. But I have seen in some chessbooks and at chess.com that the values of the pieces are described as pawn=1, knight=3, bishop=3, rook=5, queen=9, while the king is rated as infinite, even though he occupies the same amount of squares than does a knight. Bobby Fischer credited the bishop 3.25 points in his book 'Bobby Fischer Teaches Chess'.

All these estimates are wrong in my opinion. I always had a feeling that there is something that feels 'fischy' about it.

Now, the way I determine the value of the pieces regardless of the overall situation on the board on any given moment, is to choose one of the four most central squares on the board which would be d4,e4,d5, or e5 and count all the squares each piece can possibly occupy or control from that spot.

A pawn always controls 2 squares no matter where it stands. Of all the 64 squares on the field, that's 3.125%

A knight can jump to 8 squares, that's 12.5%. Same with the king, although he cannot reach as far as a knight.

A bishop has got 13 squares, that's 20.3125%

A rook manages 14 squares, that's 21.875%

The queen commands 27 squares which make 42.1875%!

So, with the pawn's 3.125% counting as 1 point, it follows through simple calculation that the knight is worth 4 (as is the king, theoretically), the bishop 6.5, the rook 7 and the queen 13.5.

I was wondering how did the other evaluations come about?

You know, I like things as precise as possible.

Good luck with the answer, Werner 'Chessonimo' Wilding

Since, as you note, the actual values vary wildly with the position, I don't see the sense in working out "exact" values. There will never be a position where they apply.

They're just meant as a tool for beginners, when they calculate a long series of exchanges, they can try to keep track of the "points" to see if they are suddenly 3 down or so at the end. No precision is needed.

At higher levels, you stop doing that and instead visualize what is left on the board, and who is better in that position.

You definitely overrate the bishop, remember it can only ever move on one colour. the only reason it is valued the same as a knnight is because of it's higher mobility. Two bishops together, however, could maybe be worth mote than 6?

One problem with your estimate is that a knight stands better on the 6th rank than 4th or 5th, so that directly influences it's value. Likewise an optimally places rook is more likely to be somewhere near the edge of the board so as to control as many squares along the rank or file and still be far away from enemy attacks.

The standard point count came about by people reckoning minor pieces to be worth 3 pawns in an endgame scenario while rooks could hold off a minor and 2 pawns, while the queen was roughly equal to 2 rooks. The queen was later recognized to be slightly weaker than 2 rooks so 1 point was removed from her point count. A single bishop may or may not be strong than a knight, but the pair is better in the vast majority of situations. That's why some masters say to count the pair as an extra 1/4 or 1/2 pawn advantage.

Tarrasch gives a pretty interesting read on his value for given exchanges, though he doesn't strictly mention points so much as fractions of a pawn.

Another factor to remember that in the opening or early game a knight is more valuable than a bishop because of limited mobility due to number of pieces on the board, and later for the opposite reason a pair of bishops is better than a knight because it can attack for a distance, but only in tandem due to the fact that it can only attack on it's own color.  Most raters give the bishop a slight count just over three and a knight three.

Imagine an empty chessboard, put a pawn on a2 , which TWO squares does it control ? It doesnt ! It only controls one !  So,  back to the drawing board for you ! 

The knight can jump over pieces as well as navigate through the board in ways other pieces cannot.  It is the only piece that can attack a queen without having to be defended. (Assuming there are no immediate tactics in the position)

You're right in this much: the value of each piece corresponds to its mobility. However, the devil is in the details. Consider for starters, the relative mobility of each piece on e4 (as you suggest) and then a2 (per Reb's suggestion). Remarkably, the rook's mobility did not decrease, but every other piece did.

To everyone: No need to get cranky over the issue, was just sharing some of my thoughts and calculations, since I saw in Bobby Fischer's book that he gives the bishop 3.25 points. ?

I know that those calculations are not applicable throughout the whole game, and it was never my intention to be right. That's baloney. But viewed from the center of the board they are as precise as possible, that's all.                    Case closed.

that's how early computers evaluated positions, of course this way is very wrong if you start dabbling with positional chess. and another side remark. rook vs bishop is a draw with correct play in most cases with very few pawns.

There could be a theoretical value once the game gets started and a completely different value -though highly relative- once we've come to a certain position(s). I tend to value knights higher than bishops but, beware, a couple of bishops can do as much 'damage' as the queen in any given open position. A well-placed knight in the centre, let's suppose white and having the opponent's white bishop gone will surely become really handy.

Good initial posting and quite an interesting discussion. Probably we won't find the right answer, like in many facets of chess. Just for the sake of argument and with no intention of opening another thread, does anyone know what the best opening is? or what's the best strategy for end games?