I am not an expert on stockfish source code, but my understanding is the following.
It is true, that the 1 piece equals 3 pawns approach is pretty accurate, surprisingly so. However as you are probably aware, when evaluating a position, we consider many other aspects as well, such as piece activity, space, king safety, etc. The difference however ...
The answer by MikroDel gives the commonly-used "Reinfeld values" of pawn=1, bishop=knight=3, rook=5, and queen=9 (kings are essentially worth an infinite number of points, because the game ends if it is lost). While this is a good guide, chess is rarely that simple. Many books will give the value of bishops as 3.5 instead of 3, simply because they are often ...
White to move:
[FEN "8/q1P1k3/8/8/8/8/6PP/7K w - - 0 1"]
Since my example is rather contrived and artificial, I'll also say that the so-called Lasker trap in the Albin Countergambit gives a more realistic setting, and one where a knight promotion is the best option as early as move 7:
1.d4 d5 2.c4 e5 3.dxe5 d4 4.e3 $2 Bb4+ 5.Bd2 dxe3! 6.Bxb4 $4 ...
The point system in chess gives a rough indication of how strong each piece is. So the short answer to your question is, yes, a rook is more valuable than a knight, and so in the vast majority of cases, if you can trade a rook for a knight, you should do it.
This does beg the question, however, about why a rook is considered more valuable. At its best, a ...
Points in chess mean nothing with respect to the actual play of the game with regards to the rules. They are only a reference to give players a general sense of what value each piece has relative to the next piece.
In essence, if you lose your queen, 9 points, but promote a pawn, you gain 9 points minus one for the pawn, so you would still be down one in ...
Rooks are more suitable for open games where there are open lines. Knight are better for more closed games. Knights have the benefit of jumping over other pieces and rooks have the ability to move quickly whereas knights move very slowly.
Also, remember that you can't checkmate with just a Knight and King, so Rooks are probably more powerful in the endgame ...
During round 9 of the Istanbul 2012 Chess Olympiads, at the Nakamura-Kramnik table of the USA vs Russia match, we've witnessed another one of those promotions to knight at move 62 by white.
The relevant position (white to play):
[fen "8/2P1k3/8/8/5p2/5KbB/3pp3/3N4 w - - 1 62"]
1. c8=N+ (1. Kxe2? f3+ 2. Kxf3 Bxc7)
We can see here that if
After answering this question, I was reminded of another important situation where underpromotion is necessary:
[FEN "8/8/8/8/8/2K5/1p5R/2k5 b - - 0 1"]
1... b1=N+! (1... b1=Q 2. Rh1++)
In this position, 1...b1=N+ is the only move to draw. Any other move will allow a quick mate, but after knighting the pawn, black sets up a drawing fortress.
Pawn - 1 point
Bishop, Knight - 3 Pawns
Rook - 5 Pawns
Queen - 9 Pawns
The evaluation depends on the position.
In some situation you will find it equal or good to give you Rook and Pawn (6 Pawns) for Bishop and Knight (6 Pawns). But it is also possible that two light pieces are more valuable than Rook + Pawn.
The value of pieces given to you will be a ...
In Claude Shannon's paper of 1949, he quotes those values as part of his evaluation function:
Most of the maxims and principles of correct play are really assertions about evaluating positions, for example: -
(1) The relative values of queen, rook, bishop, knight and pawn are about 9, 5, 3, 3, 1, respectively. Thus other things being equal (!) if we ...
As has been said, in ordinary chess the points do not count, and the only person who can definitively tell you your school's rules is your chess coach.
But that said, the purpose of looking at the points is to be a quick way to answer the question, "who is winning this game?" So if you promote, it makes sense to take away those points (and give him a point ...
There is always a situation where one piece can be better than another.
Rooks are superior to knights because they control more squares, and have more mobility. Also since they control whole ranks and files, they are able to bound the enemy pieces while knights and bishops are much more limited in that regard.
While I don't think it's reasonable to list every noteworthy situation, here are a few more that will probably be good general guidelines. You can use rules-of-thumb like this in order to evaluate material imbalances in your own games:
the bishop pair may be worth a rook and two pawns
the bishop pair and a pawn is worth a knight and a rook
a knight on the ...
There's a great analysis/article about this by GM Larry Kaufman available here.
Pawn = 1
Knight = Bishop = 3.25
Bishop Pair = 0.5
Rook = 5
Queen = 9.75
There's also a lot more detail in the article about what situations favor which groups of pieces. For example, when B+N is better than R+P, or when Q+P is better than R+R, etc.
You need to understand that the point system is only a rough guideline meant to assist you in evaluating positions or in deciding on potential exchanges. Many factors, particularly the pawn structure, influences how valuable pieces are. Rooks tend to be better in open positions with fewer pieces/pawns on the board, bishops can get hindered in closed ...
If anything, it would be advisable to trade one's queen for the opponent's rooks, not vice versa. But it all depends on the position. If my opponent's queen is particularly useful to him and dangerous to me, and my rooks haven't been well developed, especially if I'm already ahead in material, I wouldn't hesitate to exchange my rooks for the queen.
It's possible to use logistic regression (a statistical method) to estimate the predictive values. This way, you wouldn't need anyone to try the game at all.
http://www.sumsar.net/blog/2015/06/big-data-and-chess has the details. I personally tried the method, and it was a good start.
The method estimates the value of each piece by predicting how they ...
Please note that those values are "abstract", later to be modified by the specifics of the position. For example, even though a knight appears 0.8 pawns less valuable than a bishop, it could be that bigger bonuses are awarded to well-placed knights than for well-placed bishops, turning the balance around.
It's also worth noting that the "3 pawns equal a ...
I agree with Xaisoft, and just want to add that in an open game, a rook can be very effective to reduce the opponent's pawns and keep the opponent's king "in place". While it is true that knights can be mobile in a close game, they are also very predictable. That being said, personally I'd be happy to see an opponent lose both of his/her knights.
Here are some things to consider when thinking about the strength of a knight vs. a rook (and much of this goes for other pieces in relation to the knight as well).
At the height of their power a knight can only ever attack 8 squares. On an open board, if placed in the a1 square, the worst placement for a rook, a rook can attack 14. ...
There are even positions where one promotes R or B to save a draw by getting stalemated (rather than win by avoiding stalemate). One example is the Traxler-Dedrle setup:
[FEN "4rN1K/5qP1/8/8/8/8/k7/8 w - - 0 1"]
1. g8=B!! (1. g8=Q Rxf8 2. Qxf8 Qxf8) Rxf8
WTM loses with 1 g8Q? Rxf8 2 Qxf8 Qxf8+ but draws with 1 g8B!! when Rxf8 is stalemate (NB the g8B ...
Ralph Betza tried to do this and he wrote a series of six articles about this, starting with this one: http://www.chessvariants.com/piececlopedia.dir/ideal-and-practical-values.html
Ideas to determine the piece values include the following factors
average mobility (clearly the dominant factor, but hard to bring it down to numbers)
type of ...
Just to put a point on this:
Does the fact that the knight is worth 2 less points than the rook make it less valuable?
This is looking at it upside down.
What matters in an exchange is getting some gain. The points are only a simple tool for estimating that gain.
If an exchange that would be a point-wise loss gives you the opportunity to checkmate the ...
Though one cannot trade one's king for other considerations -- and in this sense the king cannot be evaluated -- the king still has a practical strength as an attacking and defending piece in the many concrete positions in which no immediate mate is in view -- especially during the endgame. This strength can indeed be evaluated. World Champion Emanuel ...
The values of the pieces derive from which piece exchanges are considered desirable and which are not. Knowledge of desirability of piece exchanges usually comes from having played many games, but it is probably also possible to mechanically extract this knowledge from a large collection of games played by skilled players.
Another option is to use an ...
A clarifying comment says "Pawns can be placed in any of the first 3 rows.
Any other piece must be placed in the back row. White moves first unless
black used less points to construct their army." So the position I gave
earlier doesn't work, but since Black is allowed to move first with fewer than
39 points there's still a forced win:
Here is a fun tactic, involving underpromotion, to finish off the game if you are two connected pawns up in a rook endgame. I saw this in an endgame manual a long time ago, but cannot find the source anymore. The tactic is totally unnecessary as white has other ways to win. Still, it's quite impressive.
[FEN "r6k/8/6PP/5RK1/8/8/8/8 w - - 0 1"]
1.Rf8+ Rxf8 ...
[FEN "8/2P5/8/8/3r4/8/2K5/k7 w - - 0 1"]
1. c8=Q? (1. c8=R!) Rc4+ 2. Qxc4
When you said it made no sense to promote to a Rook or Bishop, it brought this position to mind. Here, if White promotes to a Queen, the game is drawn, but if White promotes to a rook, White wins.
on 1. c8/Q Black would answer 1 ... Rc4+ 2, Qxc4 stalemate. But on 1. c8/R 2. Rc4+ ...