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 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 ...
The simple and obvious answer is that it all depends on the position of black's pawns and king. In general the further up the board the pawns the better for black provided the king is in contact with the pawns, preferably in front of them.
Worth pointing out that the position you give is winning for white because the pawns aren't far enough forward. From ...
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 ...
Pawn - 1 point
Knight - 3 points
Bishop - 3 points
Rook - 5 points
Queen - 9 points
Rook and Knight - 7.5 points
Rook and Bishop - 8 points
Pair of Rooks - 10 points
Three minor pieces - 10 points
Rook and two minor pieces - 11 points
N.B. The values may vary because of circumstances, but these are the basic values.
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 ...
Start with whatever and tune it.
That's how chess engine programming works - you start with some number, and then tune it. For example you start with -5, then create another version with -10. You get the two engines to play against each other, and the one that wins more often is the "correct" version that you keep.
Of course as pointed out by other ...
As per Hauke's invitation, here is the shortest possible proof game for such a position. :-) This is optimal because at least one promoted queen must move in order to give the Black king a square and it takes forty moves to promote all eight pawns. By the way, White's h pawn does give checkmate in the end.
1. a4 b5 2. axb5 a5 3. b4 Na6 4. ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
First of all, White wins in the diagram you provide, although it's not obvious at a glance how. White plays Qf2 first to stop the king from advancing. Black can't just sit there forever because the White king will eventually eat that a-pawn and come back, so they have to play h4, and then another pawn move. If Black plays g3, White responds with Qf3, and now ...
Have a look at the wikipedia article on relative chess piece values, it provides an extensive discussion on the matter.
To see how you can compare two given pieces, let's consider your bishop vs rook question at a basic level:
A rook's movement is not restricted to a color, unlike the bishop's. This makes half of the board squares inaccessible to a bishop.
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:
The answer is, as expected, "it depends". To answer directly first, 2016 Atomic World Championship (AWC) winner, tipau, put the values as:
Pawn - 1
Knight - 1.5
Bishop - 1.5
Rook - 3
Queen - 6
As a somewhat strong player myself (two top-8 finishes in the AWC) who has extensively analysed atomic chess endgames, I would tend to agree.
The king has ...
[FEN "3k4/6QP/8/4Q3/8/2Q5/QQ4QQ/RNBKQBNR w KQkq - 0 1"]
This is trivial, as already five queens can threaten the whole board. The only thing you must pay attention to is giving Black a last move. Here it is Kd7-d8.
Bonus question for Rewan: An answer with the shortest proof game :-)
The standard is usually to compare pieces to each other (i.e how many pawns is a knight worth, a bishop, a queen etc.?
Another way is to determine piece value dynamically using the idea of "absolute/potential activity" and "nominal activity". This idea is based on the number of squares any given piece controls (and I believe is partly how computer engines ...
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 ...
In my opinion, this is a very difficult question, since the piece values in antichess are not as static as in normal chess and usually highly depend on the game phase and position.
However, there are some rules of thumb which pieces tend to be stronger or weaker, see, e.g., http://poincare.matf.bg.ac.rs/~andrew/suicide/StanGold/theory.htm.
You can also try ...
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 ...
Other than the computer evaluation proving that the Q is better, the biggest problem here is that black basically starts out fully developed since his pieces already have amazing scope, and can quickly coordinate his forces, and attack.
There's no real rule for how much do doubled pawns (or any other kind of weakness on the pawn structure) worse your position. There's not even a rule for piece value, specially if you'll add bonuses for things like centralized knights or the bishop pair.
In general, doubled pawns in a minority or balanced side tend to be less important than in a majority (as ...
In Kaufman's full article, the rook's value is dependent on the number of pawns on the board (as does the knights value). The value of the rook increases as the number of pawns decreases (the value of the knight decreases as the number of pawns decrease).
So he takes into account the variation of the rooks value as pawns decrease, and thus his "redundancy ...
The queen is better. Other than being worth 9 points (compared to the pawns' combined worth of 8 points), the queen is a single powerful unit. White can only move each of his pawns one at a time, making them collectively not nearly as strong as the queen. If White attempts to use all of his 8 pawns to combat the queen, it'll take him 8 moves on each "...
The value of a piece or pawn will depend greatly upon how well it is placed. The common 1/3/3.5/5/9 values are reasonable estimates for pieces which are placed decently but not amazingly well. For various reasons, it may be easier to have the baseline score for a piece represent a piece which is either much worse than typical (so that most pieces would ...