In this Chess Problem under the spur: A. 2…Nxb4 (a little more than a third of the way down the page) I find the notation ± 2.16. (Basically, Black has spared the Queen by exchanging a Knight for two pawns.)
I thought I had a basic understanding of what ± meant, but I have never see the numerical evaluation used before until this problem, and there are others farther down the page, including ± 2.06 and a symbol that looks like an ‘=’ over a ‘+’ and -0.91.
The explanation at the end of the problem is that the numeric values come from Fritz at 13 ply. I suspect I don’t understand any of this as well as I thought since I’m getting nowhere with Google.
± means decisive advantage for white (-+ means decisive advantage for black). =/+ means a slight advantage for black. The number is basically just a numerical representation of this. They are not meant ot necessarily be read as a whole, but two separate ways of conveying similar information.
1.00 is a pawn advantage. The computer calculated the advantage and spits out a number for it. So having an extra pawn might be +1 and a castled king might be .2 or something, etc.
The numeric values are the evaluation of the position by a chess computer program (Fritz is a popular program). The evaluation is negative if black has the advantage in the position, and positive if white has the advantage. The unit of the evaluation is pawns, so +2.06 means the chess program thinks white has the better position by about 2 pawns, and -0.91 means it thinks black has the advantage by just under a pawn.
± means a large advantage for white; -+ means a large advantage for black. += or =+ mean a smaller advantage for white or black. These are all sometimes written as one symbol, like “+ over -” for ±.
“ply” means a single move. “13 ply” means the chess engine looked 13 moves ahead in its evaluation of the position.
Thanks for the quick answers all! I guess I did understand the ± notation but started to wonder if all along it had implied an actual numeric addition or subtraction.
I am fascinated by the methods used to evaluate positions in chess software. Is there a site that reproduces or discusses how these types of numbers are generated? ‘Fritz’ doesn’t seem to be specific enough.
There are some entries in Wikipedia, such as this one, which would be a good place to start.
At a basic level, there are two pieces to how a chess engine works. First, there is an evaluation function. This piece is able to look at a chess position, and assign it a value. A very basic evaluation function might just count up the material for both sides. A more advanced one might also look at things like king safety, piece mobility, pawn structure, and so on. It’s important to understand that this piece does not look ahead at possible moves; it is only evaluating the static position.
The second piece is the search or tree function, which explores the tree of possible moves from a given position. For example, for a basic complete 13-ply search, the search function would generate all possible 13-move sequences, and then apply the evaluation function to the end position of all of them. From this, the program can decide on the best play for both sides, simply by assuming white will play moves which force a higher evaluation, and black moves which force a lower evaluation.
Now, in reality, engines never just do a straight 13-ply search like this. Imagine a case where on the 13th move, white captures black’s queen. This will make the evaluation function very happy, and it will rate such a position very highly. However, it might be the case that on the next move, black can just recapture white’s queen, or even checkmate white. The engine wouldn’t realize this, because it never looks at that 14th move; this move is beyond the horizon of the search. To combat this problem, the search is modified to be a quiescense search. This means that the search function keeps adding moves until it reaches a quiet position, where there are no immediate changes coming, like captures or mates. This way, the evaluation function can be applied without (usually) falling victim to this horizon problem.