In a computer chess game, each piece is given a value (or a weight) to help quantify the strength of a move or a position. Typical values are : Queen-9, Rook-5, Knight and Bishop-3, Pawn-1, and King-10^10 or more. Some players may give a higher value to the bishop, others to the knight.
In modern chess computer games, are these values fixed during the whole game or are they varying? Moreover, has there been any study of the optimal values that would further enhance the performances of recent AI-based computer games?
Since AlphaZero was able to learn playing chess in a few hours just by simulating a great number of plays, does it use fixed values for the pieces or do they change during the game? And, as the training phase is quite short, could it be used to identify the best set of weights?
As a chess player I can only comment that a value of each piece can be different denpending on the location of the piece and many other aspects (e.g. threats to opposite pieces, especially opposite king, if the piece is a passed, advanced pawn etc). A knight on a1 square has a smaller value than his colleague on. let's say, d4. I'm not a coder of chess engines but I can imagine that the value of each piece should change dynamically after each move and any engine should take it into account.
Regular chess player.
The pieces change in value depending on how they interact and where they are on the board. A pawn's value increases as it gets closer to promotion, A/H pawns will increase more in value as they advance (as they can only be attacked from 5/8 directions. If a pawn has no other pawn in front of it, it is worth more (because of the increased chance of promotion). Other pieces on the board also affect the value. For instance, if all you have on the board are two kings and a bishop, the bishop is worth exactly zero. When all you have on the board are 2 kings and a pawn, if the pawn is unstoppable, it is worth more than 9 (a Queen at the start of play). If the pawn can be taken, it can be worth less than one point. As for AlphaZero, I have not seen the code, but it is absolutely clear from watching its games that it does not have a fixed value for pieces. Chess is a game of interaction between elements (black/white pieces and the board), a fixed value for those elements doesn't get you very far.
Hey, I am a chess international master and actually wrote a small blog post about this issue. https://ido-iba.medium.com/chess-computers-and-the-estimated-value-of-the-pieces-cc5360124be You may also find there the article about alpha zero.
I'd be glad to discuss it further if you wish.
I am a regular chess player (1850 ELO) and I also started searching and found this paper:
"Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm" Silver et al. 2017
arXiv:1712.0181
Hope this might help you!
I thinck there could be a way to set a "right statistical weight" to chess pieces by using the great computational power of Alpha Zero. For example, we can set a relative weight between to pieces by counting the number of winning/loosing/drawing matches consequencing the exchange of those pieces. It could be interesting to see if such relative weight satisfies a transitive principle, so that it could be seen as an absolute weight.
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