@Teasmeade said in #10:
> so how do you define xs(n) exactly? If it's a computer evaluation, then why do you call it "expected game score"?
I think it was defined in earlier blog as some sort of conversion function. I forgot if it was from LC0 or SF, and if it was win probability or not. I think a refresher might help.
Or I missed an episode (or had an episode....... of memory loss).
@Teasmeade said in #10:
> so how do you define xs(n) exactly? If it's a computer evaluation, then why do you call it "expected game score"?
In a previous post (https://chessenginelab.substack.com/i/154534629/better-approximations) I calculated the expected scores in classical GM games given a certain evaluation. So an expected score of 70% would mean that on average, they make 0.7 points in games where they have this advantage.
Using the expected score instead of evaluation has the advantage that the difference between a +9 and +8 position is much smaller than the difference between a +2 and +1 position.
To me, volatility describes how frequently the directional path of a piece (such as a knight, bishop, or rook) shifts during a game. It quantifies the degree of change in a piece's movement. High volatility suggests rapid and significant changes in direction, whereas low volatility means more consistent movement towards something, like the plan or a line of forced moves. Pieces that work together towards a square have low volatility while pieces all doing their own thing in different parts of the chessboard have high volatility. I would assume engines have high volatile moves, because there is no strategy involved, just pure tactics.
Volatility could also be about the rate of exchanges or the number of exchanges in a game. This method would simply count the exchanges in a game and compare it to chess ratings. Since GM's will resign early, the games will look less volatile than the players that like to see all possible exchanges. So it's not the ideal way to measure volatility and compare it to ratings.
Initially, in the opening, most pieces are aimed at the board's center. As the game progresses into the middlegame, I anticipate piece movements to become more volatile, with directions fanning out across the board. However, in the endgame, piece direction is likely to converge on the opposing king. Therefore, the volatility of piece movement is directly influenced by each player's strategic objectives and chess plan.
To quantify my concept of "volatility" in chess games, I would chart the moves out in a graph and maybe over lap them:
- Renko charts for directional shifts.
- Move average trends for each piece or lack thereof. (nbMoves/piece)
- Stochastic oscillators would capture a piece's movement and indicate periods of aggressive forward expansion or retraction which seems like a volatility index system to use. Most chess pieces tend to move forward and rarely go back to their original squares.
Our own chess insights, if compared to others, could be a way to measure volatility.
https://lichess.org/insights/Toscani/piece/phase
https://lichess.org/insights/maia9/piece/phase
I opened two tabs and flipped back and forth and discovered my Queen in the opening is more volatile that maia9's queen in the opening. Maia9's king in the endgame is more volatile than my king.
Quantify how lucky a human player is compared to an engine.
https://lichess.org/insights/maia9/luck/winPercent
https://lichess.org/insights/Toscani/luck/winPercent
Cheaters would have the same luck as an engine.
@jk_182 said in #12:
>
good. I agree about the engine evaluation not being the perfect measure.
Expected scores is better yet still inherently based on evaluation. I see you have looked into expected score as a function of the evaluation already, but it's only a few points. More data would be great.
Lastly, it seems like your approach is much simpler (which is good). You never seem to mention it although your formula is directly showing the average derivative (square, of course) of a discrete function. Once you say this, there is no need to prove the usage of standard deviation or anything like that. Volatile is change. Change is derivative. End of story.
@Toscani said in #13:
It's interesting to hear that you use the term volatility for something completely different.
I guess to be more precise, I'm talking about volatility in the expected outcome over the course of a game. After working on the post, it was clear to me that volatility is referring to the expected score, but maybe I should have been more clear.
@Toscani concepts (if I gather well) is more about a reductionist approach from board features up. And it seems to be more about position characterization than one of game time series of positions "variation" (terminology collision with chess culture here), which the general language word of volatility might refer to, and other modelling contexts like rating expectation (estimate) varaibility or stock market markers time series might influence the comprehension of the word, as well (did I make a complete sentence, yet?).
It might be more about sharpness board clues.
in some way the other direction of modelling than that of @jk_182.
in summary, on the other hand, but and... (kidding)
1) position versus game
2) modeling flow
3) connotation of words being borrowed from general language
I really like the thought you put in there. I have a remark regarding the value a. I think increasing alpha increases the sensitivity to blunders enormously.
A high change in win-expectation in only one move has significant might have significant impact on the final value. So potentially 2 might be suitable for grandmasters which ususally don't do blunders, but in other games on lower elo this might yield unexpected results.
@jk_182 I know this has nothing to do with the blog, but are you a BTS fan? bcoz of your username. Coz if you are, I am too!