For my part, I find that WDL is more amendable to interpretation. Being up 5 pawns worth of material sort of makes sense, but being told you have a 95% chance of winning makes more sense to me at first blush.
In fact, stockfish's WDL is very rudimentary: it is a function of the centipawn evaluation of the position and the value of the remaining material.
See https://github.com/official-stockfish/Stockfish/blob/a6d055d...
Also, from a computer perspective, a >= 1 pawn is usually sufficient for a computer to win 100% of the time so it's not really interesting and says very little about whether a person could win 100% of the time.
Relatedly, there is an interesting thing that lc0 has been doing as well, where it takes the contempt concept even further, and can beat you with queens odd. https://lczero.org/blog/2024/12/the-leela-piece-odds-challen... It assumes it is better than you and that it shouldn't just give up because you might be up a knight, rook or even queen.
I think you may be mistaking your understanding of stockfish as shallow in that regard.
Where the big differences might emerge is in strategic mid game positions without any clear tactics or forcing moves. There lc0 can somehow "feel" that a position seems better.
Every position is objectively plus infinity, minus infinity, or zero.
The “advantage” is an engine-specific notion that helps prune search paths.
Some chess engines don’t even evaluate an advantage.
For winning/drawn positions: "What is the smallest program that can guarantee your side to win/draw" probably adding some time constraint.
Theoretically valid, but that's not going to be a very useful/diable.
>""under perfect play all chess games be a the same single one outcome of the following (we just currently don’t know which one, “A” playing the white pieces): Mr. A says, “I resign” or Mr. B says, “I resign” or Mr. A says, “I offer a draw,” and Mr. B replies, “I accept"
1) god-mode 1/0/-1 which you could argue is the “true” position 2) engine centipawns which help the search algorithm 3) human evaluation which would distinguish between two positions in terms of a subjective difficulty
For example, two positions might be 0.0 on the eval bar but one position is an obvious draw and in the other position one player has to walk a tightrope of precise moves to draw. Just because that’s obvious to a computer doesn’t mean a human can easily draw the second position.
What I really want to know as a player is how easy it will be for me to win from this position against someone of my opponent's strength, which is admittedly a very hard thing to define, let alone compute.
So in practice, a drop in win probability greater than 14% is considered a blunder on Lichess.
For reference, lichess uses the following function to map centipawn advantage to the probability bar, derived from observed outcomes: https://github.com/lichess-org/lila/pull/11148
From an ML perspective, this is basically logistic regression with a single feature. However, once we leave the realm of theoretical centipawn value and begin to optimize predictive power, we could imagine adding in other things like the players' ELOs or time remaining per player, etc.
I think there are some interesting theoretical differences between predicted win probability derived from Stockfish CP and actual outcomes. As in, you could even imagine predicting positions where certain players struggle and steering them towards those positions. [0]
Mr. A says, “I resign” or Mr. B says, “I resign” or Mr. A says, “I offer a draw,” and Mr. B replies, “I accept.” That is, under perfect play, each chess position is either a forced win, forced draw, or forced loss. The domain of a perfect chess position evaluation function is these three cases as symbols."""
There's an interesting point I've heard of in Backgammon, somewhat related to this statement. Modern Backgammon offers "the doubling cube" as a play option. https://en.wikipedia.org/wiki/Backgammon#Doubling_cube
...basically if you think you're going to win (aka: you have a 200 centi-pawn advantage), you can offer the doubling cube to your opponent (doubling the stakes of losing). If you're playing to win $5, and halfway through you think "yep, 90% chance I'm going to win this one...", you push the doubling cube to 2x (aka: $10 consequence), and kindof like poker your opponent has to evaluate whether it's "worth it" for them to stay in the game.
You might imagine a "2xELO penalty" where White takes a Queen with a Pawn, and then offers "2x, or I'm gonna beat 'ya!". If Black say "Naaah, you just activated my trap card!" and then either accepts "2x" or pushes back at "4x", then it becomes a little more like poker... you think you can beat me, then prove it!
Not that I'm suggesting changing the rules of Chess, but overall I'm really fascinated by the concept of formalized semi-out-of-band risk-taking to potentially end games early.
- it's correct for a player to double and for the other to accept;
- it's correct for a player to double and for the other not to accept;
- the position is "too good to double," because the equity from the probability of a double or triple game exceeds the advantage you'd get from a double;
- all of the above being influenced by the match score, e.g. if I'm 3 points away from winning and you're 5 points away from winning, I could make different decisions than if it were the opposite.
Chess has none of them, the doubling cube would be exclusively a psychological power play, something like "it's theoretically drawn but I don't think you can defend it," which is not a great game dynamic.
In general, transplanting the doubling mechanic without a similarly rich context doesn't tend to work well.
Games like backgammon (that have betting and the doubling cube to continue), Go (which is calculated in stones), and bridge (again having points) have more natural intermediate scoring systems than chess.
In my opinion the "winner takes all" aspect of chess is similar to what makes analyzing voting systems difficult. In a non game context: Aspnes, Beigel, Furst, and Rudich had some amazing work on how all or nothing calculation really changes things: https://www.cs.yale.edu/homes/aspnes/papers/stoc91voting.pdf .
His POV was that "if you don't win, you lose" and my POV was "second place is better than last place". His response was: "if I play poker to get first place it's wildly different than playing for second or third place [and I may end up in last place wildly more often due to risk % or bad beats]"
I've been more used to "climbing" type performance games (ie: last place => mid-field => second place => first place) and in my gut I wanted my ELO to reflect that (top-half players are better than bottom-half players), however his very valid point was that different games have different payout matrices (eg: poker is often "top-3 payout", and first may be 10x second or third).
I think in my mind I've settled on EV-payout for multiplayer games should match the "game payout", and that maybe my gut is telling me the difference between "Casual ELO" (aka: top-half > bottom-half), and "Competitive ELO" (aka: only the winner gets paid).
It's not a bluff, since information is still 100% open to both players, but it changes dynamic a lot.
