What Is a Centipawn Advantage?

I'm not a chess engine guy, but I've talked to some, and, from what I recall, there is a very interesting difference between an engine like Leela Chess Zero (lc0) and Stockfish. Stockfish internally calculates in centipawns while lc0 calculates in WDL's. Stockfish has a model they use that converts their centipawn calculation to WDL's, but it's not _really_ WDL of the position, it's just their estimate of it according to a probabilistic model. Same in reverse applies to lc0. Why I find this interesting is that it shows how they come from different generations, with Stockfish representing the old deterministic style with deep search, and lc0 being directly inspired by Alpha Zero and the new generation of engines based on neural nets. Stockfish has by now adopted the best of both worlds (deep search with a small neural net) and is the better for it, but I still think the developers of both engines banter over who is really producing the True WDL numbers for a given position.

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.

"""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.” 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.

Surprised it didn’t mention until the very end, but since chess is deterministic, there is no objective probability.

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.

fractional tempi sounds fascinating