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.
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.
For winning/drawn positions: "What is the smallest program that can guarantee your side to win/draw" probably adding some time constraint.
It's not a bluff, since information is still 100% open to both players, but it changes dynamic a lot.
>""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"
- 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).
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.
Theoretically valid, but that's not going to be a very useful/diable.
A win by 1/2 point or 20 points it suggests a very different relative skill between the two players. Similarly the custom of the stronger player playing white without komi suggests that the point differential matters.
But I want to point out that in theory there is also something more than pure win/ lose/ draw with prefect play.
So instead you launch a desperate maneuver in a hope to either turn the game around or lose by 30 points.
By on February 19, 2026 •
Current computer chess engines include a neat feature: the analysis bar. For example here is the analysis bar from chess.com.

White to move, FEN:
rnb2rk1/ppp2ppp/3p1q1n/4p3/7P/b1PPP3/PP1BBPP1/R2QK1NR w KQ – 0 1
The analysis bar is on the left, and the white portion is 74 “centipawn units” below the midpoint (matching the -0.74 “pawn units” in the top right analysis tab). This means the analysis feels white is at a 74 centipawn disadvantage to black in this position. The question is, what is a centipawn advantage?
Lichess gives a similar analysis and score (in this case -50 centipawns).

From the Stockfish Interpretation of the Stockfish evaluation document we have: “a 1.0 pawn advantage being a 0.5 (that is 50%) win probability.” A player with a 100 centipawn advantage is thought to have a 50% chance of winning (probability taken over chess engine near-optimal variations of play). Notice this is not necessarily the traditional material value of a pawn on the board. The intent is given in a reference graph that we reproduce here.

To use this graph we lookup our centipawn advantage (or disadvantage) on the x-axis and then measure the heights we cross the win, draw, and lose curves at. This reads off estimated probabilities of each outcome. Notice at a 0 centipawn advantage a draw is considered almost inevitable under optimal play. In our case the 74 centipawn disadvantage is shorthand for claiming a 0.23 probability of a loss, a 0.77 probability of a draw, and little chance of a win.
The way the engine likely uses the graph is it estimates probabilities (W, D, L) and then finds the point on the x-axis minimizing the (possibly square) distance of these from all three curves. The resulting centipawn advantage is then an approximate summary of the engine calculation.
Some engines, such as the OSX Stockfish UI show below, report both the centipawns (in this case -98 centipawns) and probabilities together.

Chess players tend to use differences in Elo rating to measure advantage between players. So they may be more comfortable with Elo differences than with probabilities. One can convert centipawns to Elo difference using the following graph.

We see the relation is not linear. The flattish portion in the middle is due to the fact that the centipawn system models draws separate from wins and losses, whereas the Elo system treats draws as half-wins. A 100 centipawn advantage corresponds to an Elo difference of about 190. An Elo difference of 100 is about 80 centipawns.
Chess does not have an in-game point system (unlike games like Go). We are left to choose our own domain of advantage measure. Common choices include: probability, Elo difference, material (pawn and piece counts), position, or time (moves or tempi). The common evaluation taught is an “all things being equal” chess piece relative value with the following simplified values.

Converting probabilities into centipawns is an attempt to use a unit familiar with chess players. In math terms: it is using a logistic link instead of a probability or likelihood ratio.
In chess one is usually not in “an all things being equal” situation. A given pawn may be protecting a piece, so may be worth much more than a point. For example here is the Stockfish estimated change in centipawn advantage for each single piece removal from the standard initial chess board.

Notice not all the pawns are priced at the same number of centipawns. The average value for white pawns is 128 (for white to move) and the average value for black pawns is 154 (again for white to move). So the pawns are averaging to a bit more than 100. It makes sense that the centipawn score can not simultaneously be completely calibrated to the claimed 100 centipawns is a 50% chance of winning and to an actual pawn on the board always being worth 100 centipawn advantage.
Beyond the usual “a pawn is worth 2 or 3 tempi” rule it would be interesting to work out a directly theory of “fractional tempi” for chess in the spirit of “Winning Ways for Your Mathematical Plays” by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy. One idea would be to play over an ensemble of boards, where players alternate over choosing which board to move on (ignoring if it is the white or black turn on each board). Another idea is adding a small random chance of getting an additional move. Some concept like this might allow expressing positional advantage in a direct fractional tempo unit.
Shannon pointed out (Shannon, C. E. (1950). XXII. Programming a computer for playing chess. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 41(314), 256–275. https://doi.org/10.1080/14786445008521796) 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.
As we don’t currently have access to this perfect evaluation function we settle for other evaluation domains such as piece/material values (augmented with positional features), tempi, estimated probabilities, and differences in Elo or matchmaking rating. Total material value plus position came first, as it is easiest to evaluate. Probabilities came quite late as they could not be mechanically estimated in a satisfactorily manner until the 1990s.
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