"""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."""
...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.
The doubling cube works well in Backgammon because it is a rare example of a popular game with randomness, without hidden information (every information set contains exactly one node of the decision tree, if you want to get extremely technical,) and, critically, with "different endings" (normal win, gammon, backgammon.) Doubling decisions are especially interesting because while they're always objective (it could never be the case that perfect players disagree on the correct move, that requires nontrivial information sets,) it could be the case that:
- 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 .
Go is also winner take all. It's psychologically satisfying to have a big win, in the same way that it's psychologically satisfying to achieve a brilliant checkmate, but in any ordinary game or tournament (outside of certain gambling setups), a win by 1/2 point is the same as a win by 20+ points.
"""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.
The doubling cube works well in Backgammon because it is a rare example of a popular game with randomness, without hidden information (every information set contains exactly one node of the decision tree, if you want to get extremely technical,) and, critically, with "different endings" (normal win, gammon, backgammon.) Doubling decisions are especially interesting because while they're always objective (it could never be the case that perfect players disagree on the correct move, that requires nontrivial information sets,) it could be the case that:
- 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.
This is an important point. Thank you.
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 .
Go is also winner take all. It's psychologically satisfying to have a big win, in the same way that it's psychologically satisfying to achieve a brilliant checkmate, but in any ordinary game or tournament (outside of certain gambling setups), a win by 1/2 point is the same as a win by 20+ points.
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.
There are also objective measures for more fine position evaluation.
For winning/drawn positions: "What is the smallest program that can guarantee your side to win/draw" probably adding some time constraint.
That is a neat variation.