I had a similar naive thought, but it doesnt resolve easily. For starters, Black can do the same thing just a move behind.
Second, if you ever hang your queen two ways at once - one of them could be a less optimal take (-5 is not as good as -8)
Third, whoever is a move ahead in a race of taking pieces will be the first to run out of weak pieces to take. Their available move pool is shrinking faster. Not sure how it would play out, black would need to cater to it by removing defenders and hanging pieces of their own, etc.
That said, first move advantage does seem strong still due to how forcing a queen can be. An example would be 1.e4..e5 2.Qh5..d5 3.Qxf7#
The best way to find out the best strategy for Human Chess is to train AlphaZero to play it, and learn from its example. Then we can make a Human Human Chess variant where you lose the game by playing the top move suggested by this newly trained engine.
It is an interesting theoretical question whether we can have Aleph Zero Human Chess where Human(Human(...(Chess))) is applied infinitely, approaching Aleph Zero trainings of AlphaZero, or we get a redundant variant after some application where further application of Human() no longer produces a new variant.
The answer is no: every time you apply Human(), you reduce by one the number of legal moves at every given game state. After some finite number of iterations, there are no longer any legal opening moves.
With this variant, since there are a finite number of legal board positions in chess, and Human^n chess is simply chess with a finite number of moves prohibited at each board position (claiming is the same as resigning, in this formulation), there are a finite number of distinct Human^n chess, so the mapping Human^n-1 chess -> Human^n chess must eventually reach a cycle (potentially of length 1, i.e. a fixed point).
I’m not sure about a straight-up cycle. I think it requires determinism, whereas the engine is not necessarily deterministic (eg. NN based ones like AlphaZero).
I think it’s possible that at least 1 position (and probably a lot more) will have more than 1 optimal solution. If the engine is not fully deterministic, then it’s possible instead of a normal cycle, there are a fixed set of strategies at each n that form a cycle, but no single sequence that repeats.
The other thing that would compound this is that no current chess engine solves the game fully. There would be even more positions that have multiple “optimal” solutions if the engine only looks ahead to bounded x.
That's a good point about non-determinism, although I wonder if there are known convergence/stability results in the ML literature that allow you to effectively ignore that detail (i.e. it seems plausible that you could get something like "human^n chess always stabilizes at some fixed amount of training time/computational power"). You can also just fix the randomization seed, but that's obviously a less satisfying result.
> The other thing that would compound this is that no current chess engine solves the game fully. There would be even more positions that have multiple “optimal” solutions if the engine only looks ahead to bounded x.
I'm not sure this is an obstacle; we're explicitly excluding the computer's preferred move, rather than the necessarily optimal move, after all. You could easily play human chess with the engine from (e.g.) Battle Chess, which honestly is sort of an interesting idea in its own right.
Second, if you ever hang your queen two ways at once - one of them could be a less optimal take (-5 is not as good as -8)
Third, whoever is a move ahead in a race of taking pieces will be the first to run out of weak pieces to take. Their available move pool is shrinking faster. Not sure how it would play out, black would need to cater to it by removing defenders and hanging pieces of their own, etc.
That said, first move advantage does seem strong still due to how forcing a queen can be. An example would be 1.e4..e5 2.Qh5..d5 3.Qxf7#