Yep, I thought of a similar method: (1) Find a trend between Elo and the entropy of moves during the middle-game. (2) Estimate the middle-game entropy of optimal chess. But the obstacle is (2), there’s probably high-entropy optimal strategies!
Here’s an attack I’m thinking about:
Consider epsilon-chess, which is like chess except with probability epsilon the pieces move randomly, say epsilon=10^-5. In this environment, the optimal strategies probably have very low entropy because the quality function has a continuous range so argmax won’t be faced with any ties. This makes the question better defined: there’s likely to be a single optimal policy, which is also deterministic.
This is inspired by @Dalcy’s PIBBSS project (unpublished, but I’ll send you link in DM).
Yep, I thought of a similar method: (1) Find a trend between Elo and the entropy of moves during the middle-game. (2) Estimate the middle-game entropy of optimal chess. But the obstacle is (2), there’s probably high-entropy optimal strategies!
Here’s an attack I’m thinking about:
Consider epsilon-chess, which is like chess except with probability epsilon the pieces move randomly, say epsilon=10^-5. In this environment, the optimal strategies probably have very low entropy because the quality function has a continuous range so argmax won’t be faced with any ties. This makes the question better defined: there’s likely to be a single optimal policy, which is also deterministic.
This is inspired by @Dalcy’s PIBBSS project (unpublished, but I’ll send you link in DM).
Very cool, thanks! I agree that Dalcy’s epsilon-game picture makes arguments about ELO vs. optimality more principled