I agree with everything here. Thank you for interesting references and links as well!.
One point I would like to make:
>>On top of that, for poker, you'd need LLM to somehow implement continual resolving/ReBeL (for equilibrium guarantees). To do all of this, you need either i) LLM call the CPU implementation of the resolver or ii) the LLM to execute instructions like a CPU.
Maybe we don't. Maybe there are general patterns that LLM could pick up so it could make good decisions in all branches without resolving anything, just looking at the current state. For example LLM could learn to automatically scale calling/betting ranges depending on the bet size once it sees enough examples of solutions coming from algorithms that use resolving.
I guess what I am getting at is that intuitively there is not that much information in poker solutions in comparison to chess so there are more general patterns LLMs could pick up on.
I remember the discussion about the time heads-up limit holdem was solved and arguments that it's bigger than chess. I think it's clear now that solution to limit holdem is much smaller than solution to chess is going to be (and we haven't even started on compression there that could use internal structure of the game). My intuition is that no-limit might still be smaller than chess.
>>I see. The same applies for Chess however -- you can play mixed strategies there too, with similar property - you can linearly interpolate expected value between losing (-1) and winning (1).
I mean that in chess the same move in seemingly similar situation might be completely wrong or very right and a little detail can turn it from the latter to the former. You need a very "precise" pattern recognition to be able to distinguish between those situations. In poker if you know 100% calling with a top pair is right vs a river pot bet you will not make a huge mistakes if you 100% call vs 80% pot bet for example.
When NN based engines appeared (early versions of Lc0) it was instantly clear they have amazing positional "understanding" but get lost quickly when the position required a precise sequence of moves.
>>On top of that, for poker, you'd need LLM to somehow implement continual resolving/ReBeL (for equilibrium guarantees). To do all of this, you need either i) LLM call the CPU implementation of the resolver or ii) the LLM to execute instructions like a CPU.
Maybe we don't. Maybe there are general patterns that LLM could pick up so it could make good decisions in all branches without resolving anything, just looking at the current state. For example LLM could learn to automatically scale calling/betting ranges depending on the bet size once it sees enough examples of solutions coming from algorithms that use resolving.
I guess what I am getting at is that intuitively there is not that much information in poker solutions in comparison to chess so there are more general patterns LLMs could pick up on.
I remember the discussion about the time heads-up limit holdem was solved and arguments that it's bigger than chess. I think it's clear now that solution to limit holdem is much smaller than solution to chess is going to be (and we haven't even started on compression there that could use internal structure of the game). My intuition is that no-limit might still be smaller than chess.
>>I see. The same applies for Chess however -- you can play mixed strategies there too, with similar property - you can linearly interpolate expected value between losing (-1) and winning (1).
I mean that in chess the same move in seemingly similar situation might be completely wrong or very right and a little detail can turn it from the latter to the former. You need a very "precise" pattern recognition to be able to distinguish between those situations. In poker if you know 100% calling with a top pair is right vs a river pot bet you will not make a huge mistakes if you 100% call vs 80% pot bet for example.
When NN based engines appeared (early versions of Lc0) it was instantly clear they have amazing positional "understanding" but get lost quickly when the position required a precise sequence of moves.