I agree it is possible to build an LLM to play poker, with appropriate tool calling, in principle.
I think it's useful to distinguish what LLMs can do in a) theory, b) non-LLM approaches we know work and c) how to do it with LLMs.
In a) theory, LLMs with the "thinking" rollouts are equivalent to (finite-tape) Turing machine, so they can do anything a computer can, so a solution exists (given large-enough neural net/rollout). To do the sampling, I agree the LLM can use an external tool call. This a good start!
For b) to achieve strong performance in poker, we know you can do continual resolving (e.g. search + gadget)
For c) "Quantization" as you suggested is an interesting approach, but it goes against the spirit of "let's have a big neural net that can do any general task". You gave an example how to quantize for a state that has 2 actions. But what about 3? 4? Or N?
So in practice, to achieve such generality, you need to output in the token space.
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.
I do believe i) is practically doable today, to e.g. finetune an LLM to incorporate value function in its weights and call a resolver tool, but not something ChatGPT and others can do (to come to my original parent post).
Also, in such finetuning process, you will likely trade-off the LLM generality for specialization.
> you can do a k-NN or some other simple approximation. [..] You can say that about any other game then, no?
Yes, you can approximate value function with any model (k-NN, neural net, etc).
> In poker if you call 25% more or 35% more if the bet size is 20% smaller is unlikely to result in a huge blunder. Chess is more volatile and thus you need more "precision" telling patterns apart.
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).
Overall, I think being able to incorporate a value function within an LLM is super interesting research, there are some works there, e.g. Cicero [6], and certainly more should be done, e.g. have a neural net to be both a language model and be able to do AlphaZero-style search.
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.
I think it's useful to distinguish what LLMs can do in a) theory, b) non-LLM approaches we know work and c) how to do it with LLMs.
In a) theory, LLMs with the "thinking" rollouts are equivalent to (finite-tape) Turing machine, so they can do anything a computer can, so a solution exists (given large-enough neural net/rollout). To do the sampling, I agree the LLM can use an external tool call. This a good start!
For b) to achieve strong performance in poker, we know you can do continual resolving (e.g. search + gadget)
For c) "Quantization" as you suggested is an interesting approach, but it goes against the spirit of "let's have a big neural net that can do any general task". You gave an example how to quantize for a state that has 2 actions. But what about 3? 4? Or N? So in practice, to achieve such generality, you need to output in the token space.
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.
I do believe i) is practically doable today, to e.g. finetune an LLM to incorporate value function in its weights and call a resolver tool, but not something ChatGPT and others can do (to come to my original parent post). Also, in such finetuning process, you will likely trade-off the LLM generality for specialization.
> you can do a k-NN or some other simple approximation. [..] You can say that about any other game then, no?
Yes, you can approximate value function with any model (k-NN, neural net, etc).
> In poker if you call 25% more or 35% more if the bet size is 20% smaller is unlikely to result in a huge blunder. Chess is more volatile and thus you need more "precision" telling patterns apart.
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).
Overall, I think being able to incorporate a value function within an LLM is super interesting research, there are some works there, e.g. Cicero [6], and certainly more should be done, e.g. have a neural net to be both a language model and be able to do AlphaZero-style search.
[6] https://www.science.org/doi/10.1126/science.ade9097