Poker-AI.org

After many years of exploitive bots, I thought I'd have a play with optimal bots. I have yet to produce a bot worth shouting about, let alone unleash on the world, so this is a hypothetical question.

So, optimal bots are produced by some form of strategy convergence. That is, they devise strategies to beat an existing strategy until they can't improve any more. That produces some form of game tree which tells us what to do in each situation. The theory is that we are unbeatable, so if someone plays our strategy, it's a draw, if not, they lose.

So let's say I've build my 400TB game tree for full ring NL, we sit down in EP, UTG fires off a 200BB open shove.

We take a look at our game tree to work out what we should do, but this action is so sub-optimal, that no node exists. It's not something we'd ever do, and therefore we don't know how to respond to it. How do we deal with this kind of situation if an optimal bot is unleashed on the real world?

Well, if you solved the full game, it would account for that opponent action, albeit suboptimal. However, for abstract games, you would do state translation if a branch doesn't exist in your game.

I can't get my head around how we'd solve that, even in the full game tree.

The situation in my head is this:
For us to solve it, we have to be able to put him on a range, but we assume everyone is playing optimally. As no optimal player makes that move, there's no range we can attribute to that action, and therefore it can't be solved.

Please explain where my thought process is going wrong.

In the full game tree there are sub-optimal actions, there are all actions in the full game tree. I doesn't mean your strategy will converge to use them all, though.

I understand that, but if an action is never taken, how do we attribute a range to that action to be able to solve it?

You still probe the action....

But what would the range of that action be?

What algorithm are you using, CS-CFRM?

This is purely hypothetical at the mo. I don't understand how we can solve a node that has no range associated with it.

I can only answer pragmatically -- look at probing CFRM.

If s(i) = 0 then there is no strategy update, but you still traverse the tree and update child nodes.

why is that difficult to solve? You assume the worst until told otherwise as an unknown..so your range is something like AA-TT, AQ, AK

Oh..nevermind..if they are playing optimally how to do you solve it. I keep forgetting you guys are going for the NE which is way way over my head...

Maybe you could get an answer to your question by using amax's cfrm code to solve one card poker.

I've got a 1 card poker solver that I wrote. But in 1 card poker there are no actions that are never taken. Every node therefore has an associated range and can be solved.

I'm working 'outside the box' as they say here. Designing a new method of machine learning that specifically aims to (pseudo) solve complex high variance games with massive game trees. But I can't figure out in my head how to deal with this problem.

My eventual aim is to produce a decent 6 Max optimal bot.

I think http://www.cs.cmu.edu/~ggordon/poker/ disagrees. player 1 never bets on the first round if he holds a 6

- Or do you mean actions that are never taken regardless of holding?
- Could you force your algorithm to take all actions at least once at the beginning of training?

This

If I was to force it to take an action, that still wouldn't be a realistic range for that action, so that node still wouldn't be solvable.

The pseudo optimal strategy needs to perform the action for us to have a pseudo optimal range on that node. If that action is never taken by the strategy, that node can't possibly have a range.

I think CFRM and Fictitious Play both force actions to be taken at least once in the way the action probabilities are initialised. As the algorithm runs the probability of unrealistic actions drops quickly, but the response action to the unrealistic action is still in place. If your algorithm is significantly different to CFRM or Fictitious Play then I can see you might have a problem, but without knowing more about the algorithm it is difficult to comment.

Anyway, another suggestion: just use the response of a "nearby" node

Ok, so let's say an action is forced, and Mr_X shoves 32o UTG, then everyone folds to us on the BB. Our optimal response to that is to call with everything. If that's the only time the action is forced, then our response to call with everything will remain in place. While their initial move was definitely suboptimal, so it our response, and it'll never be updated.

Would this problem also occur with fictitious play / CFRM?

In CFRM and FP the action probabilities don't jump from their initial values to 0 or 1 in one iteration so I don't think what you describe actually happens. There has to be some advantage to such a slow method

I don't know if this is relevant to the discussion, but this isn't quite true. There are lots of strategies that will draw with a NE strategy.

Also, I don't know if having more than 2 players affects things either.

Either way, we're still not going to know what the correct response is to a shove UTG.