in addition to convergence issues, i'd be nervous also about systematic errors introduced by the way you limit the size of the game tree.

e.g. limiting strategic options postflop could decrease the positional advantage and favor the BB. and any simplifications that, say, reduce the number of cards that can come off on later streets, will make it more valuable to get to postflop with certain hands (and thus play hands preflop relatively loose/passively compared to solutions for the full game), etc.

hard to say. cool stuff though.

There are lots of ways to investigate this that I haven't taken the time to do yet. Memory size limits the number of information sets, but there are lots of different tradeoffs to be made between the number of bet sizes and how aggressively boards and card strength are grouped together. If two very different allocations turn out to produce nearly identical preflop strategies, I think that would be a strong indication that the approximation is good (and vice versa). It is far from trivial how to perform the card grouping/bucketing, for example how much emphasis to put on board texture and how much on hand strength. I think that doing this right within limited resources requires a lot of poker knowledge (as well as programming expertise to minimize memory overhead and make it fast enough). Thanks for your comments!

Just out of interest, have you been able to 'grade' your algorithm by pitching it against its Nemesis, or some approximation thereof?

I assume you mean one of the strategies produced by the algorithm? No, not really, because I think this is difficult to do and is not so meaningful when I'm still working on ways to make it better. If you search my old posts in the Poker Theory section you will find a post where I describe that I could beat the 20 BB strategy by 0.010 big blinds per hand with a "purified" version of itself, but that really only proves that the convergence is not complete and says nothing about how much it could be exploited for.

K, yeah I was just wondering if you had some measure of how close you were to 'true GTO'.

bump

I am not sure that a GTO computer actually exists postflop... assuming this you can rank the best options based on 2 criteria:

1. Postflop, being in position is better than out of position.
2. If playing one option is the best, than when you reverse positions you are in the worst position.

Option B is essentially Option A except your OOP postflop. So in order the best options from best to worst are:

1. A) as the small blind.
2. B) as the small blind
3. B) as the big blind
4. A) as the big blind

However, if a game theory optimal computer postflop does actually exist, then it would probably be best to play GTO push fold strategies preflop as you are more likely to make mistakes postflop vs said computer.

As a result, then the best options are:

1. A) as the big blind (where you have a slight edge playing nash)
2. B) as the big blind (where you can force the computer to play push fold)
3. B) as the small blind
4. A) as the small blind