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We have some strategy profile with probabilities for each action at each decision/node but how do we get the opponent response? Do we run the code on itself twice, one for hero and one for villain?

Because I can't continue with villain always calling because as you can imagine that gives the wrong EVs. I got to play around with Pio recently and was amazed at the results and how quickly it "converged" so it's something that's used everywhere but I'm just missing what it is?

hi,

I am estimating villain range using:

1) his player stats. e.g. if he folds vs cbet on flop 50%, then I approximately fold his 50% of range and keep top 50% range.
2) rules. E.g. nobody ever folds full hause, or set if no flush is possible, or straight. Most people will fold low equity hands vs first barrel etc. More rules you have it can be better. I use my poker experience to set those rules.
3) Player category. Fish will call more combos, will call lighter, will overplay value hands. Bad regulars will also call lighter and overplay.

Is this how most commercial softwares do it? I don't remember them asking me for stats like those to compute a result. Also how do you decide what hands villain will raise you with on the river, for example, where stats should be more sparse

It's not always about stats but also about poker experience like said mlatinjo.
If you want to play with stats, you also need to code a part where no one informations is known from your opponent.

You can resume a situation like that :
- In this scenario (board texture, previous actions, pot3Bet .... ) I will say that vilain will raise river with an overpair or better, call TPBK etc ... .

I understand all that but I'd prefer a non-rule-based approach. It seems impractical to implement it in this way, there are far too many board combinations, actions, card ranks to consider for this to be effective. Also, there is no guarantee that a nash equilibria is reached if we ourselves choose opponent's action in an unbalanced fixed fashion such as "raise missed draw always"

I have bot ranges, bot's perceived ranges (what villains think that our range looks like) and villain ranges.
E.g. if i estimate villain's range on river raise, i estimate what value hands he raises using equity vs bot's perceived range and then add % of bluff to that raise range using population bluff raise frequency or player bluff frequency if enough sample.

yes i agree.

You will find that a non rule based approach will not work well. You have to have a combination of rules and equity. Equity is not a good indicator of playability and you will find that raw equity will get you into trouble more often then you think. You would be surprised but it really does not take that many rules to cover all the scenarios. Weak flushes, bottom str8s, under boats etc have pretty good raw equity but they will break your bank if overplayed.

Formulas have issues as well and do not take into account board texture. Just last night my bot bet folded as the EV was better then check calling second set OOP. The math was fine but the problem was it bet to fold on the 6 of clubs which was a total blank on the river. The bet made no sense but the math was correct. Another example of areas in which rules are needed. I bet into the leader on a card that made zero difference on the river. Villain obviously called and it lost. Without blockers or a river scare card it just does not make sense.

True but your opponent estimated range does.
You can entirely explain the scenario, posting vilain hands and we will see where is the problem.

Is it really not that many rules? Also, a small note to make as you're all talking about making an AI to take on online games for profit whereas what I'm trying to make is closer to commerical GTO solvers. So I thought the solver would require opponent to be playing close to GTO too? Sorry for the confusion

edit: It seems self play is the answer here

villain range has nothing to do with being able to rep a value bet on a blank river card. I may have the correct FE vs his range but he will call much lighter if he does not believe me or even bluff raise me. In either scenario I will lose the same amount but there is more implied FE on a scare card or if I have blockers to the nuts.

Yeah its really not that many rules at all. My bot is for PLO and I really do not have that many rules for a much more complicated game then NLH. I would think the ultimate solver would use programmable population frequencies for the limits its playing in. No human can play GTO so having it solve for a GTO opponent does not make much sense to me.

To make my AI I knew the known frequencies I wanted be at. I then constructed balanced ranges and ran them thru a simple simulator to see where they settled at over all board types. The bluffs needed rule sets as I wanted to be very specific on what hands it was betting as a bluff. Equity is not a good indicator at all imo. It is a decent indicator for the value hands but some of them need to be controlled with rules to keep it out of trouble as mentioned above.

If you want to know anything about GTO ask mlatinjo above. He is GTO God.

Lots of good information, thanks for the replies guys