I wonder how much EV it would lose against a maximum exploitative gto strategy, and if it would be useful to improve the understanding of the favorite roles of each hand in any given spot.

Is it possible?

Has anyone tried this?

Thanks

It's possible in Piosolver menu -> Tree -> Round Strategy.

I ran a simple tree and then rounded the strategies of both players over flop+turn+river and then checked exploitability.

Rounding | Exploitability
No rounding | 0.2% (1bb/100)
10% rounding | 0.8% (4bb/100)
25% rounding | 2.7% (15bb/100)
50% rounding | 8% (45bb/100)
100% rounding (pure strategy) | 30% (165bb/100)

So versus the Nemesis (clairvoyant and maximally exploitative opponent), a pure strategy would be extremely exploitable.

I usually round my sims to 25% to simplify the solution and remove the worst solver noise.
No way I could remember and implement anything beyond 25% rounding anyway.

I don't think this is exactly what he means.
If you actually solved with a pure strategy in the first place and didn't have to round it after, I believe exploitability would be pretty low. Probably about 0 on flop and maybe a little bit as ranges get narrow, but it wouldn't be too big of a drag on the whole strategy imo.
And no I don't think solvers can do this

It's possible in theory;;


Imagine... Counting to a million. Now if a metronome could go on forever, it would technically count to infinity



But infinity is a concept that only exists in theory.


A human could strategically beat this number counter, or rather, find weaknesses, if the seconds in between the metronome deviated between 1.000000000... seconds.


Bugs exist in bots.



Now...;;;;


If you played a bot that played rock paper scissors 33.33 recurring but did a different timing for rock than paper or scissors,,,,,


Win

I think it would still be very very high. Like you can exclude so many cards as the opposing player (almost all actions of the pure player reduce his range significantly). So probably best for the pure player to only have one sizing most (all?) of the time. So if you solve with a lot of sizings and then round the exploitability will obviously be humongous (if multiple sizings are actually played). Anyways the exploitability is not realistic in any sense since nobody would know your exact strategy (the exploitability shown is realized by the perfect counter strategy).

Use the tendencies of your villain to determine your action at mixed strategy nodes.

Yes, it's possible.

The keyword you're looking for is called "Pure CFR". It has been done by academics, but never implemented into commercial solver projects as far as I know.

https://github.com/rggibson/open-pure-cfr

How they reach equilibrium when it's not guaranteed with pure strategy.

The question is not clear. One way to interpret the question would be given a game tree (involving 2 players) find a least exploitable pure strategy of say player 1 though this question would be of purely academic nature (since the question (interpreted in this way) is NOT relevant in any way to actual play).

I'm not 100% confident, but pretty sure the "pure" in Pure CFR refers only to the strategy profiles being pure (ie playing best response like in e.g. Fictitous Play). The resulting overall ranges would still be mixed, as these are the (weighted) averages of the played strategy profiles over all iterations.

I thought the same thing but didn't write anything since I'm only 99.99% sure and I'd need to invest 1 hour to be 100% sure which I didn't want to do.

I am not sure if I understood your question, but do you mean playing pure strategies with each combo, or with range?

With range, I believe you always lose something, varying from small and insignificant to a lot.

With each combo, the issue I have (and maybe this is due to a still limited theory understanding) is that in a world where you are not going pure with your range, wouldn't always taking pure actions with combos leave one of your ranges (let's say, checking or betting when they are the possible choices) unprotected? I mean, equilibrium has to be somewhat exact, frequency wise, and poker combos are discrete in nature, like, you don't have 4.954 combos of 99, you have 6, 3, 1 or 0 depending on blockers.

You're right, my mistake. I was under the impression that 'pure cfr' would produce pure strategies, but the averaged strategies, what we see at the end, is still mixed.