1. Is Piosolver=GTO? How does it work? If Piosolver=GTO which mean poker is already solved?

2. What make us think the result from Piosolver is reliable?

3. What if you put 100% opening range from UTG vs reasonable range from any position? How does Piosolver come up with a profitable/ unexploitable/ balance strategy?

Thanks!

This is beginners questions

I'll admit this is a suitable response in this thread

Poker isn't entirely solved, but if you input the exact ranges for 2 players into a solver like Pio, it can compute the optimal strategy for each player. I think it does the calculations by "brute-force": running every hand in one range vs every hand in the other range and working out which bet-size works best, then re-running the calculations if the opponent alters his strategy (e.g. by folding or calling more often). It's essentially running billions of simulations of a game a bit like rock-paper-scissors. It's just in poker there are more than 3 plays. There are hundreds of possible combos.

Calculating takes a long time (or computer power) if ranges are wide and you give it multiple bet-sizes to choose from, but you can get an approximation of the equilibrium strategy (for a particular board texture) fairly quickly with typical 6-max ranges and a simplified betting structure.

There's more explanation of how it works in the official thread: https://forumserver.twoplustwo.com/1...oldem-1516187/

Thanks for the reply! What I don’t understand is how can Pio come up with a unexploitable/ balance/ +EV/ strategy even if we opening 100% of hand?

Unexploitable is not the same thing as +EV.
Unexploitable strategies can still be overall -EV...it just means that as soon as you deviate from the strat and when you are playing against a perfect GTO player it will be worse.

so in my example, if we input 100% opening range in Pio, Pio will come up with a unexploitable/ balance strategies but it will still be -EV losing money overall.

Most intuitive example is probably SB vs Button. If both play GTO then the Big Blind will be -EV (because the button has more information)

Given enough processing power, it can find the optimal strategy for any ranges whether they are super-tight or super wide.

e.g. If a villain's strategy is to only play AA and KK, you should (presumably) only play AA against him, because no other hand will win often enough to break even against such a strong range.

If villain is playing ATC then the "max EV" strategy against it would be to play about 50% of hands, since every hand in that 50% range will at least breakeven vs ATC.
(FWIW, a 49.32% range of 22+,A2s+,K2s+,Q2s+,J6s+,T7s+,98s,A2o+,K2o+,Q5o+,J8 o+,T9o contains every hand that has 50% or more equity vs ATC).

In real life, someone might open 15% UTG (6-max) and the BTN might only be able to profitably play 8% of hands against him.
In a HU game, the SB/BTN might open 90% of hands, and the BB defends about 50%. (I don't know the typical frequencies that HU experts play, but the strategy is somewhat akin to "defend about half as wide as the opener's range").

The point is, whichever opening strategy is used, there will be a counter strategy that does best against it. If someone opens with a narrow range, only a small proportion of hands will be profitable against it. If someone opens wide, then a large proportion of hands will be +EV. Pio just crunches the numbers to find that equilbrium.

It's the same concept that you use when facing an open or a 3-bet. If a nit 3-bets you, you think "He's gonna have QQ+/AK a lot, so I should fold all of my weak hands as they won't make money vs the nit", but if an aggrotard 3-bets you, you think "He's so FOS that I can probably 4-bet AJ for value". If you tell Pio what villain's range is, it can calculate which hands will make money against it.

Not to discredit your post overall as it's reasonable, but your intuition about hu is pretty far off here.

I'll drop a bit of knowledge here:

75bb deep vs a standardish (2.5x) open from the bb, we're defending around 75% of hands. Vs a mr, we're actually defending over 85%.

25bb deep in a hyper, we're also defending roughly 80% overall OOP vs the min open. Maybe you didn't quite account for the smaller open sizes, but keep in mind that playing hu it will be an unmitigated disaster if you're openfolding close to half of your BBs.

As an aside, Arty, from seeing some of your posts around here and your PG+C thread I really really think you'd have a blast playing some husngs. Parsing through ranges and interpreting theory is a ton of fun when players have 70%+ of hands on the flop and still very wide ranges ott after cb/c in a bunch of spots. Doubt you'll take my recommendation seriously, but I really do think you'd have a good time with it!

Is the HUs pre flop solved? What is the optimal GTO opening range HUs? the defending range from BB should tighter or looser than the opening range from BTN? Is it profitable +EV to open ATC 100% range from BTN?

I've posted all the info I'm willing to publicly post about that. If you're interested in more info, there are multiple publicly available preflop range packs for sale, or you could find a private coach or join a stable that has private solutions. Nobody will share those sorts of details openly lol, I probably posted too much as is. My post is based on solver trees, though, so they are gtoish.

FWIW, I was thinking about HU cash with 100bb stacks and 3x opens, but I'm not sure how much the BB defends even in those circumstances. If it's now common for people to minraise or 2.5x, then calling much wider would make sense.

I've played a few HUSNGs vs whales at microstakes, and it's kind of fun to have such wide ranges, but it would take me ages to get up to speed with the sover dudes that play them professionally and I'm no longer at a stage where I want to do much studying. :/

Yeah, 3xing has fallen a bit out of favor even in 100 cash. Off the top of my head though, defending range will still be over 60%. Sizes around 2.5x are more common in which case we have to be defending a bunch still.

As one of those solver guys playing (semi)professionally, it's not as hard as you think, but it is true that it takes some effort to catch up! Idk the exact situation on unibet, but on PS I can say people don't really do much solver work until at least $30s, so I'd imagine its similar unless unibet has a husng bot problem.

Fair enough that you just want to play cash, I do think you'd find it a good time though

I think there is a fundamental misunderstanding here of what GTO means. Game Theory Optimal is a term for describing a strategy that approaches unexploitability, not a strategy that is "optimal" in terms of overall EV. The word "optimal" in GTO doesn't mean the same as "optimal" in other contexts, and I would avoid conflating the two.

As for GTO opening ranges, an AI w/ a GTO strategy is going to do some extremely complex range and bet size balancing which is impossible for humans to replicate, and is going to be less than maximum EV when there is an exploitative line available.

If you want to learn how the programs that people generally use work, I would watch some videos of someone using PioSolver or GTO+ so you have an idea of how you would use one, and what information they will provide. Here's one small youtube series for GTO+. https://www.youtube.com/channel/UC0i...Or1IQz66N4w-1A

If you want to know how Libratus, the AI that stomped some of the best HU players in the world, works, here's a lecture by the designers. Pretty heavy in pure game theory and not a lot of actionable poker tips, but good for context. PLEASE WATCH THIS IF YOU DO NOTHING ELSE: https://www.youtube.com/watch?v=2dX0lwaQRX0

whats all this gto ****? you just play with huge balls and gut instincts. this is beginner questions.