I'm wondering how is GTO solved exactly where its a fact that the play is GTO correct vs just a opinion.

So here are a couple examples

We use whole-cards vs opponents range to work out if its the correct play

or

Using something like brute force or pio solvers where the scenario is repeated millions of times until its established that its the correct play.


Also the first one whole-cards vs opponents range can be flawed

What about the second one repeating a play millions of times has that got some flaw in it too?

I mean when we are looking at a spot, how do we work out and come to the conclusion that the play is correct and not based in opinion instead?

The most important assumption is that you play hands with expectation > or = 0 exclusively, and that you never fold a hand that would be profitable to play.

If you could do this, you could play the one* truly unexploitable strategy postflop.

If you can't do this, which none of us can, you will be exploitable in one way or another. However, that's ok because there's still lots of poker to be played.

*using the term loosely.

I might have worded it wrongly a bit too, i was trying to ask and work out how we study the game, and how we come to the conclusion a play is correct?

Take for example supercomputers who used brute force playing over millions of hands at limit holdem until they figured out the correct play, are these supercomputers flawed in anyway? and will their method always be more accurate then those that use their opinion and input ranges vs their own hands?

Well, a true GTO solved solution would involve every possible combination of opponents unknown cards versus every possible run out of the board.

Thus, the hand can only be *solved* in a manner that we refer to as *from every possible river backwards*.

So, the solvers that humans use depend on the assumed ranges the humans input. This is a great learning tool, but is still only an approximation and still only as good as the ranges input.

Or...

You can study the mathematics involved in a certain spot, and know that a certain bet must fold out a certain portion of potential calls, in order for the caller to be balanced. Whether or not a human caller makes a balance fold or call depends entirely on that human and the ranges that human plays.

So to study GTO, you can either have the math, which is solvable but gives no info on actual ranges, or you can have solvers which will take the ranges you provide and apply that math.

So, if you have a pretty good idea on the ranges that your opponents play, the solvers will give you the closest approximation of GTO, but will leave out lots of plays that do not involve holdings which you think are unlikely. Also solvers leave out lots of bet sizing that a truly balanced player might use. We humans like to bet 1/3 pot to full pot. This is unbalanced itself and not GTO.

The brute force computations of AI supercomputers are not flawed, but also have not become fast enough to play anything other than heads up poker.

Heads up LIMIT poker unless you also use narrow betting and stack assumptions for NL.

I used to agree. However, now I believe Libratus will beat any human heads up NL for any stack sizes, over a decent sample size.

That may be true but my point is that HU NL still isn't solved. When it is, that algorithm will beat Libratus.

Totally valid point. You are correct.

thanks for detail explanation!

What do you mean by algorithm? pio solvers?

I mean i understand what a algorithm is, but just wondering if you are talking about pio solver when you say algorithm?

No, I used the term generically. A decision tree is an algorithm.

ok thanks

then you obviously didn't get it