I love those articles on game theory, but it is tough to apply those conclusions in Hold'em for instance. Not easy to figure out if top-pair with a jack kicker belongs to my top 14% on that given board or if a busted queen-high flushdraw belongs to my bottom 7%. It would be much easier to know if I took every hand to the river.

One way to proceed would be to work though tons of flops and ranges with Flopzilla or similar software. That's quite a task though.

Funny, but I expected zero replies, because most people should have the same problem. Those who don't, won't give it away

I just wrote my range on a piece of paper in the right strength-order, corrected every hand for it's combo's, then take 100/combo's. add the % from top to bottom to get cumulative %. Start with a small range, and keep on making them bigger, after a while you can do it without paper!
also: Sure there is software around that will do this for you, I just don't know it...

http://www.cs.cmu.edu/~gilpin/

You can find a few articles there about their GTO-player. Some pretty decent hardware took a couple of days to compute the turn/river distributions and even this model is just an approximation. In other words, for a human this task is impossible.

GTO works nicely in pre-flop all-in play, but other than that...

David continued that lovely little article. Again we read that we should do x with a certain % of our distribution etc. and there are even exact calculations with EVs of 8 cents for certain plays and so on. Well, that's all pretty nice if it wasn't for the rake.

So the bottom line is: If you play in a homegame without rake and are allowed to bring your 10.000 pages with printed decision trees, percentages and handranges for every single distribution to the table, you will have a decent chance to at least break even in the end. Unfortunately people don't play 5-Card-Draw anymore...

Btw, it is in the best interest of pokerrooms that everyone plays GTO. The pokerroom will eventually rake all the money, because (except for certain variance) none of the players goes broke too early.

If two GTO-players are playing each other, they are wasting their time. They are creating nothing but variance and it is actually a case where quitting while ahead is ok. If they are playing each other in an environment with a 5% rake, they are not only wasting their time, they are costing themselves money, so playing the game is actually harmful for them.

The best course of action for such players is either to write books on poker or to play tournaments where they basically buy a lottery ticket to win a share of the dead money from all the beginners in the field. Since good books make it tougher to be successful in tournaments, eventually it all boils down to writing books. So shortly before the pros abandon the sinking ship, they should all write something about how to play. And this, ladies and gentlemen, is 2+2 in a nutshell!

Kind of reminds me of FTP in MTTs from 10$-20$/10$rbuys (my experience). Everyone has a rock symbol beside their s/n and only way to chip up is with coin-flips pre-flop....

There seems to be consensus that Limit-HE can be (has been) solved. This is convincing because we got a fixed number of streets and we can cut off trees that include re-re-re-raising at a certain point. In NL-HE the combination of multiple betting streets, variable betsizes and different stack-to-pot-ratios makes it basically impossible to map out all possibilities or solve it with primitive models. That is why people feel more comfortable with preflop all-in decisions.

A beautiful theory, for a beautiful mind (pun intended in some way).
So poker GTO in theory,to a normal human mind becomes a philosophical yoga excessive in the long run (+eV nevertheless), rather than a set of sharpened templates(I multitable as most and that's what I am trying to get out of it)?
Or a combination of both, with mathematical side needing a crutch (GTO poker SW equivalent to poker stove).
When I was playing nl10 back long time ago, everyone were ether nits or fish with nothing in between. Table full of nits were basically playing the "perfect strategy", hence grinding the rake for the room (I called it passing the pancakes around).So I can see where your point is coming from about two players playing GTO vs each other, because I actually sat down and using equilab and calculator came up with a calculation that if everyone had perfect Pre flop range and perfect post flop play, it would basically come down to mathematical variance, and at any given time the person that would win, would be the one that hit the top of their range at that given time, hence more pre-flop eV dependent to make my calculation easier.
Well to cut the long story short, I cam up with a % that indicated, that perfect game in poker is a downwards spiral (money spiraling out of the spiral at certain % depending on how perfect the preflop/postflop the game is for certain limit). This was for cash games by the way.

Isn't this why you need to learn how to read people? Reading people is something i rarely see discussed on here, but I can't tell if thats because you really can't apply that skill universally or that very few on 2+2 actually care about it. It can really give you that edge if you can figure out what part of the range your player is on a given hand. I don't really think a person can benefit from playing GTO unless their online playing 20 tables at once so you can really kill the variance, it doesn't really apply in live play imo because you don't see enough hands in a session to limit the variance, whereas online you can see 1000's of hands in a session if you play enough tables and for a long enough time

Plenty of live reads/tells discussion in hand analysis section.
GTO is kind of a "game" with yourself (how I see it), where you take optimal/unexploitable route when ever given a choice.
Lots of videos/training/book/coaching are mostly about exploiting the exploitable.
We are given a weapon to do damage, while forgetting to equip a shield.
This is when GTO comes into effect.
We are trying to set up a foundation to avoid being exploited, and gain the maximum and loose the minimum.
From my understanding of nash equalibrium, the theory tries to reach equlibrium in every situation, where as in poker we bend the rules to achieve the maximum favorite outcome.
This is why once we go past the basic theory, we start moving into decision trees and plans, and as explained above by Shandrax, we can only do so much if we're in a perfect world scenario in LHE, but it gets complicated once more choices are at present.
I am midstakes player, and GTO is a great arsenal to have at our disposal, but I think it's a must at higher stakes, where fields become smaller, and we have to go into battle with regs quite often, who will try to exploit us.This is especially true starting from nl100 cash.

Don't get me wrong, I love game theory. The problem that I have is when people are coming up with oversimplified models and are trying to calculate them to death. The same goes for concrete math based on totally vague assumptions that may or may not be true. There is no point in trying to be precise if your premise is based on gut feelings as the imprecision carries over to the final result.

@Ibomon I hear ya, thats why i started coming here I have some understanding of math principles but wanted to learn how to apply it to poker. The thing with a Nash equilibrium is it does not have to be optimal result (and very often isn't). Rather it merely represents a point (out of possibly many) where neither party stands to gain by any immediate changes to their strategy, even if one side is not getting much or anything at all. I'm not sure how Nash Equilibriums are applicable to poker unless you can force your opponent into a Nash equilibrium where he is always losing and his only moves make him lose more which is impossible. Really if both players played to Nash equilibrium your basically just hoping to get lucky so I have a hard time seeing why thats something I should be aiming for..

"GTO is good for you!"...every morning says David Sklansky mirror...but...

not for the first time writes with errors and ignores criticism)) but maybe I'm wrong))) so

Einstein's last work - Norman Zadeh’s Simple GTO Game, Part Two


question to solve the problem and the actual mathematics...EV...

#1. Why in the calculation of the expectation you take into consideration the dead money in the bank that you do not belong. Once we placed a bet in the pot, we have it does not belong.

Thus in fact you EV differs from the calculated actual. ...and if we fold EV can not be a minus, it EV=0.

#2 As for solving the problem

EV player B (who wants to find an optimal strategy against a player A) its the sum of EV(bet) - when player A line is chek-call and EV(call) - when A bet first, taking into account the probability (P):

EV(B)= EV(bet)*P(bet)+EV(call)*P(call)

When Hero (B) bet $2 in pot $2 vs (A) line CHEK-CALL, he can wins $4 (final pot $6, we put $2 in last round), or wins $1 if they split, or B will lose $2.

1. Range A = 40-68%, Range B = 0-40%. A wins $4
2. Range A = 40-68%, Range B = 40-68%, A wins $1
3. If range B = 68-100%, he will not put because lose $2

Top-68% - optimal range to bet for player В vs player А chek. 40/68=0.5882 or 58.82%

EV(bet)=$4*58.82%+$1*41.18%=$2.76

For EV(call) the same method. Also calculate the zero call and find that it range = 84% (not 76% like in you work). Its realy GTO call. So EV(call)=$1.12

Finaly EV(B)=$2.76*28%*68%+$1.12*72%*84%=$1.20 and EV(A)=-$1.2

Best Regards

course moderators can delete my message, as in the last time I wrote about the other work. It will be on their conscience). Enjoy)))