wut? very confused are you.

could be misinterpreting what youre writing, but this isnt right.

the defense threshold you identified is shared between the two players, so here it could be v2 needs to defend 30% of his range, and then given v2 has folded you should defend 50% of yours (defending 50% of the 70% of the time that v2 has folded means you collectively are defending 65% of the time). those %s will vary based on how the various ranges interact with the flop (ie if v2's range whiffs entirely, defense may fall largely on you esp bc you are still left to act).

as a dangerous non-sequitor, gto doesnt actually require that you prevent atc from bluffing profitably

i would not recommend applying defense analysis like this to these spots, i dont think it is very helpful. besides, without knowing the %s each player needs to defend, it ends up being a lot of guesswork anyways.

as for the actual hand, id just fold flop and make a note. it would be odd for v1 to lead into a whale and the pfr without a pretty strong range. the fact he has a donking range is noteworthy, though.

v1's lead seems pretty suspect here, but who knows what he thinks of v2 and you

I said let's pretend it's HU, just making a point to someone who said folding A4 is not overfolding even if we were HU. It's even in the part you quoted

okay fair. thats what i get for posting before noon.

Did you read the description of V1? how often does a solid reg cold call a 6x raise OOP with a 3 in his hand let alone donk three sts with it. and 87? IMO pre flop i still think 87s is somewhat unlikely, and mighty sure he won't lead into a fish and a strong range with a gutter. But yes, he can have set, but i think 77-TT turning into a is just as if not more likely. I call here

A lot of "solid" guys do some really horrible ****, so yeah, you can't discount 53s. Especially guys with huge egos. Hero said villain was sort of solid/ a big winning player. Anyone who donks flop, bets that turn especially with that sizing and then follows it up on the river is 77-TT is a losing spewtard player. It's just so beyond bad in this spot I don't think I have to explain why.

There are lots of losing/ breakeven guys who are otherwise pretty solid.. but they do what you're doing now- they ignore reality and logic, and instead construct bs/ unrealistic ranges to justify some really bad plays.

If your strategy is to fold 100% of hands preflop, then Villain cannot unilaterally improve his outcomes. His maximum win per hand is fixed. Hero's loss per hand is fixed.

Therefore, folding 100% of hands preflop is a GTO strategy. It is also -ev.

Wow this is just so horribly horribly wrong.

Just to be clear here, it is very possible to not play GTO and still break even against a GTO strategy. Specifically that would happen if we are playing the same actions as a GTO strategy, but at the incorrect frequencies. GTO will not profit against wrong frequencies.

Well said.

The reality is that V took a very strange/creative line that was probably a losing play in the long run but he binked the river so obv it has us second guessing our play.

I think what it tells us is that V has hero's PF raising range capped to Broadway cards and overpairs, so he is leading here expecting you to fold your air most of the time, as well as being able to bluff you off of a one pair hand when the board starts to get more and more connected and scary for a hand like TT to call large bets.

V didn't expect us to show up with A4 here, so effectively, we outplayed him in this hand.

So with that said, I would say nice hand to the OP. Especially if you will be facing this opponent more in the future.

When a LAG sucks out on you, you're gonna lose a lot of money. You don't need a PhD in math to know that.

Either this is the most unintentionally hilarious thread in twoplustwo history or there are a lot of trolls on this forum.

Prove it, please.

If that is correct, may you do us all a favour and explain what GTO means then?

I am not an expert on GTO stuff by any means, but as far as i know Lapidator is pretty on point with his explenation principles so far.

First, "GTO" isn't really much of a technical term. But generally what people mean when they say "GTO" is a Nash Equilibrium strategy.

An equilibrium occurs when two opponents continuously try to improve their position/EV against one another, and eventually reach a 0 EV deadlock (for a zero sum game like poker), where neither can make any adjustments to improve against their opponent. Both players are then playing a GTO strategy.

Now keep in mind that both players are choosing actions with the highest EV. If there were a higher EV action, that would be selected instead.

The example given was folding every hand preflop. It should be self-apparent that shoving aces has a higher EV than folding, so the strategy of "fold every hand preflop" cannot be GTO.

Or I could have simply stated that GTO is, by definition, never a -EV strategy (assuming neither player has an inherent advantage - e.g., they both play button 50%, etc). That is "proof" enough that the post about folding hands is wrong.

Re: GTO... As a way to visualize this, imagine two sumo wrestlers of equal size, weight, and strength in a deadlock in the center of the ring. Each pushing against one another and each continuously making infinitesimally small micro-adjustments to counter their opponent, but neither able to gain an advantage. That is an equilibrium, or "game theoretic optimal" play.

The example of folding every hand preflop would be like one of the sumo wrestlers just instantly falling to the ground and curling up in a ball, and essentially forfeiting. That is certainly not game-theoretic-optimal.

ITT: Bad advice

Please close this mess

It's funny because your post in above (#89) is rather accurate. But this post is plain wrong. GTO play guarantees that 1. We will have an EV of 0 in a game with no rake and theoretically optimal opponents and 2. We will have an EV > 0 in a game with no rake and at least 1 non-optimal opponent.

You cannot play a theoretically optimal strategy if your frequencies are wrong. GTO will always profit against a strategy which includes non-optimal freq's in a non-raked game.

The catch 22 is that once someone is playing a strategy with incorrect frequencies, we will maximize our EV by playing an exploitative strategy designed to exploit those frequency mistakes. GTO strategy would still be profitable, but not as profitable as the exploitative one.

An example: Let's imagine OP's hand against some random 1/2 OMC who never bets without TPTK or better. His flop bluff frequency is far too low. So we should always exploitaively fold A4 here. But against an optimal opponent, we must meet the minimum defending frequency or he will be able to profitably bluff us with atc.

TLDR: GTO will profit against a strategy involving incorrect freq's in a rakeless game, but an exploitative strategy will profit more by capitalizing on the incorrect freq's.

Why do people post about Gto when they have no fundamental understanding of it.....not pointing any fingers...
GTO is a mathematical model for playing ANY chance based game that is unexploitable regardless of any adjustment our opponent makes.... In a zero sum game a Gto strategy will Always break even.....
The problem with applying it to poker is that it only deals with exploitability.... In a poker game with no blinds the Gto strategy would be to never play a hand.... It is a Gto strategy to not sit at the table because you cannot be exploited....
A Gto strategy does not exsist because of this.... But we can make individual Gto decisions in a certain situation.... This decision will be a long term break even play.... Bluffing 50% pot if we know we will be called 25% of the time.....but even this is not a pure Gto play because how can we ever know that we will be called precisely 25% of the time....

Hate Gto discussions.....
It is just a theoretical unexploitable ideal that allows us to make a break even long term decision when we can't work out how to exploit our villan, or or we are being exploited....

We may as well be having a discussion about which flavour of pie is best to eat at the table for the relevancy of GTO to llsnl....
I vote for blueberry btw, and if anyone disagrees your wrong and you can go **** yourself

No, you're wrong. My original post is correct. Refer to posts #3 and #7 in this thread I started in the Poker Theory forum:
http://forumserver.twoplustwo.com/15...o-bot-1660842/

Also, I never said we can play a theoretically optimal strategy with the wrong frequencies. It's just that a theoretically optimal strategy (meaning equilibrium strategy) will not punish us for playing the wrong frequencies, so long as we are choosing from the right set of actions. An exploitative strategy obviously will punish us though, as that is basically the definition of having a "wrong" frequency. So yeah, wrong frequencies implies not GTO, but it does not imply that GTO is profitable against that strategy.

You seem to fail to realize that there is a difference between "GTO" and "maximum EV". They are not necessarily the same thing.

E.g. you agree to play 10,000 hands against a random player in NLHE. You sit down at the table only to find that the randomly selected player is literally the best HU-NLHE specialist on the planet. What would be your best strategy in an informal sense? It would be a strategy that eliminates Villain's edge.

In a slightly more formal sense: You wish to employ a strategy that makes it impossible for Villain to do anything productive to counter your strategy.

Folding 100% of hands preflop satisfies this goal. It is a GTO strategy. It may not be the best one, but it satisfies the requirement. Villain is completely incapable of affecting the outcome.

Your suggestion that folding everything except AA which you open shove does not meet the criteria though. Villain could guess your strategy, and move to exploit it by folding everything except his AA, when you open shove. Villain can choose a strategy that exploits your strategy to maximize his win rate. Therefore, your strategy is not GTO, even if it is more plus EV vs. a 100% fold pre strategy.

Whether one strategy is higher EV vs another actually has nothing to do with whether the strategy itself is GTO -- in a strict sense.

In a HU situation with identically zero rake, to wit: zero-sum game, yes, GTO vs. GTO would be EV=0 for both players.

But in 3+ player games, this is not strictly the case since, e.g. you could face collusion (conscious or incidental). In this case, GTO might be -EV on the whole.

^folding every hand is only a Gto strategy if there are no blinds.... A Gto strategy is unexploitable, if you fold every hand you are eyeing exploited, because villan can raise every hand and exploit us... This is obvious is it not....

I apologize if I'm misreading, but I don't see anything in that thread indicating you would break even?

I do see advice involving playing a non-optimal strat in order to minimize losses because playing optimally is an impossible goal.

Imagine a toy problem where we are facing a river shove and the GTO correct frequencies for a specific hand are to call 30% of the time and fold 70% of the time. I think a source of confusion here is that generally people think in terms of "percent of range." Because we have 1326 possible hands to divide our calls/folds, there will probably only be a few hands where GTO will actually have to play a mixed strategy and call/fold with random frequencies. The rest would be always call or always fold.

Anyway, for that specific hand, EV(call) = EV(fold) against a GTO opponent. If it did not, we would choose the higher of the two EVs and choose that action. But since the two EVs are the same, we can choose among the two at any frequency we want and be breakeven against GTO. We will lose, however, against a strategy specifically trying to exploit us, when we play the wrong frequencies.

As long as hero can benefit from choosing another strategy relative to his opponents strategy then he is not GTO.

By the way, it's also unclear in your example as to whether or not V can improve his EV per hand - perhaps he isn't adjusting properly to hero's pure always folding strat and is folding as well at some frequency. His maximum win per hand in that strategy remains fixed but he can improve upon it by choosing to always call.

Right sometimes they can be the same, but a GTO solution will never have an overall EV<0 by definition (in HU poker). It will always strive to improve upon the current strategy choice no matter what strategy the opponent is using.

Anyways yeah this all silly in this forum.

Cliffs? ��