I'll try and destroy this idea that playing balanced means sacrificing ev :

Let's take an unbalanced situation as a starting point :

We're always betting strong hands and that leaves our checking range completely capped.

What should villain do? He should put tons of money in when we check (his value range + bluffing range gets much wider).

Now what happens when we move a few nut combos from our betting range to our checking range?

Since villain is going crazy when we check, the ev of checking with strong hands will skyrocket and be much higher than when we bet.

As we add more and more strong hands into the checking range, their ev go down (villain should be less aggressive).

By the same token, as we remove more and more strong hands from our betting range, their ev go up (villain should call more).

It boils down to this simple fact : the weaker our range, the more chips villain should put in the pot.

At equilibrium the frequencies are such that the ev of checking will be equal to the ev of betting. We are perfectly balanced and never taking a lesser ev line, or never sacrificing ev!

Those frequencies depend partly on which player have a "range advantage". The bigger our advantage, the more we should tend to bet strong hands because :

a) Villain's range does not contain as many strong hands so it will be harder for him to attack our weak range (We have to cap our checking range to the point where villain should attack at such a frequency that we're indifferent to betting and checking).

b) It gives villain the opportunity to keep the pot small when we're strong.

The author of the book is using the term as a particular street, at least in the pic of the page I posted (Afterall the full path through the tree is only the addition of particular streets where the frequencies are at equilibrium)

Everything you said (except possibly the math part, I can't tell since I'm a noob) seems on point to me.

is anyone else getting annoyed by this guys bullheadedness or is it just me

weve led you to water like 6 times and pretty much dunked your head in the tank and you won't drink
half of what you quote proves what we've been saying, the other half either demonstrates your lack of understanding, confusion with semantics, or straight up psychological disorder.


for the tenth time
the net gto strat is the most +ev strat overall vs the net of all opponents
vs an individual opponent, it will not b the most +ev strat (unless ofc this opponent is gto, where we will be 0ev)
likewise, no line in a given hand is going to be the most immediately +ev in a vacuum, as we are often sacrificing immediate ev gain for overall balance. if the fact that we sometimes mix strats between betting and checking doesn't make this crystal clear for you, nothing will.

actually ojune ur right, i take back everything i say. idk anything about solver or gto really...where do you play and what are your accs, i would like you to teach me a lesson on gto .. maybe ill try my hand at HU w u.. i have about 5k roll to donate to you for ur understanding n would like to get my feet wet. maybe we play 4 tables at once for enhanced experience

Maybe you should try and understand what I wrote, you'd gain a lot from it. But maybe that's out of your cognitive abilities. I do have hope some people here will understand.

tell me your point in three sentences or less

If we play perfectly balanced the frequencies of all our actions for our entire range on a particular board played an infinite times against an opponent is optimal such that it is unexploitable which means that the worst possible outcome for us is a tie. This is what solved means.
The best outcome for us is dependant on villains play.

At equilibrium, both players have optimal frequencies which means that if one players deviates from them, he will lose total EV.
In a particular hand on a particular board, it can be beneficial for the total EV to take an action that doesn´t have the highest EV, to sacrifice EV if you will.

You were doing well until the last sentence

Umm except it's definitely not a tie on a particular board. One player will have a higher ev, usually the one with the "stronger range".

I agree but do you agree that it can be total EV positive (two ranges, one board, infinite amount of hands) for us to choose an action that does not have the highest EV in at least one hand? To sacrifice EV in some hands in order to gain in total EV?

Absolutely not, it's a common misconception. The best line is always chosen and when more than one is taken (which is most of the time) then it means they yield the same ev. There is no exception. Look at the right part of the screenshot the palidan posted (post #14), the solver consistently pick the highest ev line and when it mixes (TT for instance), the ev is almost the same (122,93 ; 123,03 ; 123,53). It's not exactly the same because it's not fully solved.

When you play exploitatively, no mixed strategy is used because by definition one line is better than the other (If someone overfolds then you should ALWAYS bluff and if someone overcalls then you should NEVER bluff. This is assuming your read is rock solid and that they won't adapt, which is rarely the case in practice so you should usually not deviate too drastically from optimal play)

Okay it's time to Thor drop the hammer down on this debate.

Ojune is correct (what I initially thought).

My source? Only the guy that invented PIO SOLVER (good luck getting a higher authority).

I asked him this question in the PIO thread.



source:

Final-****ing-ly...

Make sure to read post #104 if you want to try and understand mixed strategies Doodoo

for the love of god i never said A, youre not even saying what i said.

Yes the solver will take the "highest ****NET**** EV line when it weighs all lines against each other, WHILE maintaining balance."
this in no way means that its the most EV + line for the given situation. The most EV+ line would be playing one hand at a time in a way that maximally exploits opponent tendencies and completely foregoing balance. ie if you were a superuser you would know and nodelock for all of opponents tendencies and come up with a COMPLETELY different set of solutions than the "catch all gto strat" that solver gives you.

nowhere is game theory optimal EVER defined as the most profitable strat, in fact, reduced to completion its 0sum, since, the entire premise of game theory is just finding an unexploitable ie break even strat.

if this entire time your argument has been, that when you look at the EV win/loss for each play the solver makes that its always choosing the bigger number/mixed numbers converge to equal thats not even what were talking about. its been about 6 pages of people explaining the intricate details of how a jet engine works while you keep insisting that the plane goes fast. then you message the designer of the plane and ask him which is true, A. THE CAR GOES SLOW or B the plane goes fast and he confirms the plane goes fast and you think you invented fire.

that # isnt a measure of *absolute* profit. this is a measure of profit lost vs another GTO mirror on average.
what you think solver is saying, WHEN YOU DO ____ HERE YOU ARE LOSING/WINNING X$$ vs joebob123 on pokerstars?? how the FK would it know ??

and for gods sake if youre gonna ask the guy a question at least say what i said, not something i already told you was improperly worded like three times.

Lol, stop embarassing yourself, you've been crystal clear in the thread with your sacrificing ev non sense. There is no sacrificing ev, not in gto and not in exploitative play...

Exhibit A:



Exhibit B:



What you said was "COMPLETELY WRONG," was confirmed to be "correct." Which means you were wrong. Everything has been documented.

you take the highest EV line if you're looking at the EV # in the solver. thats like DAY 1 LEARNING HOW TO USE PIO STUFF.. NO ***** SH*T
thats not the HIGHEST EV LINE in absolute terms, what about that dont you get?

do either of you two even work with it??? i swear to god youre like arguing with me over how to customize the skins when you dont even use it

i guess my mistake was thinking you guys were familiar with it and were actually making some kind of point, when really your big breakthough is looking at the EV number that the solver gives you and thinking that it always going with the bigger one is some kind of breakthrough.

that is not the absolute EV that is the EV net vs another GTO.

The delusion is real..

Irrelevant questions in bold. You are just trying to back track here - it's fine. You were wrong. It is not a big deal.

Now who is making ad hominem attacks?

whatever guys, congrats. you taught me the basic interface of the solver gives you an EV number. and then msg'd the creator of pio to ask him if i was wrong about something i didnt even say.

and those arent adhom attacks. im actually curious if either of you two are actually familiar with it, its quite relevant.

I've rarely seen such a lack of good faith. And feel free to let me know when you want to get that ass whooping at wc3.

i would like to play you H.U at poker.. what stakes do you play? would you be down
we can get a table with 3 seats and you and doodoo can collude vs me

No, I would like to play wc3 where variance can't possibly help you

I think you guys just all aren't understanding each other. Take one of the simplest example's possible that demonstrates the same concept perfectly:

The Nash equilibrium of Rock, Paper, Scissors is a random mixed 33% strategy which is max EV at equilibrium and unexploitable, but the second you notice somebody throwing one of those at a higher frequency than the others (playing exploitably), then exploiting that fact by throwing the one the beats that at a higher frequency is higher EV assuming villain is clueless.

Villains always play exploitably to some degree because the full Nash equilibrium strategy is unknown, therefore whenever you notice significant deviation from known approximate GTO strat, deviating to exploit that versus that specific player is higher EV if they are clueless. But that EV gain comes with the trade-off that you are now playing more exploitably to the non-clueless.

This was my private message to you -



This was your response



But that is NOT correct --after asking someone that knows GTO better than anyone in the forum (inventor of PIO SOLVER).

I've noticed this a lot -people try to backtrack or use hindsight bias and either trick themselves into thinking they knew something the whole time or just lie to themselves to protect their ego, I'm not sure which one it is.

No one in this forum plays nosebleeds - we all play micros or small stakes at best. We don't know sh.it about poker. Start acting like it.

Swing and a miss for you as well.

Quoted from Punter

"If it was possible to increase your EV than it wouldn't be Equilibrium by definition."