I have been wrestling with this question and wanted to get some feedback from the forum. It is regarding Game Theory and the use of mixed frequencies.

So we know that GTO will always take the highest EV line at all times - and that if a certain line is mixed (meaning bet or check) then by definition the EV must be the same for both betting and checking.

Okay - well if this is true (it is). Then how come every mixed frequency is not exactly 50/50 for both bet and check? Why do some solves have certain hands betting at 90% frequency and checking at 10% frequency? Or Vice Versa?

This is absolute not what GTO is or does.

GTO is a strategy designed to break-even against other GTO opponents, it's designed to make no money and to be unexploitable.

It makes some money when people deviate from GTO (make mistakes) but unless you're playing a computer, you always make more money by playing exploitative poker.

Because you become exploitable by doing anything 100% of the time and GTO is designed to be unexploitable, not to make profit.

Mixing up your move only 10-20% of the time makes a huge difference.

Assuming you are exploiting your opponents correctly and assuming they dont counter-adjust

On topic: The GTO strategy in rock-paper-scissors would be to play 33/33/33 so it has something to do with runouts and how ranges interact with them

what above posters said.

it is NOT the most "ev" since the most ev would be a specifically tailored strat for each particular opponent you play.

it is, however, going to be +ev vs everyone, and will only be break even vs another GTO mirror. it will not be -ev.

the reason the frequencies are not 50/50 is because there are plenty of situations that arent 50/50. if the river pot is 100 and i bet 50, do you have to be good here 50% of the time to call? what if i bet 75, 200?

if i open and the flop comes Axx, do i have to cbet here 50% of the time? how often does my range hit this flop, how often does the callers range hit it?

bet sizings and the ranges probability of hitting different boards greatly influences the frequencies, thus its going to be different %s in different situations because there are multiple variables.

GTO always bets the very top of its range 100% of the time - so it definitely does some things at 100% frequency.

Also - are you saying GTO intentionally takes lower EV lines sometimes? Solvers always take the highest EV line.

This question should go here. Possibly get responses you want.

Always betting leaves your check range vulnerable
Also makes check/raises capped
Maybe there are some rare situations where it's correct to do something at 100% frequency

I don't use solvers, I have some idea of what GTO is, but I'm not very interested in the details

Always taking the highest EV line could potentially also make you exploitable, so it would be GTO to take a line with less EV to keep yourself from being exploitable

Highest EV lines against non-GTO players (everyone) are always exploitable so by definition GTO does not use the highest EV lines

So I don't want to get another infraction for "making fun of someone," but literally none of what you said is accurate.

It is very obvious you have never used a solver. No you have no idea what GTO is.

yeah i am going to post it there. this thread is a dumpster fire.

Its because the solver is taking the macro view of our entire range and not just looking at one hand that falls within that range. If the EV of betting and checking hand X is the same, the solver can calculate that checking hand X 5% of the time increases the EV of the check branch of our game tree and thus increases the overall EV of our range since we know that betting and checking hand X has the same EV.

But how do we prove this?

Node lock the mixed strategy hands to bet or check and see how it affects the overall EV.

i tried to send doodoo a PM to reprimand him



solver will take -ev lines all of the time. its playing its range for balance & protection, it will sacrifice ev on one hand purely to protect its calling range, and frequencies.

the NET overall strat is +ev but each hand in a vacuum absolutely is not



doodoos response :lol aren't you like 16? No you are completely wrong. Solver always take highest EV lines.

you have no clue what is going on.

guys i tried to private message him and inform him but he didnt listen



i run sims all day in the computer lab during study hall, there are tons of times we check back the nuts, why would we always bet the nuts? here are a few samples of recent trees, there are plenty more where we mix strat the nuts.its completely contingent upon how strong/weak our range is.
further more, no hand is the most +ev line in the vacuum. the NET result of how we play our entire range is the most +ev, but each hand individually ? no way, we sacrifice ev with each hand to balance our range.
BOOOYAAAHH BABY TALK 2 THE HAND

lol

The only reason the EVs are mixed is because at the ratios the solver presents everything is perfectly balanced. If you **** with the ratios of a single combo the EVs of the rest of your strategy (other combos) will change.

simple lessons = correct

Can you confirm that solvers always take the highest EV line?

they dont, the net of the strategy is the highest +ev strategy. each hand in a vacuum is not the highest EV line for that hand.

it's always going to breakeven vs another optimal strategy over infinite hands with all ranges being equal, within a range and against opponent's entire range, and throughout all permutations of the game tree. Taking the "highest EV" line would be exploiting an opponent, and deviating from balance.

Think of it this way, if you were to 3-bet someone and they called, and they played GTO vs your GTO strategy, their range would still be at an EV disadvantage. If the roles were reversed, and you were to both play balanced once again, whatever they lost by defending and playing an inferior EV range they now gain back by being at an advantage.

Don't forget to berate everybody who tries to offer advice but misinterprets something or is slightly wrong because they're human.

here is a concrete example from a hand you posted, betting AQ on QJ8r BTN vs HJ when they defended a 3-bet. When you bet the flop with TPTK, with your action, you were saying : I am deviating from balance, I am taking a higher EV line with this combo (you were supposing) than would be correct in equilibrium because I think that my opponent will defend wide enough that I can move a hand in the the middle of my range on this board into the value portion of my range. By doing that, you have allowed yourself to be exploited by getting checkraised and blown off of your strong showdown value / equity. Whether or not that action is justifiable or not is up to you to decide, but doing so is moving away from balance, gaining EV where a solver would see that the EV of checking and betting is similar, and looking at opponent's entire range taken against yours, see that it doesn't overall gain a lot by betting.

But I think in this example betting and checking were mixed and betting was the higher frequency play. So when an action is mixed it is the same EV.

My main question was really - why when mixed frequencies occur are the percentages so crazy sometimes? For example I've seen 98% bet/2% check scenarios but they are the same EV?

it wasn't betting high frequency with the offsuit combos. The solver preferred to use suited AQ with backdoors to bet, as they could stand a checkraise, and were more durable over a multiplicity of runouts! Although I haven't studied the specifics, I would guess that it is betting :
1: enough combos and not too many combos to keep ratios of value : bluff in check
2: betting hands which meet a certain equity threshold

and moving more offsuit AQ combos into the bet category is indeed an exploit as we are taking a hand which in equilibrium is supposed to be similar in EV for betting and checking, and saying that it gains so much by betting that we should instead bet it for value against an opponent's non optimal strategy. It's putting your frequencies out of whack. Again, that is not necessarily a bad thing, it's just saying that we are going to take a non optimal (in a GTO sense) action because we have observed that villain is playing non optimally.

Upswing article

"4 GTO Myths That Way Too Many Poker Players Believe"

-> "A GTO strategy would always take the most profitable line. Wrong......"

https://www.google.com/url?sa=i&sour...66079040504430

I have no idea what this thread's about but???