Doug, you basically quoted what i said and repeated it in different words, except for adding to the definition of GTO as being balanced, unexploitable... and maximizes expectation.

im confused...

There are strategies that meet the conditions you laid out that are not GTO. I'm picking a nit in what you said, suggesting that you're missing a point in it. The differences in what I said and what you did would be the whole point of GTO, being the O part.

People like to throw around math terms. Some of those terms have specific meanings, it is math expressed in English. By using the terms poorly, the math is left behind. It is kind of like the stuff above about "exploiting" non maximized lines. You can have balanced lines that aren't maximized -- they aren't GTO, they're just balanced. People above are talking about "exploiting those lines" by not having minimal EV against them. The line can be unexploitable while still not minimizing your opponent's EV. From the point of view of Boz and others, they are exploiting that line by having better EV than they might otherwise -- this misses what exploitation is.

Ok, I get this and I was wrong, but would like to make a point: I think there needs to be a practical allowance made for the use of the terms, based on context. GT is theoretical; you can't actually know what your opponent's range is, so you're always ignoring (or accepting) a margin of error when solving (or "proving") the problem. Right? That was the intent of my comment, and if I'm off base then I apologize again.

About a hundred years ago I was working with some friends to develop a more-nuanced version of the old TradeWars game. (A lot of what we did eventually found its way into Masters Of Orion II.) One of the people I was working with was a mathematician, who would get bent out of shape every time anybody used the word "random". It got a little tiresome.

Oh, and my wife is a lawyer. "Proof/prove" is another one of those loaded words.

In the context of a bunch of people talking about GTO and unexploitable, much of what was said above is wrong. Not just stuff you said, bunches of stuff. There's no emotion in that. Once we start throwing the words balance, exploit, and GTO (not really a word ) around, you're going to have to expect math to come in. Bellatrix meant something specific when she said "prove it" -- she's not challenging anyone's manhood, she's asking them to do math. Most of us aren't mathy enough to do what she asked, so it is perfectly fine to say back to her "I don't have enough math to do it, could you explain why I'm wrong". You're kind of digging a deeper hole here b/c not knowing the opponent's range isn't that important here-- he's cbetting 100%.

In a proof, there is no margin. You have a set of assumptions. If you want to disprove her assertion that cbetting 100% is best, all you have to do is provide an example to the contrary. If the math is correct, there are no exceptions. People are throwing around terms to back up their arguments, by doing so they invite what you're characterizing as nit-picking. Be glad you aren't Private Joker getting DeathDonkey game theory love, that was harsh and this is gentle. None of this math nittery even comes up if people just say "cbetting 100% isn't best and here's why".

In the end it doesn't matter the exact terms that much. You can ignore all this stuff. OTOH, the places where Bellatrix disagrees with someone are an opportunity -- a really good math person disagrees with what is being said. Start by assuming she's right. What is it that was said that she disagrees with? That's a place where someone can learn something. Don't get mad and claim it was a semantic argument. Learn math from someone who took the time to put together a 30 freaking part video series on these concepts. Assume that she has no invested emotion in shooting you down and that she's trying to help you understand.

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BTW, for people who have the Mathematics of Poker at home, the discussion here about balanced vs. exploitable play is covered pretty clearly on page 372. My points in my disussion with Nemesis are better made by Bill and Jerrod in the 3rd paragraph. I don't really want to copy chunks of the book on to the forum w/o permission.

I stated what I believe as fact. Maybe that was a mistake, but I think posts come across better when they're not full of "I think" or "imo". I wasn't trying to disprove her, but rather give her something to disprove. If you can disprove my claim that you exploit a range that is wider than gto by check raising more than optimal(who's to say what that really is?) then you'll have convinced me, but I don't know how to disprove it.

You're missing the definition of exploit. You can't exploit a balanced range. Again, the MoP section on balance on page 372 has a very clear explanation of all this.

If the cbetting strategy is suboptimal, you can gain value. However, it is impossible to exploit this strategy. This perfectly balanced strategy of cbetting 100% cannot be exploited, QED.

Funny, but no content. Back to NC thread, Trolly.

Theres really no way I expect to say something super valuable about HU because its not my format, but doing the same thing no matter what happens is technically a degenerate strategy (i don't mean those kind of degens, think cryptography).

Checking can induce action and create edges. If you just bet all the time predictably then its not difficult.

You know what I've noticed? Nobody panics when things go "according to plan."
- The Joker

Mostly, in a modern HU LHE hand between OK or better opponents, the hand begins after the raiser cbets. The OOP player w/o initiative is checking 100% and the raiser is cbetting 100%. The hand starts when the OOP player calls/folds/raises. There are exceptions to this, but the vast majority of hands between decent players go this way.

A degenerate strategy? Maybe. If you can find edge in not taking the standard line that is good. If you can find a balanced line that is better than cbetting 100%, even better. The thing to be concerned about is in losing a lot of value looking for a more interesting strategy. You can do OK just thinking the hand hasn't started. I don't cbet 100%, but I'm pretty sure in the spots where I pass. If there is doubt, I fire and deal with the consequences.

imo, a much more interesting spot is being the OOP player and considering whether or not you should have a c/r range on given board textures. Finding the perfect spot to not cbet likely falls somewhat out of the OOP decision as well. Once you have a great handle on when to c/r as the OOP player and when to call/fold, you'll understand a lot more about the IP spot.

I am really sorry, I don't have much time atm. Last lecture times, gotta fail some students (I'm not kidding, I'm really sad about it).

Anyway, I will try to answer on Tuesday or Wednesday, but just a few definitions.

- A balanced strategy cannot be exploited. c-betting 0% is balanced and cannot be exploited, for example.
- A GTO strategy is the balanced strategy that maximizes value. It seems much more likely that 100% cbet will maximize value than 0% cbet.
- I have not encountered balanced strategies that cbet a number < 100% that still maximize value (you're letting go of too many value hands for the sake of balance), but I'm certainly willing to be persuaded otherwise. I just don't know
- GTO is quite easy to calculate on the river without the presence of draws. It is almost impossible to do so in flop situations (idk how good Polaris is there). Sonia, who plays exploitative, does check back some flops though.

datsmahname, exactly, you create edges by exploiting your opponent, I agree.
I would've loved to hear some examples, though ;-) (I have gotten owned by some playing some high stakes players at SSHE HULE, e.g.)

Yeah I would love them as well. Its really exciting for me to go beyond "scripted behavior" and try and really justify alternative options with higher payoffs.

HU isn't my game, so when I do play HU its against a spot. Here, we can of course get value with standard lines, but purely scripted play (like 100% c-bet) feels like wearing blinders because we don't get to see what he does if we check back and can miss value by avoiding these scenarios.

sry about your failing students. sad time of year.

Hmmmm. I always thought that GTO is a strategy, which does not allow your opponent increase his EV through changing of his strategy. May be it is equivalent to what you wrote in bold, but I do not immediately see the equivalence.

Probably we have as first to agree on the same terminology.

Yep, that is what I meant by unexploitable, no matter what opponent does, he can't improve his EV by changing strategy. However the O means that your EV is maximized at the same time. Example coming in a few minutes while I write the post.

100% c-betting is "balanced" in HUHU in that it doesn't give your opponent an extra level of information about your current hand. This is one important part of GTO, but not the only one. You also want to play with an appropriate amount of aggression for your current situation (e.g. your equity edge and other unmeasurables such as the exact advantage of having position over 3 more streets of play).

I think the best way to see if a given play is GTO is to flip your perspective and look at the hand from your opponent's perspective: is there anything they can do to exploit you? If all their options look equally unattractive you could be close to GTO.

In this example, if SB always c-bets the flop then BB can try a strategy of not 3-betting preflop and then check-raising lots of flops. Because SB always c-bets this strategy is guaranteed to "work" in that it can always get at least the same amount by the flop as 3-betting preflop and c-betting.

Now give the SB an 85% preflop range, and the BB a 95% range. Fire up Equilab/Pokerstove, and start looking at the equities of these two ranges on a bunch of different flops. Is the SB's equity edge high enough to bet every flop with his entire range? To show that c-betting 100% isn't GTO all you have to show is that this potential BB strategy might be a good one. There are lots of flops I can think of where SB doesn't really have "enough" equity to bet his whole range.

Of course there are lots of flops, and lots of hand ranges that you can hold after opening from an earlier position than the typical HUHU hand ranges. So there are many situations where always c-betting 100% would be a really great approximation to GTO. Plus it's balanced and an easy strategy to play. But is 100 c-betting always GTO in every LHE situation?

I have to answer no.