I'm in bed so I can't really explain at the moment. Youre wrong about range construction and gto poker. Sorry.

No need to apologize. Just explain when you have the chance.

For starters, the equilibrium opening ranges for 3+ player poker remain unknown, thus calling any multiway strategy "gto" is a mistake.

Equilibrium strategies for real poker are mixed strategies at nearly every decision point; including value hands and bluffs at 100% frequencies will not lead to an equilibrium strategy.

The indifference principle is useful only for certain all in situations and some river situations; when ranges are asymmetrical, using a frequency based approach to decide how much of our range we should fold isn't going to give us an equilibrium strategy.

True indifference is about forcing our opponent to play a mixed strategy in order to maximize his expectation. We do this by playing a mixed strategy of our own. If our opponent plays a pure strategy, then we should also play a pure strategy.

Traditional definitions of value and bluff are being abandoned for preflop, flop, and turn strategies; the profitability of a hand is what matters. Hands derive expectation in a number of ways so putting hands into nice neat categories doesn't tell the whole story. Categorizing hands is a mistake.

You'll notice that I called it a "GTO-style" of play. I never claimed that what is suggested is GTO or that GTO is even known.

This is true, but irrelevant. It's also irrelevant to the analysis. The range construction process is about building intuition and understanding for how hand ranges interact with each other. The intention is not to declare that this is *THE* way to play the hand.

This is where I believe that you are likely to be making significant overadjustment errors. The arbitrary approach to picking hands with which you alter at random frequencies is likely causing more errors than it is improving your EV by mixing your strategies.

It was never claimed that this is giving us an equilibrium strategy.

This is true insofar as you assume that your opponent's pure strategy is also a fixed strategy. That is, your opponent will never adjust. At the lower levels, this might be true. But this mentality would also lead to a stagnation of overall poker skill development. If you intend to move up, then you should begin to develop habits that are applicable at the higher levels. Feeling out what a baseline strategy might look like is the start of an iteration of strategies, not the end product that should stand for all time.

I'd rather have a methodical choice of mixed strategies than a haphazard approach of "I think I would adjust my KK and KQ completely arbitrarily."

Nobody ever claimed that it did.

Blanket statements like this built on a faulty reading of the post is also a mistake. You seem to have some sort of vendetta against GTO-style play in favor of a more old-school "feel" sort of approach to poker. That's fine. It's your money; play how you want to play. You can even be 100% dismissive of anything remotely reeking of a different theoretical approach to the game.

But those who are able to read and think carefully can see right through the strawman argument you've created against the analysis that was presented.

Not at all. In fact I <3 gto. However, the post linked upthread only has a connection with gto poker because it's about limit texas holdem. Any other similarities between this supposed "gto style" are superficial at best, and utterly misguiding to be frank.

It's building bad intuition imo.

Then please stop using the term "gto style."

I disagree. When I'm active at a table with lots of preflop raises and postflop action, I get called down much more often compared with the rare times that I'm card dead preflop.

Yes, frets entire post is exactly about value:bluff ratios and combos. This approach is only effective on the river.

You're wrong. If you had kept up with any of the modern ideas about gto poker, you would know why.

It's not random. It's an exploitation of the opponents calling frequency with hands that I consider to be marginal. They call down more often when they think I'm too loose, thus I value bet slightly thinner than I would as default.

Meh. Given that the two common approaches are GTO-style and exploitative, and that Fret's is clearly not exploitative, I find no issue with the usage. That you want to be particular about it is your own issue.

I'll simply repeat myself: Nobody ever claimed that it tells the whole story. A methodical approximation of the solution on a board in which the hand strengths are relatively well defined is better than a haphazard approach.

I'm always amused when people say this sort of thing. Maybe you're right, but you've provided no real evidence for your statement.

How about this: You give me your modern GTO-style analysis.

How much do you think your EV changes by changing your style on precisely these two hands in this particular situation? And on what basis have you chosen just these two particular hands?

I don't disagree with the theory. I just find the application to be arbitrary.

Frets approach is neither exploitive nor gto.

I agree, but neither option is as good as a properly mixed strategy that is built on maximally exploiting the opponent's best counter strategy.

It's about maximizing expectation. Assume the opponent plays gto: if we are to maximize our expectation vs this opponent, we must play a mixed strategy or else we will not maximize our expectation vs this opponent with few exceptions. Any deviation from equilibrium will result in a loss of ev equal to or greater than zero.

Assume the opponent plays some other non equilibrium strategy, whether it be static or mixed: there will be a maximally exploitive pure strategy that will have an expectation higher than gto would have vs the same opponent. However, when we change our strategy in an attempt to exploit, we become vulnerable to counter exploitation, which is why it's important to exploit exclusively on the margins, with the exception of closing the action with a fold or a call, which must either end the hand on the river, or be an all in situation.

1) not much. Just a fraction of a big bet.

2) When we have Ax, we block some of our opponent's Ax combos, which makes a value bet quite clear. With KK, our opponent has more Ax combos than when we hold an Ace, thus there will be a significant ev difference between betting KK and Ax here, despite the hands being "close" in absolute value. With KQ, the same logic applies. With QJ, the same logic applies, but if I bet that hand for value, then I become slightly more vulnerable to counter exploitation; gotta draw the line somewhere.

(1) How significant of a difference do you estimate this to be?
(2) This is precisely the arbitrary nature of your analysis that leads me to believe you're prone to overadjustment. The analysis appears to be not particularly meaningful.

1) very slight difference.

2) ok.

This doesn't bode well for the strength of your analysis.

I thought u wanted me to compare the ev of checking or betting KK, which I think is a small difference. The ev of betting KK vs betting Ax will be significant.

Because you asked me this:

Then you pulled the old bait and switch, which isn't nice.

.

With Ax, I expect to have the best hand over 90% of the time, so my ev will be near (pot).

With KK, I expect to have the best hand much less often, perhaps as little as 60% of the time, so my ev will be nowhere near (pot).

What sort of hand range do you think villain has here?

Like I said it will depend on my cards because of the blocking effect. When I hold KK, I expect my opponent to have Ax or better much more often than when I hold Ax.

You are creating a far from convincing argument that you have any real sense of game theory at all.

Let me put it this way: Do you think that card removal effects account for 30% of a player's hand range?

I haven't done the math or stoves and I'm not really in the mood for your **** tonight. I said enough already. Take it or leave it.

Your mood is irrelevant to me. And I don't need an answer tonight.

But that you've cited a 30% equity swing on the basis of card removal effects alone doesn't speak well of your analysis. And until you present something else to support your argument, I see no reason to believe anything you've said.

Ok.

So anyway, for anyone who wants to play around with hand ranges, it would be interesting to see what villain's hand range must look like for there to be a 30% equity drop changing hero's hand from A3 to KK on a A72 board against an identical* range.

Given that your two hole cards don't contain an ace, there are 13 aces and 37 non-aces in the deck, which means there are 481 unpaired-ace hands and 6 pocket aces for a total of 487 hands.

If you hold one ace and one non-ace, there are 12 aces and 38 non-aces in the deck. This leads to 456 unpaired-ace hands and 3 pocket aces for a total of 459 hands. That's not a big difference.

(*All equity calculators automatically take card removal effects into account because if you hold A, the simulator will not deal another A when it's working through the hand ranges. We would say that the ranges are identical if they describe the same collection of hole card combinations even if they don't have exactly the same collection of hands in them when card removal effects are taken into consideration.)

You got the board wrong and we were talking about river equity. Try taking out hands that the small blind would raise somewhere during the hand and also taking out hands that the small blind would fold as the hand progresses. Then run equity calculations and you'll see a significant difference in equity between KdKx and A2o vs the small blinds likely river calling range. Depending on how many naked Ax combos you assume the small blind would raise on the flop or turn, and how often you think the small blind raises preflop, you should find a difference in equity of 20% to 30% when you compare KdKx and A2o.

lmfao at including this in your combo count.

Right. Because this is *really* convincing with regards to the conversation we've been having about Fret's analysis.

Wait... you're asking *ME* to give you hand ranges? After I asked you to give it and your answer was "Well, it depends on what I hold"?

Finally, we're getting to some meat. What do you think the "likely river calling range" looks like?

I'm just showing you all the numbers instead of trying to pull numbers out of my rear end. It's actually the *most* favorable aspect of card removal effects because it reduces the number of those types of hands in half as opposed to dropping just a few percent.