WHPH

Could you expand on what you mean about your RCE stat not beaing exactly indifferent because of ranges?

Again, I don't think you understand my question. Of course we make money because the game isn't solved - hence people make "bad" decisions, but that practical argument doesn't answer my theoretical question. At least not in my understanding.

Ironically, I'm actually in the middle of the preparation for an exam in a game theory course I'm taking as a part of my bachelors degree in Economics and Management. I probably should have waited to participate in this discussion after I've covered the whole curriculum - or at least the part covering games covering poker. I will return when I've covered the DGII part, hoping we can discuss on a more equal level then.

Thank you for your answers, by the way.

I don't think you're understanding my hypothetical question with that response. I know we're unable to calculate the equilibrium ranges full-scale, but that's not an argument for why we're making money in theory.

Let me give it a little more thought and I will think about a better formulation and come back.

Yeah, obviously. But if only one of the players is playing the equilibrium (shitty word to write) strategy, then the game would breakeven regardless of strategy played by player two, right?

There's a reply button by the way. :)

But if I'm losing money going all in with QQ-JJ, then I'm not really indifferent between calling and folding? You're probably referring to a pot where we're indifferent to calling/folding after a 3bet or 4bet, but then again we're probably not indifferent between our actions in the initial preflop node?

I know the example is very much restrictive. I made it up because of TheNumba1's statement about the equilibrium strategy winning the pot "invested so far". I couldn't really see how this would earn us money if we're truly playing an equilibrium strategy where we're making villain indifferent on every street. But as Joe Sham stated below, this would make us win the blinds.

That's true! I knew I missed something. Thank you.

My next line of thought: The initial pot before our first raise must be the blinds. What if we assume a poker game without blinds and again truly make villain indifferent between calling or folding - where we again assume villain has no other options for the sake of an easier discussion - both preflop and on every street postflop. Then where's the profit of our equilibrium strategy even though villain doesn't play the same equilibrium strategy? How can he make mistakes if we're making him indifferent on all streets?

Like in Roshambo (rock, paper, scissors). If we play a NE-strategy - picking uniformly random between the three options - the game will automatically tie. Would this happen in poker to without rake? If in a HU match one player plays an equilibrium strategy, would this force the two players to break-even regardless of villains strategy?

Can you please elaborate? Maybe give en mathematical example? I think I just confused myself by the following chain of thought: If we play an "equilibrium strategy" and truly make villain indifferent between calling or folding - where we assume villain has no other options for the sake of an easier discussion - both preflop and on every street postflop, where's the profit? 

How is it an accurate approximation of nature? Where do we see fractals?

What is so awesome about fractals?

It's probably fine. I'm most likely just a little biased, as my 3bet sizings are probably smaller than most peoples. I do however think that 4x OOP is way too much as a standard 3b sizing.

Apart from your too high 3bet, I think the line is fine. Your EV + your FE are probably enough to cbet this board, as villain looks like a big station, making his flop range very, very wide.

I don't like your choice of hand for a c/r, as it makes you c/r with a seemingly high frequency. A better choice, i.e. Ah3h, also increases your equity when called, thus increasing your overall payoff of the c/r and consequently your winrate.  

The problem with your idea of playing the trap-bluff-game is that the 5c on the turn decreases the combinations of value c/r's in your flop c/r-range, hence leaning your overall range more towards bluffs than value.

I agree with c/f flop btw.

While it's highly entertaining with some 300/600 live action, I actually think this is one of your worst (less good!!) videos, as I think it's hard for us mortals to learn very much from a video like this, besides the CREV analysis-part. Too few hands I guess.

That being said, I do love your videos and your approach to the game. If you ever need an idea for a video, I would love seeing some videos from you with a more exploitive standpoint. You kind of have the perfect starting point to discuss how to exploit different inferior strategies found at the lower stakes, as you're probably one of the best players in terms of balance/theory/"GTO". 

Keep up the good work.

Agree about MoP. It's almost embarrassing how they deviate from the norm within mathematical- and statistical notations. It's still in many ways pioneering book, but it could be so much better. It's also kind of a disgrace how they have managed to confuse the poker community by throwing around standard terms within game theory however they saw fit, i.e. their use of "GTO".

Have you read Jandas book?

I'm not sure your question makes sense. If villain calls 30% of the time regardless of your sizing, the best sizing is obviously to shove with the nuts.

If you think he cares about your sizing, you want to bet 2,33 times pot (isolate x in 1-(x/(x+1))=0,3), as this implies you're bluffing with a frequency of 30% of the combinations in your value range, if you're using minimum defence frequencies as equilibriums.

I think ATo works better in a 4bet range vs. the NL100 SB 3b ranges I play against, as I don't think they're 3betting as wide as their equity actually allows them to, nevertheless wide enough to be unbalanced in their call 4b/5b ranges.

It's probably a fold on the river as played. I think you're folding way too much if you fold turn, even though I often feel it's the best play $-wise, but I can't find enough potential bluffs from villain to justify a call on the river with AT, exploitive or not.

I think it's a board + run-out you can bet relatively wide against a presumed bad balanced NL50-player. Even though I think you can do it exploitably, I like to be somehow balanced anyways. I don't think you have enough flush combinations in your range to balance the wideness of the range I think you can bet, thus I think this is a mandatory bet.

Thank you for your answer. I don't know how I missed the very first comment.

No offence, but any decent 3/6 player should know that a nice readable layout is a much better path towards any good pokerdiscussion. This is just confusing. Redo OP and I'm sure you'll get good answers.

We might not make all the (1-alpha)-calls here, which is a kind of a ridiculous estimate of game theoretically optimal frequencies anyways, but I don't think folding the absolut top of your range without very significant reads can ever be good - not on 50nl Bovada either.

It can happen though, at least in the computable part of the theory we understand so far, that you're in a situation where you have to fold your entire range. I do however think that those situations will happen primarily as a result of an inferior composition of our range.

Seems like a trivial call turn and call river, as it's impossible to balance a shoving range on the turn. If you fold here, you're folding everything except boats and quads. That would be pretty easy to exploit.

Why do you think betting flop is "max exploit"? Exploitative or not, I wouldn't call betting TPTK stabbing a lot. Especially not on a flop like this where TPTK is, in essence, the top of our range.

I think it's close between jam or call flop + any turn. It probably doesn't matter. Flip a coin, just never fold :-)

I 3b pre.

I think river is a c/c, not a lead. His range contains a lot of bluffs on this runout. You want to keep these bluffs in his range. By leading you're only getting value from a very small part of his range, thus decreasing your EV.

As played, on the river, you can probably fold.

I think preflop and flop seems standard, except I'd open to 3bb instead of 3,5bb. You might want to raise turn, as he theoretically can give himself quite a good price here against your range, but I think flatting is fine too in practice. It's quite hard to call calling on the river a mistake when given a price of 4,3 to 1, thus I call.

I just think it fits better in a pre flatting range in at spot like this, if it isn't a value squueze.

NFD or not I'd expect UTGs flat sqz-range to be kind of Ax-heavy, and thus my reversed implied odds statement. But again, I might be wrong.

You're probably the best judge on whether or not you can make an exploitable fold, but I think it's a snapcall considering your range. You 3bet AA, JJ, probably TT and some KQ. Even if you don't 3bet some KQ hands, there's still only something like three combination of KQ in your river-range as played, not taking into account whether or not you check back some of those combinations on the turn. Consequently, 66 is the top of your range.

You're welcome, and I agree!
If you really like reading, as it's a 918 pages academic mean mother******, The Cambridge Handbook of Expertise and Expert Performance looks like a very good read too.