so what % should i steal?

a steal is neutral ev PF, WAY better than fold which is -50bb/100?
so how do i calculate the optimal steal %?

some math:

This is not a math question.

There is no optimal steal, only constant adjustments to your opponent and the situation. If you're looking for a GTO solution, I'm not 100% sure, but I think you would basically have to solve poker to figure it out, which is no easy task.

but , if u fold bb, u lose 100bb/100, so, preflop should be able to solve for optimal defense range?

I am not sure I understand this post or the "logic" here. It could honestly be me.
But, if i understant this, it seems like OP "proved" that optimal defense % is 100%, no?

Sweet, problem solved!

IMHO OP, this is not as simple as you think. At best you are going to solve a toy game in which the action freezes when the flop comes and hands play to showdown. That's gonna take a bit more math, and its not going to get you all that far anyway.

Poker is so complex that humans beat modern computers at HU poker (NLH anyway). Think about that. The math you're doing in OP looks to me like trying to come up with a simple equation to solve preflop poker. Its never gonna hapen. Sometimes we have to settle for a bit of sound reasoning and our faulty human intuition to get aproximations.

The dangers of using GTO and MOP concepts with poker is that poker is a very convoluted form of strategy game. Trying to solve a pf problem like this with GT is just completely impractical given that you would need to estimate dozens of very tough to predict variables.

In short, GTO is best used in broader situations like pf by creating thresholds. Yes, you lose 50bb/100 when you fold the BTN. Yes, you're risking 1.5bb to win 1.5bb (1:1) with a min-raise. And thus yes, if your opponent folds > 50% of the time you are profiting with ATC (a huge improvement over losing 50bb/100).. And somewhere lies another possible threshold where if your opponent is defending X% (> 50%) and playing well post-flop, the profitability of opening 72o approaches -50bb/100 and potentially surpasses it (to make it a fold). But because it would demand a ton of post-flop analysis/math and would only result in a vague estimate, you're better off using approximations (and concrete thresholds) than actually trying to "solve" pre-flop situations like this.

It's also pretty important to note that just because strategy X > strategy Y or that strategy X is auto-profiting money, that it doesn't necessarily mean strategy X is your best option.

I think the best you can do is try to solve for how frequently you need to be defending in order for your opponent to not be auto profiting with an open with ATC. The best method though is to try to just play every hand that you think is +EV.

Sometimes this might result in you defending a tighter range and getting exploited pre, but making up the EV postflop by taking a stronger range to the flop and your opponent not adjusting.

The earlier the street, the harder it is to solve. You can solve for GTO on the river fairly easily with known variables. But solving a preflop spot means solving the thousands (probably way more) possible situations that can occur as a result of that spot, and comparing them to the EV of alternative options (which you would also have to solve for).

This game is way more complicated than it looks if you break things down this small.

Nice post Lefort

The EV of folding is always $0.

Well yeah.. but we're looking at the specifics of the hand in it's entirety, not just the discrete junction of folding pre-flop.

(post blind) + (fold pf) = -50bb/100 + 0bb/100 = -50bb/100

(post blind) + (raise pf) = -50bb/100 + Xbb/100

A. Before blinds are payed
B. After blinds are payed


I just woke up, so I might be wrong, but:

This doesn't make sense. You profit if villain folds > 50% of the time from point B. From point A. you need to win:

0EV(Minraise) = L/(W+L) = 2/(1 + 2) = 66,67% ~ 67%

= EV(Not posting blind) = $0

+1,..
This

People talk about this a lot. Has anyone actually proven that you "have to" stop opponent from showing ANY auto profit opening bttn with ATC?

This would be true and obvious if the action ended preflop but there is a positional advantage post flop which makes me think it COULD be GTO to defend with a range that allows some profit with ATC. Obviously the profit would HAVE to be <1BB/hand, but does it HAVE to be O?

BTW,I personally defend with top half of the deck+ (prolly around 55%) but i came at the problem from a totally different angle. Its just a coincidence and nice little bonus that my defense range won't allow bttn to auto profit ATC. But I am also sure that my range is not GTO and actually COULD be too loose.

Serious question; does anyone really KNOW that GTO defense vs bttn raise won't alllow auto profit?

yea i'm more interested in ignoring the postflop, which we can't really solve.

so HU preflop, what's the 'optimal' steal %? doesn't the fact that folding = -50bb/100 means that we should be stealing wider etc? all these equations solve for 'breakeven' on steals, but they seem to be ignoring how much you lose by folding? or am i completely messed?

also applies to 6max, where the button is worth 25 50bb/100 or so, so therefore folding it instead of stealing/defending = -25bb/100

Jesus you people are retarded. EV is all comparison. All that ev equation says is that by folding you will lose however much more than if you had not played the hand at all. So from now on if you know you're going to have a hand you'd fold preflop, don't post your blind. Wow you're a ****ing genius. Sick math skillz.