In No Limit Holdem, assuming two players of equal skill, what % equity would we want our range to have vs said villain when flatting both in position and out of position?

How much would this change per villain to act behind us?

Thanks!

too vague? not really a cut and dry answer? I'm only referring to preflop flatting ranges.

Yes, the question is quite broad. But, to get things started, here is strictly a math answer for a particular situation.

Pot is 1.5bb. Villain open raises to B and it folds to you in the big blind. You have to invest B-1 to flat call.

Showdown EV = eq*(1.5 +B) – (1-eq)*(B-1)

Set EV to 0 and you find

eq = (B-1)/(0.5 + 2B)

Example: Villain raises to 3BB, or B=3. Break-even equity = 2/6.5 = 30.8%.

Now, as stated, this is a showdown math result ignoring future bet possibilities, how you characterized villain, his stats, stack sizes, position, etc.

For example, If you were on the button and you assume blinds would fold, then doing a similar analysis results in a needed equity of 40% if villain raises to 3bb. But, because you will have position and possibly implied odds such as with a small/medium pair, you might call with somewhat less. If you think one of the blinds will call, then that increases the pot odds but lowers your winning chance. It also then becomes a multi-way situation, which complicates the math quite a bit.

I appreciate your response but what you're ignoring is exactly what I'm asking about.

I understand maybe nobody out there wants to give out their work but would somebody at least explain the process? I'm willing to put in the work myself by going through one hand at a time and running the equity vs a villains range... but what equity do it want or how do I decide what equity I would want?

for example, if at a 6 max table, I open UTG with a 16% range and an exact clone of me is UTG+1... what % equity would they want hands that they're flatting with to have given the fact that they have position but 4 people to act behind them? how much equity would they want if said clone was in the BB and everybody folded around to them out of position?

The math is much more complicated than you think. Also equity is the wrong metric to measure what you're asking imho.

too complicated for someone with a base level understanding of algebra?

where do I begin with this topic then? flatting is something I know is a flaw in my game but I don't really know how to go about solving it.

I'd think "too complicated for current supercomputers to solve within our lifetime" would be better. You're basically asking for solution of NLHE, IMO, as you can't solve these things partially ("how to play flop", "what's the correct flatting range", "what's a good turn strategy"), you need to solve it all at once.

I believe neural networks and other self-learning computing methods are the current hot topics.

I think it'd be a mistake to coldcall an utg raise without an exploitive postflop plan. I 3 bet or fold in that spot usually unless I expected lots of callers behind me.

I also think it'd be a mistake to coldcall a cutoff raise from the button without an exploitive postflop plan except with the strongest drawing hands like KJs+, QTs+, JTs, T9s. Even if you coldcall those hands, your range is extremely narrow and readable, which is a liability.

However, if you find an opponent that either gives lots of free cards or is very bluffable, then sure I think you can start coldcalling more preflop, but not without either read imo. The problem is that you're going to flop a lot of middle pairs with the strong preflop drawing hands. If you don't have a plan to either exploit by bluffing or winning stacks more often than you should be able to in a vacuum, then you're going to end up in a lot of bad spots.

"I could be wrong and it's a terrible tragedy."

I think pasita hit on this pretty well. You're asking for a solution to all of NLHE which is much more complicated than just simple algebra.


You can start by using the whole how much do I need to defend % thing but it shouldn't be a rigid structure. Much more important to think about how you came to the conclusion on what to defend NOT what you defend in scenario xyz.

I also think this is much too hard to calculate.
I would recommend buying cardrunnersev and trying to get a few approximations to this or other similar questions you have. The act of trying this will probably teach you a great deal for both poker and probability.

thanks for the responses!

so, as a follow up, how are people who are playing mid stakes 6 max anonymous tables going about developing default ranges if this stuff isn't solvable?

I've recently started mixing in some anon tables and a some players are just soooo super solid (at least they appear to be to me ). they also appear to almost not be adjusting at all vs me unless we get a couple hundred hands with each other in any given particular session. I really think this is the way to go vs those who appear to be regulars because you have no real reads on super small samples unless they really jump out as glaring.