Assuming a full ring game with no rake and antes starting the pot off at 3.5BBs. Lets say we're in the BB and face a 3x open. We now have to call 2BBs to win 6.5BBs (or 3.25-1). When converted to a percentage 3.25-1 is roughly 23.5%.

Now taking into consideration the concept of equity realization and reverse implied odds and whatever need be, theoretically how do we determine how often we should be defending, say vs a UTG open as opposed to a BTN open?

Please include any math if possible.


*side question* given the much better than normal odds we're getting in said game, would this allow us to flat more out of the SB, because we're less worried about being squeezed?

probably like 70% or something, i dont play ante games though

what are you basing that off? If btn is opening 50% of hands you think we can profitably defend 70% of our hands? Seems a bit optimistic imo, though I think its close. I'd assume a bit less.

If anyone can offer some mathematical insight into this would be greatly appreciated

There's no math that can answer this, you'd have to solve all possible postflop situations first.

It's probably around 70% though like Brokenstars said, since the BTN range and pot odds are similar to the BB vs BTN 2x spot in a no-ante game.

does this take into account the concept of equity realization? 70% seems really icky to me, this is practically any 2 suited cards and hands like k3o and q5o. I can't imagine profitably defending hands like that even when getting these odds and no rake.

If we are defending 70% how wide do you reckon that we generally 3bet?

70% range vs 50% range does hold 48.5 total equity so maybe this is right. So how many 3bets would we have in our 70% of hands? So folding 30% of hands is sort of the "fee" of being oop with a capped range given we call all hands?

considering the large size/antes you should be 3betting a lot... probably 17-19% would be my guess

I think thats about right as well

Just a random question:
Do you think that when we're shorter in NLH, we should generally be 3betting more SB vs BTN or less than when we're deep?
or does the 3b% not change much at al?

probably more (both theoretically and likely exploitatively) though i doubt the change is drastic

I think the frequency would be similar but the hands/range would be a bit different. Example; if we're playing 3b/fold from sb vs btn then deep stacked you can 3b low PP's and low suited connectors, whereas shortstacked I think we're not 3betting those hands all that much and a hand like A9o would work better as a 3b if we're shortstacked. I don't have any solvers or anything to back this up its just my understanding.

If we're 10bbs deep for example we prefer 3b jamming a9o and we're probably folding 45s