I have an excel shoving calculator that's usually used from the perspective of the person
doing the shoving but there's no reason it can't be used from the other direction.
Let's start by assuming that you've got no bluffs in your range and if you're 3betting that range for value, you're calling a shove with that entire range. What's important here is not your range per se but that villain has zero fold equity, whether they know it or not. YOU know it, so we can plug that into the equation.
Since villain has no FE, they need roughly 43% equity for the shove to be break-even.
For villain's range, I started with the obvious 99+AQs+,AKo that seems all but guaranteed to be in a rational 4b/shoving range. That range is 65.96 vs. your ATs.
Then I threw on the better broadways; 99+A9s+,A9o+,KQs,KQo. Now villain has 51.46% vs. your ATs.
If I throw in all pairs the equity doesn't budge much (13.12% of hands), now 51.36%.
I think the remainder of the "value" hands are happy to see a flop, would QJs shove here? I can't say I see that very often at all at these depths, excluding the occasional spaz monkey (saw 32o shove yesterday).
So how much of a bluff range do we have to see in order for this to be b/e for villain? At the 51.36% equity where we last had our villain, their shove is a +t197 move.
Suppose I add J2s-J7s, T2s-T6s, another ~3.3% of hands. When I add a bluffing range, which is awful infrequent, this is about what I use; it's at the edge of my calling range, isn't likely to be dominated and continue aggression with a lot of equity when the a flush draw hits the flop.
Unfortunately, villain is still 47.06% vs. this range so the shove is still +t96 for villain (and therefore a call is -t96 for you).
I think that in order to make this a bad shove for villain, and by extension, your call of that shove to be +EV, it's necessary for villain to have both a modest 4b/shoving bluffing range AND including every broadway hand, which makes villain a 39.12% dog, and therefore their shove is -t91.
If we change your holding to AJs, vs. a range like all pairs, A9+, KQ and a modest 3% bluffing range, villain is a 47.06% dog, making a call of the shove -t97 for you.
If we again change your holdings to AQs, and leave villain's range where it was for the AJs example, villain is a 43.28 dog and so the call of the shove is roughly b/e for you (+t7).
So my conclusion is, provided villain is shoving with only pairs, strong premiums (top 13%) and a smattering of bluffs (3.5%), for a total of 16.44% of hands:
- calling the shove with ATs is significantly -EV.
- calling the shove with AJs is modestly -EV.
- calling the shove with AQs is b/e.
It's also worth noting that adding and removing 22-88 has, at most, a 2% change in equity.
For reference, the equation I used is:
(FE * CPS) + (1 - FE) * ((PE * (CPS + SRS)) - ((1 - PE) * SRS))
Where:
FE = Fold Equity
CPS = Current Pot Size
PE = Pot Equity
SRS = Smallest Remaining Stack
I've sanity checked this equation by plugging in:
FE = 0%
CPS = 333
PE = 33%
SRS = 333
ie, if there's a pot sized bet, one needs to only be good 1/3 of the time, which makes sense.
It is ENTIRELY possible that I've made an error here so if anyone can spot it, please say so.
A
