I really appreciated the math breakdown—super helpful! I’m adjusting my assumptions slightly.
Updated Assumptions:
Let’s consider the button’s range as AJ+, 55 to TT, excluding JJ to AA due to the weak 3-bet sizing.
Button's Full Range:
Broadway Hands (AJ+):
AJo (12 combos), AJs (4 combos)
AQo (12 combos) → reduced to 9 combos due to Q♠ blocker.
AQs (4 combos) → reduced to 3 combos due to Q♠ blocker.
AKo (12 combos), AKs (4 combos)
Pocket Pairs (55-TT):
55 to TT (6+6+6+6+6+3 combos) → reduced by 3 combos for TT due to Q♠ blocker.
Total Combos: 48 (Broadways) + 33 (Pairs) = 81 combinations.
Pot Size and EV Calculation:
The pot size before I shove $180 is $86. Assuming everyone else folds except the button, the pot would be $386 if they call.
I assume the button calls with 88+ and AQs+, which totals 34 combos (15 pocket pairs + 3 suited broadways + 16 offsuit broadways). This represents about 42% of their range. Against this calling range, QTs has roughly 28% equity.
So the EV calculation looks like this: 58%×$86+42%×(28%×386−150)=$30
Breakeven Fold Equity:
Solving for the breakeven fold equity, we find it’s around 35%, which equates to about 27 combos out of the 81 in the button’s range.
Under this assumption, the hands likely to fold include 55 to 77 (18 combos) and AJo (12 combos), which add up to 30 combos—slightly exceeding the breakeven point.
Conclusion:
Your analysis was incredibly inspiring and got me thinking more deeply about the situation. Based on these reasonable assumptions, if I’m willing to embrace some variance, then a 4-bet shove here appears to be a decent option.
Quote:
Originally Posted by Garick
I mean yeah, assuming that we're also assuming that all the other Vs will fold. But while we're assuming, why not just assume that the flop will come Js9sKs and we flop a straight-flush against V's TPTK?
But just to do the math for you, if you shove under the only have to worry about BTN assumption, the he has AK assumption, and the he only calls with AKs assumption (likely the worst assumption of the three, as most players will call with AK almost always in this obvious squeeze spot), it looks like this.
75% of the time, everyone folds and you win ~120 (hard to tell with the info "almost everyone calls") for an EV of $90.
25% of the time, you risk $170 by shoving and he calls with AKs. When that happens, 63.22% of the time you will lose your $170 (-107.47) and 36.78% of the time you luckbox a win of the $120 that was already in the pot and the $150 more that V put in (+99.31) for an overall expectation of losing $8.16 whenever he calls.
So 75% of the time you win 120 and 25% of the time you lose (on average) $8.16. (.75x120)-(.25x8.16)=90-2.04= an EV of +$87.96 on this play, given those assumptions.
But! They are bad assumptions. BB already called a 3-bet, so he has something to worry about. LJ called the 3-bet with K9s, so we know there are other players with some gamble in them. And BTN folding AKo there seems really unlikely. I showed you the math to give an example of how to do an equity calculation that includes FE, but don't take from that the idea that this would have been a great shove.