semi-hijack, and super long post - sry..but this spot reminds of something i meant to post a while ago...i thought "SOAH" made a real nice post on 2p2 and made me think of pushing vs calling in 3bet pots...i dunno how related this is but whatever it got me thinking about it.


No Limit Holdem Ring game
Blinds: $10/$20
3 players
Converter

Stack sizes:
Button: $1964.00
Hero: $2167.00
BB: $4540.00

Pre-flop: (3 players) Hero is SB with {JJ, J9, AT}
Button raises to $80, Hero raises to $280, BB folds, Button calls.

Flop: Tc 9s 5h ($580, 2 players)
Hero bets $411, Button raises all-in $1684, Hero?

results: hero called with J9 i think and villain showed 88. OP's point was JJ/J9/AT all seem like similar hands except J9 has best equity.

so the question became, If button has 88, should he call, fold, raise, or push the flop?

SOAH wrote this part:
there's ~$1400 in the pot after we call... assuming he has two overcards, he has 27% equity... which is nearly $400 in equity. So if we KNOW that's what he has and both players play "perfect" on the remaining streets, then calling instead of pushing costs us almost $400... even if he has something with fewer outs, he can still bluff at those cards... if you factor in things like him improving to a flush draw and shoving turn, or just randomly deciding to bluff for whatever reason, we could end up losing this pot in one form or another at least 1/3 of the time... so calling instead of pushing when we're ahead could be as much as $500 worse on average.

If we're behind on the flop, then shoving it in and getting called loses us about $1300 on average (~10% equity saves us $400)... if we call and call all-in on the turn when we hit an 8 and fold otherwise, then our EV is about -$330 (this is assuming you're against a range of 99+ and ATs, btw)

So basically if I did all the math right, then calling is $500 worse than pushing if you're ahead, and pushing is $1000 worse than calling if behind.... which means that if we're ahead 2/3 of the time on the flop, then it doesn't matter which line we take. In order to be ahead 2/3 of the time we'd need to be against a range of something like 22+, 54s+, AJo+, A8s+, KQs (13% of total starting hands). This might be a little too loose... but not too far off.

this also doesn't take into account some stuff like how half the people responding to this poll would fold a T or 9 to a push, and obviously the assumptions about how often you get bluffed out are just rough guesses... but the point is that I don't see how pushing can be called ridiculous or terrible, at worst it's a small mistake imo, none of the options are really that great.