[holdme]

okay, we're facing the turn riase. let's say 44 is in villain's range. villain then has aa, kk, or 44. i've heard several times in this thread:
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heck my edit. if you, in villains shoes, think 44 is good enough to value3bet because we have like AK or A8 and call with that, then you have to shove the river because AK or A8 WILL NOT FOLD but will check behind

assuming two semi-decent players, ranges don't change between the turn and the river (barring a v v v v unlikely bluff 3bet on the turn from villain)

for villain: turn 3bet range = river shove range
for hero: turn 3bet call range = river call range

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which means for all intensive purposes, villains turn 3bet=shove. hero has about 660 behind. pretend villain shoved. there is about 940 in the pot, meaning hero is getting <1.5:1 on a call with 33% equity (we are ahead of 44, behind aa and kk) versus hero's range. this makes it an easy fold on the turn.

edit: i just read danibus' post. he expects that op would 3bet ak pf. this makes it an easier fold because villain would not vbet 44 if ak is not in hero's range.