BB should have range advantage and more nut combos because of the over-pairs in his range, BTN should have A-high and no made hand about half the time so I think we should bet small on the flop with our whole range maybe 1/3 pot.
BTN should call with anything that has decent equity versus Hero's small flop bet ,OTT the equities change a bit and equities are about equal, the 8c should be good for BTN's range by improving his 8x to trips like A8s,K8s,Q8s and T8s, his 22 and J8s make boats (4% of range), he has made a flush a small amount of the time aswell,
On The Turn
BTN = 50.2%
HERO= 48.8%
Tie= 1.8%
I think this should lead hero to check more often and when he does bet choose a larger sizing and bet polarized, KK would be a good candidate for that. When villain calls your large bet on the turn his range is strong, he has good top pairs, flushes, trips and boats. from the stats I get I see your shove as an OK play since he should have top pair combos 39 of 71 total combos and this is more than half justifying a value bet and extracting value from worse but it is close, the rest of his combos are like I mentioned all flushes, trips, boats , that beat Hero's KK. so I think river could be played as bet or check.
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