Grunch:
I'm betting the turn if Villain is floating too much. It seems like he's calling c-bets essentially if he hits any pair, or has any draw, which maybe is a little too much, maybe not (depending on who he's playing), but I think his flop calling range is definitely wide enough that we can value bet the turn here.
As played, villain already has 95/278ths of his stack in, i.e. the effective stack is at the threshold of pot-commitment, so we're never calling here. I guess I'm shoving AI and hoping Villain has TP, or even another overpair, but I'm not thrilled about it. Maybe I'm folding here in honor of Baluga if Villain has 0 AF on the T and R over 100 hands or something.
The real puzzle of this hand is Villain's starting stack size, and in general the effective stack: what line gives us the best chance to get his money in while he's behind, given his 56bb starting stack?
I suppose we wouldn't be out of line raising to 5x pre if he's this loose. I think a villain like this will call $0.25 if he'll call $0.20, but I could be wrong. This gives us a 10bb pot on the flop, and the effective stack would then be 50bb. If we slightly over-bet the flop, maybe dumping 15bbs in (well, I guess that's not slightly over-betting, but stay with me here), and supposing Villain calls, then the T pot is 40bb, and Villain has 35bb behind. We can then shove any T without regret. Villain is pot-committed here once he's dumped
1/3(56bb) = 18 or 19 bbs = $0.90 to $0.95 into the pot.
It's difficult to raise 5x pre and over-bet the flop, but we know Villain will never fold TP, and might very well commit himself on the flop without knowing it. The thing with over-betting is that, against thinking, decent opponents, they'll only call with hands that beat us (which yes, doesn't apply to PF in this case, but certainly applies to every street thereafter). Against this Villain, I think he'll call an over-bet on the flop enough times to make this line profitable, but I'm open to correction. At least with this line we make the hand easier to play. I'm not sure it is best, but we should be thinking of the effective stack size and how best to keep our AA out of reverse implied odds hell.
I mean, another solution would be to keep the pot small by raising less pre, and x/xing the F, but that seems less like a solution and more like capitulation.
I'm not sure if it would have gone this well, but here is my fantasy, not inconceivable against villains like this:
Poker Stars, $0.02/$0.05 No Limit Hold'em Cash, 5 Players
Poker Tools Powered By
Holdem Manager - The Ultimate
Poker Software Suite.
MP: $5.30 (106 bb)
CO: $4.50 (90 bb)
BTN: $9.95 (199 bb)
Hero (SB): $5.46 (109.2 bb)
BB: $2.78 (55.6 bb)
Preflop: Hero is SB with A
A
3 folds,
Hero raises to $0.25, BB calls with junk $0.20
Flop: ($0.50) 3
8
7
(2 players)
Hero bets $0.75, BB stupidly calls $0.75
Turn: ($2) 5
(2 players)
Hero fist-pump snap shoves, after pausing momentarily to not give a tell;
BB bets calls $1.78 AI with TP sometimes , two-pair sometimes , but we don't really care because we got him committed when he was behind, and we still have outs