This is a spot from yesterday where i'm often lost on what's optimal. Villain is apathy and i'm sure i'm a random to him. My initial plan was to bet/fold flop and check/fold turn because i thought he's gonna have more showdown value hands than pure floats (only AK and AJ basically) and i expected the showdownvaluehands to check back alot. On the other hand i could b/f again to get value from JJ KK AQ KQ etc i guess. Thoughts?

Poker Stars No Limit Hold'em Tournament - t10.00/t20.00 Blinds - 9 players
The Official 2+2 Hand Converter By DeucesCracked Poker Videos

CO: t2845.00 142.25 BBs
BTN: t2283.00 114.15 BBs
SB: t2980.00 149 BBs
Hero (BB): t2950.00 147.50 BBs
UTG: t3000.00 150 BBs
UTG+1: t3140.00 157 BBs
UTG+2: t2970.00 148.50 BBs
MP1: t3325.00 166.25 BBs
MP2: t2920.00 146 BBs

Pre Flop: (t30) Hero is BB with A A
3 folds, MP1 raises to t60, 4 folds, Hero raises to t215, MP1 calls t155

Flop: (t440) T 9 Q (2 players)
Hero bets t280.00, MP1 calls t280

Turn: (t1000) 4 (2 players)
Hero ...

Bet/fold is good.

The central problem here is that you probably don't have a balanced 3-betting range in this spot, and he probably doesn't expect you to. With so much money behind, that gives him a lot of leeway to outplay you post-flop.

I haven't played much with Apathy, but if you're a random to him, I would expect him to play better hands fast to prevent his action getting killed, bluff infrequently when you check (maybe four combos of AJs and that's it, and those bluff river instead of turn sometimes against a random), and not call twice with one-pair hands that don't improve. On balance, I think I like c/f turn and b/f brick rivers when he checks behind. I think you get owned less, for smaller pots, on the river when it runs out badly, and get value from one pair hands more frequently when it runs out well. I think turn is close between c/c and c/f, but the assumption I'm least certain of is that he fast plays better hands, and we have blockers to AQ, which is by far the most likely worse hand to bet turn here.

EDIT

It's possible with stacks, positions, and this villain, that, like Focault said, {empty 3-betting range} > {balanced 3-betting range} > {unbalanced 3-betting range} in theory, but as a perceived random with a presumably Scandi location, in practice I would have an unbalanced 3-betting range composed entirely of value hands and expect his perception to be that your range has some random Scandi spew in it.

bah bet/fold it for value

Since everyone wants to bet-fold I am curious if you guys dont expect him to raise 99/TT otf given how narrow heros percieved range. I just don't see why he would flat the flop with either of those

check/c ott. c/c most rivers up to like 60% ish of pot if villain checks behind ott, c/f river if villain bets it.

it matters alot that villain has position on us here, they can 100% c on the flop vs us with their entire playing range, especially vs a player they perceive to be really good or spewy.