You are saying max value so I am assuming you are risking a club that would result in a backdoor flush or a card that would complete a straight such as 9, 7 or Q. SO I would bet enough to set up about a 2/3 pot sized bet on the river: 

If my math's right the villain still has 86820- 2000-3975 = 80845 and you cover him.  the pot is 18750 so if you bet 15000  on the turn the pot on the river will be 48750 and the villain will be left with 65845.  You can river bet then 40000 leaving him with a decision to call and be left with 25845 so he might shove it all depending on his hand strength.

I guess you can bet a bit less on the turn and a bit more on the river if you thoikn you can induce on the turn and you are not concerned with draws, but if he only calls you cant reallly get it in on the river.

thx guys, heres how the turn went

Hero (MP1): BB = 49.2, t98358

pAAt401 (MP2): BB = 7.5, t15072

xcygnus1 (CO): BB = 3.8, t7572

Karen424 (BTN): BB = 12.8, t25552

RadLongBoard (SB): BB = 13.0, t26062

4k.falc (BB): BB = 43.4, t86820

guccyka (UTG): BB = 23.7, t47430

Lauo T (UTG+1): BB = 61.4, t122886

larsbenny (UTG+2): BB = 33.7, t67321

Pre Flop: (t4800) Hero is MP1 with A A

3 folds, Hero raises to t4000, 4 folds, 4k.falc calls t2000

Flop: (t10800) T 8 A (2 players)

4k.falc checks, Hero bets t3975, 4k.falc calls t3975

Turn: (t18750) J (2 players)

4k.falc checks, Hero bets t12950, 4k.falc calls t12950

River: (t44650) A (2 players)

4k.falc checks, Hero bets
 

i obvioulsy quad up on the riv, that's how i roll.  But this is where i def got my sizing wrong. What would you bet here and why?

Nice bet size on the Turn.  The Guy has to have something if he called you on the turn and since lots of HAnds hit this board (see below).  He seems to want to get to showdown, but it is doubtful he feels he has the nuts or close to it, and if he does feel that way whatever you bet is irrelevant since he will come over the top and you will get max  value, with all that in mind, I would think you need him to call an amount that leaves him with enough chips to keep playing, especially on a tourney like this one where hopes of millions are at stake so:

The Pot  is 44650 ,The Villain has 68795, and you cover him….

I think you should bet around 25000-29000,  you leave him room to 3 bet shove if he feels that strong, and if he is looking for a showdown you let him keep 40000 chips which is 20-22 BBS and he might feel he can call his strong hand and if he is worng still have a shot

By the way, I have made the mistake of shoving trying to look bluffy in these spots and gotten too many folds that I regret….certainly a leak I am trying to fix, but in these big time tourneys and after folding hands for hours and getting Quad Aces, sometimes I get caught up in the aggression. 

I wouldn't bet small here thinking he doesnt have much, there are lots of Hands that hit this board (T 8 A J A) hard that he could have called both flop and turn with,  of course excluding your AA:

  JJ, TT, 88, KQ,  Q9, 97, and Lots of double  hands:

He might also have KQ  (so you don't have the nuts )  or have KK and QQ even though  its less likely due to no 3bet PF.  He also might have had a bunch of 2 pair hands that got counter fitted by the 2nd Ace that might not call the bet on the river.

I hope we get to see what he had.

Flop: (t10800) T 8 A (2 players)

4k.falc checks, Hero bets t3975, 4k.falc calls t3975

Turn: (t18750) J (2 players)

4k.falc checks, Hero bets t12950, 4k.falc calls t12950

River: (t44650) A (2 players)

4k.falc checks, Hero bets t22950, 4k.falc calls t22950

Final Pot: t90550

Hero shows A A (four of a kind, Aces)

4k.falc mucks 8 9

Hero wins t90550

The reason i think that i messed up the river bet (shoulda bet bigger) is for the same reason as i bet big on the turn. I think he either made his hand and is calling or he missed and is folding. With the Ace on the riv, there aren't a lot of one pair hands or two pair hands remaining that he's calling with. I barrelled 3 streets after raising from MP1 preflop, my hand is strongly weighted towards AJ+ here. Either he made his flush (or played some sort of straight/set badly) and will call/raise any bet, or he's folding his missed straight draws & 1 pair hands.

I did actually type 27950 into the bet box then deleted the 7 for a 2 making it 22950. I know its only 5k difference but had i have thought about his river calling range more and my perceived range, i may have even bet something like 32k – 38k.

does that sound about right or have i missed something in the analysis? I am very keen to work on my bet sizing since it's something that could make the difference between being able to withstand a suckout or two along the road. Any input is appreciated (especially any pros?)