Full Tilt No-Limit Hold'em, $0.25 BB (5 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

SB ($15.20)
BB ($38.70)
Hero ($43.95)
MP ($3)
Button ($24.25)

Preflop: Hero is UTG with K, A.
Hero raises to $0.85, 3 folds, BB raises to $2.25, Hero calls $1.15.

Flop: ($4.35) A, T, 4 (2 players)
BB bets $3.75, Hero calls $3.75.

Turn: ($11.85) 3 (2 players)
BB bets $11.6, Hero calls $11.60.

River: ($35.05) J (2 players)
BB bets $21.35 (All-In), Hero calls $21.35.

Final Pot: $77.75

I've never mathematically broken down a hand before and figured that this was a good one to attempt. After he flipped over AJ at showdown, I wondered if I'd messed up on the turn. Assuming his hand is AK-AJ (for the sake of simplicity/the hand range I put him on), what is our EV of raising or calling on the turn? I think I have the EV of raising correct...

Pokerstove equity ranges:
AK-75.9%
His range - 24.1%

EV of pushing him all-in on the turn: 35.05x + (1-x)(.759*56.40+.241*-21.35)
- x being the probability he'll fold

The above calculation assumes he'll push the river no matter what. Obviously the situation is more complex. How would we incorporate the y-variable of him pushing on the river? As for the EV of calling, I'm totally lost... how would we work that one out? Help!

The EV of flat calling on the turn is based on how the river action will take place with things such as:

Will he check/fold a scare card on the river
How often will be bet the river unimproved
Will he call a bet from you on the river if a blank falls on the river
How big of a bet will he call or how big of a bet will you make
Other misc. items

As the hand went down, I really don't like how passively you played it. You got the flop you wanted, so put in a little raise there and hope that he has AQ and does something stupid.

In the actual hand, I don't mind the flop flat call vs. a typical opponent. Drawing hands are not a big part of his range, and you are way ahead here most of the time. Don't give KK and QQ an easy decision. Ofcourse this could change if you play a LAG style and people question your flop raises, but I don't think that is the case. The fact that you have position also plays a big role here in the sense that we are assured of the chance to put money in on the turn without taking his lead away just yet.

I definately shove the turn though. Once he made that PSB he is close to commitment, so take it to the felt.

As for your calculations, you are making poker too hard for yourself I think. No need to quantify a hand like that.