[meep_42]

Assume: Villain does not have a Q.
Assume: Villain has one A or K and a blank.
Assume: Villain will call a turn raise and check the river if he misses or hits. Villain will bet if not raised on the turn.

Villain is drawing to 3 outs (he will fold to a river bet/raise if he misses).

39 of 45 times: Villain will miss his draw to the A or K.
If Hero raises the turn, Hero wins 2 BB. (the bet/call of the turn raise)
If Hero calls the turn, raises the river, Hero wins 2 BB (the bets on the turn/river)

3 of 45 times: Villain makes his A or K
If Hero raises the turn, Hero loses 2 BB (the raise, folds the river)
If Hero calls the turn, Hero loses 1.5 BB (fold the river sometimes, read dependant)

3 of 45 times, Villain pairs his kicker
If Hero raises the turn, Hero makes 2BB on the turn, and 3 BB on the river (average between calling a raise/3-bet/cap) for 5 BB.
If Hero raises the river, Hero makes 1BB on the turn and 3 BB on the river for 4 total.

Raise the turn: (39/45)*2+(3/45)*-2+(3/45)*5=1.73+-.133+.333
==+1.93BB
Raise the river: (39/45)*2+(3/45)*-1.5+(3/45)*4=1.73+-.1+.27
==+1.9BB

So, they're about even, raising the river becomes less profitable the more times you call when an A or K hits the river.

-d