*GRUNCH*
I'm betting turn or check/raising. By check/raising, worse can call us (any ace-X, a big single
(i.e. K
9
), straight, ect.
As played, first step to solving this is range.
You didn't say what position villain was in. This matters, HUGE. If he was UTG, there's a chance of AK, AA, or KK in his range. If he was on the button, there's almost no chance of those hands.
I'll assume MP. Since he's tight pre, we can remove ace rag offsuit from his range. We can also remove K9 or worse. Also, you didn't specify what "tight pre" means. Is he passive pre, often limping with like AJ or AQ. Is he tight in raising pre but loose in limping?
Against a river range of 10% bluffs, 90% made hands, where the made hands are:
AJ, A10, A9, king high flush, Jack high flush, 9
8
, KJ (no flush), K
Q
(any KQo with the K
)...
Let's assume he will fold A9, 9
8
, straights, and the bluffs.
EV calling = .9(.67391*$140 - .32609*$65) + .1($65) = +$59.6
Time for combinatorics: Combos folding hands =
A9 = 8 combos
98s = 1 combo
straights = 15 combos + 18 combos = 33 combos
total folding combos = 42 combos
Total calling combos =
A10 = 6 combos
AJ = 6 combos
king and jack high flush = 2 combos
Total calling combos = 14 combos
So he folds 42/56 times, or 75% of the time, calling 25% of the time. Note: I didn't include the 10% bluffs since I'm including that separately in the EV calculation.
EV shoving = .1($140) + .9(.75*$140 - .25*$315) = $14 + .9($26.2) = +$37.58
Conclusion: EV calling is +$59.6 while EV shoving is +$37.58. Since EVcall>EVshove, I'd call river. If the EVs were almost the same, I'd shove since it's great for our image.
Is this big analysis necessary to get to the right answer? Yes I'd say so...it ended up being fairly close, only about a $25 difference in EV, and it's near impossible to know that without doing the EV calcs.