Villain bets 25% of the pot on the river. That $3 into a $12 pot.

60% of the time he's 'bluffing'. That means we win $15 60% of the time at the expense of $3, and we lose $3 40% of the time.

Expectation: 0.6*(15) - 0.4(3) = 9 - 1.2 = + $7.80

Let's say instead we decide to bet for value. If you have a read on a player that he big bet bluffs the river a lot then you simply check and call!!! So i'm not concerning myself with that now.

A decent sized value bet is what, $8 ?

What % of hands in his 60% 'bluff' range does he call with? Say 20%?

For our $8 we will take down a $12 + $8 pot then 20% of the time. The other 80% of the time we're losing $8 in this spot.

Expectation: 0.2*(20) - 0.8*(8) = 4 - 6.4 = -$2.40.

I'm pretty sure you just picked a few arbitrary numbers, so I have picked one myself, the 20%.

Why don't you determine the range of hands he continues with on the river and then pick out all the ones he beats us and work out what % of his range those hands are.