On the river we have to call 1150/3000= .38% of the time we need to be right.
Here is where combinatorics, pokerstove, and general assumptions about population tendencies is your friend.
Just to give an idea of how you should approach these situations:
Value hand combos unknowns may do this with: KJ, 4 combos; 22/44 6 combos, discounted AK and KQ due to 3bet pre so we'll say 3 combos, K9 6 combos, we'll give 1 combo of slowplayed AA pre, Jd/QT987653d for 8 combos.
Total Value Combos: 28 hands. Obviously this is just a guess, it will fluctuate depending on villain, but in these situations you have to make some kind of educated guess.
Bluff combos unknowns may do this with: discounted 53, we'll just do the suited combos for 4, frustrated K2 and K4 discounted to 6 combos, discounted A2/A3 combos for 10, and the rest will be a vast, vast amount of diamond combos: Looking in pokerstove, I counted 35 diamond combos, chopping off the ****tiest ones like 92dd or T3dd.
Total Bluff Combos: 55
Total Hand Combos: 83
Assuming villain took the same line with all the aforementioned hands, he beats us here 28/83= 33% of the time. In other words, we are good 67%. According to the pot odds, we need to be good 38%, thus we should call.
However, this is blatantly wrong. We have no reads, no idea what villain is capable of. Against a population tendency, I think randoms are much more weighted to value here. Against the population, we can usually remove most of the bluffs, leaving us with much worse odds to call the river.
This is a long, roundabout way to tell you to do your equity calculations.
Edit: We can definitely add some random air/spazz combos, but I'm tired and you get the idea.