[Shandrax]

That's of course correct. All the possible hands have to be analyzed in relation to villain's pre-flop selection. If I remember correctly then villain was on the button, so he will open with lots of hands.

The theory to judge the chances that I was using is rather simple:
There is a number of hands that beat you -> X
There is a number of hands that you can beat -> Y
There is a number of hands that can be logically excluded -> E

Your chances on the river are (Y-E)/X and if that is in line with the pot odds you are getting, then it's at least a call.

What you are saying is that E is very high, so the chances to win the showdown are extremely slim and that might well be the case. Even then it is not a clear fold. Given the pot odds you should still bluff-raise with the correct frequency.

Therefore the correct answer to the question is a percentage mix. Advice advocating a pure strategy like always check/call (like my own) or always bet/fold must be wrong.