Quote Originally Posted by Lukie
If you are facing a bet or raise on the river and you only beat a bluff, you never have correct pot odds to call. Fold or raise instead.
No - this is incorrect. (If you do actually beat a bluff - ie. you have A high)

You estimate what % of his range is a bluff in this spot, if the pot odds
are offering you better than that you should call...
(ie. you estimate he is bluffing 33% of the time, he bets 10 into 20,
so you have to call 10 to win 30 (3-1) 2/3 you lose 10 (66%) 1/3
you win 30 with A high (the 33% he is bluffing) - a very + ev call)

If you fold in this spot as suggested you lose valuable ev.
If you raise he folds 33% of the time he had a bluff (you gain 0ev here as opposed to calling.) but he calls you up to 66% of the time when he has a real hand. (so you lose major ev putting money in the pot with a worse hand.)

The theorem could read -
If you dont even beat a bluff you should raise/fold.

(ie. never call you will always lose, but if you estimate his range is heavily enough weighted towards a bluff or a perhaps a marginal hand he is betting thinly (that he will fold to a raise) then you can re-bluff/raise
if you have enough fold equity to warrant it.)