My thoughts are this. There absolutely are times when you know you're beat, Usually when you can't beat top pair and it's a bet and a call to you. Even getting 10:1, maybe you beat the bettor often enough, but you won't beat the caller often enough.
You also will fold on the river when you miss a draw, no matter how big the pot is.
On the other hand, if you think you're not folding on the river too much, maybe you're not folding on the turn often enough? Just a random thought.
Clearly, when the pot gets to 12 BB and it's bet-fold to you, your opponent only needs to be bluffing 8% of the time to make the call +EV. In fact, calling isn't very wrong even when there's an overcall. After all, it's only one more bet, and folding the winner would be a disaster.
I remember a hand I once posted on 2+2 where I three-bet an EP raiser with QQ, and it ended up capped 4 ways preflop. The flop came Ac-Kc-3d, it was checked to me, I checked, the LP player bet, one fold, one call, and I called. Some body criticized that play saying 18:1 was not good enough pot odds to "chase my 2-outer (I did not have a club)". What's wrong with that criticism is 18:1 is a 6% shot. I guarantee you, my QQ is the best hand there almost 6% of the time. Then some other know-it-all pointed out that the Qc wasn't really an out because it would "give somebody the flush." Well, hold on. It doesn't give somebody the flush 100% of the time (probably more like 40% of the time), and 30% of the time it *does* give somebody the flush, I hit one of my 10 outs on the river and win the hand anyway.
The point of all this that once the pot gets to a certain size, folding becomes clearly wrong no matter how possible it is that you're drawing slim or dead.
Poker is about making good decisions. There's a big difference between making a slightly -EV decision when the pot is 4 BB and making the same slightly -EV decision when the pot is 20 BB.
The first question you ask at any point in a poker hand when evaluating your decision should always be "how big is the pot?"
If on the river there are 5 BB in the pot and you have TP/WK, and one person bets and the other folds, go ahead and fold. That's fine. But if on the river of a rock and roll hand there's a 4-flush on the board, 24 BB in the pot and one guy bets and the other folds, I hope you never fold top 2-pair (no flush). I know I won't.
Well, that was a long and rambling reply.
