Most players underbluff rivers, especially on replay. The notable exception? When it’s headsup and the preflop raiser shows weakness, many players see it as a green light to steal the pot.
It is important to remember that one big reason we check turns with the weaker part of our value range is to incentivize villain to bluff his air.
That’s a spot where I would usually ask myself, “Is what I have better than the river?” Although in this case the river paired the board which increases the chance of bluff.
Well, I hope this little hand disabuses you of that thought process! 
Well, in this one I got an overfold out of him. ; )
42o
I was playing the board. : D
Here’s one. - Hand #1282003369 (sorry it’s not letting me link to the hand, I’m getting an error)
Pre ~ AKo on the BT. I’m ready to open but HJ opens first for 3.5x. Now this guy is fairly aggressive and likes to steal so I’m ready to come overtop of him, but then the CO calls and she just sat down a coupe of hands before and I’ve never played her. So I flat call. Chances that HJ has KK or better is pretty slim but chances that ONE of them has KK or better is not quite so slim. In any event, CO has overcards, just hopefully not a pair.
Flop ~ 886-rb. Nobody has this. Impossible. I’m ready to bet, just a question of sizing. HJ checks. I’m not surprised but I am very interested in CO’s action. She bets about 1/3rd. This could be a bluff, value with overpair, or just a feeler. I tank a bit and flat. HJ bails. Not surprised at all.
Turn ~ Bricky 4, all 4 suits on the board and no way that she has 75. She checks it to me. I want to bet (and maybe I should have) but my reasoning is that if I bet here and get called/raised, I’m borderline pot committed, so for playability sake I check back.
River ~ Brick 3. She checks. I tank, count out roughly 1/3rd pot and bet. She lays down real quick.
Honestly, I think that there’s a chance that I pushed her off a chop, but more likely I had her outkicked. I really want to know what she had. Probably AQ or AJ. But there is no way that I’m checking back that river. I have to be ahead here. 99 and up aren’t taking that line and there’s no way that she hit the runout, so technically this isn’t a bluff since there are no hands ahead of me that would fold. Or do you think that she could fold something like JJ here thinking that I had AA? I don’t think so.
How would you have played the hand? Maybe I should have just shoved it all pre. : P
Either CO is a solid player, in which case they wouldn’t be flatting KK here often, or they’re some random new player who can have any two cards. The best you’re likely to be up against is a low pocket pair. This is a shove every time in my book.
On the flop, if HJ is aggressive pre and CO flats like population, both ranges are extremely wide. I don’t understand why you think neither have hit this board before they’ve acted. I think you still have to call, I just think your hand reading is off.
Turn check is good - you have showdown value after they check, and if your are ahead you don’t really need much protection. There’s no reason to bet here.
River - Check or bet are both good. I think 54 is actually quite a likely hand, so if bet gets that to fold, then I think it’s better than check.