Quote Originally Posted by Ragnar4

We got 0 dollars vaule at the river with our bet. I don't think opp would call 25 cents at river here either. The deeper thinking is this: Our opponent has probably given up at the river with the intent to fold because he missed, meaning he wouldn't call anything, maybe a minbet. It looks to me like opponent missed a draw, and you don't call showdowns with busted draws. But you can bluff showdowns with missed draws.
If opp can't call a bet, but could be persuaded to bluff, why isn't checking to induce a good play?
OK, say your opponent didn't hit his hand half of the time and currently has 0 showdown value
the other half of the time he has Ax and is willing to call a pot-sized bet, but is too afraid you have a better kicker to bet after you check (I've seen people check down flushes on paired boards, so this is definitely realistic and common)

how often does the villain have to bluff his no showdown value hands with a pot sized bet to make checking the river better than value-towning him the times he has trips?