Turning counterfeited hand into a bluff

One of the most frustrating things that can happen in big bet hold'em is having an opponents over pair in bad shape with two pair and then getting counterfeited on the river. It's extremely annoying especially when we expected to make a good amount of value on the river. For some reason though, even if players recognize that they are up against a probable better hand, they will just check and give up--not realizing that this very well might be a good spot to turn your hand into a bluff. In reality especially on non drawy boards bottom two that has become counterfeit has no showdown value at all.

Let's look at the following example. Say a good, tight opener raises from early position to $40 in a $5-$10 No limit game and we call with 5♠ 4♠ with $2000 effective stacks. The board comes out T♣ 5♥ 4♦ and our opponent bets $75. We hope that this player he has an overpair so we start to build a pot up right away and make it $250. He calls rather quickly. The turn comes an 8♠, he checks and we bet $375. Our opponent thinks for a long time and calls. The river is a horrifying T♦. Our opponent checks and we check back our worthless two pair. He tables JJ and takes down a nice size pot.

I'm never a huge fan of bluffing players off of overpairs at the lower levels but sometimes this can be a rare spot to do it in. Especially on a non draw heavy board where top pair has now paired its difficult for our opponent to put us on a hand that he beats. There were no real draws on this flop and now he can't even beat top pair, although if you think a little bit deeper, and we are a good player, it's really tough for us to have just trip Ts. However, in general recreational live players are bad hand readers and get scared of boards that actually don't make a lot of sense.

Of course you can also be counterfeited by another card pairing besides top pair. Say, for example, instead of the T coming on the river an 8 paired. Now we have the same counterfeited, worthless two pair but our opponent maybe far less likely to fold a hand like KK, which has now made Ks up on the river. For this same reason if we actually flopped a set instead of bottom two we should absolutely bomb the river for value with our full house when checked to especially if we are almost certain that our opponent has an overpair.