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Value betting is an even trickier art than bluffing. Discounting some rare but substantially complicating factors such as the risk of a check-raise bluff, a value bet on the river shows a profit if it is called by a worse hand more often than it is called by a better hand.
That doesnӴ mean that you should be losing money on 40-45% of your value bets. Often, when you value bet the river, you will have a hand that is way ahead of your opponentӳ calling range and will rarely if ever run into a stronger holding. However, your thinnest value bets should run into better hands with approximately this frequency. If you never make a bet like the one in example (4), where you find yourself betting for value into a hand that is just barely stronger than yours, then you are probably missing a lot of value by checking when your opponent would have called with many slightly weaker hands.
I deliberately chose an example where you were in position and your opponent had already checked. When you are out of position, deciding whether to fire a thin value bet is more complicated, since you must consider the expected value of your bet relative to checking and either calling or folding. But especially when in position against a non-tricky opponent, you can and should bet for value with anything that might be called by worse.
Following from that, your opponent should be calling your river bets very often, frequently with a hand thatӳ better than yours. As frustrating as it can be to see him table a hand that had you beat all along, you need to realize that this is actually a good sign. As long as this one of the better hands in his range, you should be happy to ship him the pot. Just think of all the times that he calls with JT, J9, or 98 as your compensation for occasionally running into AT. You should accept this result with the same equanimity that you accept that miracle Ace on the river.