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The only time we want villains to fold when we bet is when we don't have showdown value, or when we're pretty sure they are folding a better hand. This means that when we semi-bluff with a draw, a fold is a great result.
When we have a pair like JJ on an board with 1 or 2 overcards, it's highly unlikely that we're making a better hand fold. Therefore, if we bet and get a fold, we didn't really accomplish anything except to "protect our hand." Protecting your hand is vastly overrated IMO, especially when we have position and have the option of checking behind and keeping the pot small when we're not sure that we have the best hand.
That said, betting this turn isn't horrible if you have a read that villain knows where the fold button is. Someone who called from the small blind with KXs and then called you on the flop isn't going to like their hand much on the turn. If you want them to fold, though, you're going to have to bet like you mean it. Betting less than half pot just doesn't cut it. You might even have to 3-barrel the river to get a K to fold, so it's up to you if you feel like you want to risk that many chips. Of course you have to fold when a K comes on the river and villain leads big. I'm putting them on QJ or some K like 95% of the time at this point.
The whole point of my post, though, is to point out that you have to have a clear reason for betting. We're never betting simply because we think Villain might fold. We have 3 major reasons for betting:
1) We expect the range of hands that continue against us to be worse than our holdings. This is value-betting. When the board comes KT6 and we're holding AK, there is a ton of value in betting. The only better hands that are continuing (generally) are KT, AA, KK, TT, and 66. There are tons of worse hands continuing (AT, KQ, KJ, QQ, JJ, QJ, QT, JT, 98, 97, 87, any flush draws, etc.).
2) We probably have the best hand right now, but it's vulnerable. Villain likely has 6 or more outs to a better hand than us, and we're happy to take the pot down now. An example of this is when we raise with AQ and get called by a loose player. The board comes KK6. Since Villain is unlikely to have a K (but could, of course), our AQ is likely to be the best hand, but Villain has at least 3 outs and possibly 6 to beat our hand, and we'd love to take down a raised pot right now.
3) Our villain is likely to fold a better hand. These are most profitable when they are semi-bluffs. Let's say that we are holding 98s and the board comes J76. We have an open-ended straight draw, meaning that we have at least 8 outs to the best hand. We think villain likely is holding broadway cards (some Js, but more As, Ks, and Qs), so we bet here with our draw. Villain folds a lot of hands that are actually beating us right now (any overcard is beating us). For the times when Villain does call with a paired J, we have 8 outs to improve our hand and get more money later on (implied odds).
An example that is not a semi-bluff is when we open in early position with a low pocket pair (say 33) and a tight player flat calls us: this is often a low pair. The board comes something like AKT: we are highly likely to have the worst hand. But we raised preflop, so to the player who called us with 66, it looks like there is no way they have the best hand at this point. With a hand like 33 on this board, our opponent is folding a huge percentage of their calling range, most of which are beating us right now, so there is a lot of value in bluffing here.
Of course, there are other reasons for betting, but these are the 3 main ones we should be focusing on. At low stakes, we are mainly betting for value. When better hands call us and worse hands fold, there is no value.
Sometimes we do bet because we want our opponent to fold, but we don't approach this from the mindset of, "I'm going to bet and hope you fold." Instead, we consider that we have a vulnerable hand and Villain is highly likely to fold; or that villain has a range of hands that is mostly beating us, part of which will fold to a bet, and the other part of which we have a chance of beating and extracting more money from down the line.
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