[BenA]

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The obvious answer is no, but if you never bet for value you can never bluff bet. All of your bluffs must be check raises and will be more costly when they fail. How often should you value bet, if at all? Can sacrificing value on one hand to make a bluff profitable on a future hand be worth it? What role does pot size play in all of this?

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I'll start with this part first. You bring up a good point and ask a good question. I'd like to add something that perhaps you hadn't thought of. If your opponent is, in fact, a thinking observant player (which I assume from 'other than that he plays' optimally), then not only will he begin to realize that when you bet out, you are bluffing, but he will also begin to figure out that you are check-calling for value. He would immediately alter his strategy. So the obvious answer, which you already pointed out, is that you MUST vary your play sometimes. But it only needs to be enough to throw off your opponent. And yes, game theory can help here. You could do something simple like decide to bet out with any good hand that holds a queen, (I'm too lazy to figure out what percentage that might be of hands). In other words, you randomize your decisions so that even the most observant opponent can't figure out your plan.

Oh yeah, and you need to be doing c/raising with a lot of your good hands. If he somehow continues to always bet when you check to him, even after a few of these, then do this like 50% of the time with hands you think are ahead, especially if you think he'll call with a worse hand and that being 3-bet isn't a large danger.

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OOP in a FL game against an opponent who always bets when checked to, but other than that plays optimally (against your strategy, which he knows) is it ever correct to bet for value?

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Here, I don't think there is enough information. Other things I'd like to know are:

1) How often does villain raise with a good hand, and does he ever do so as a bluff?
2) How likely is villain to call your bet with a worse hand on the river?
3) How likely is he to call a check-raise with a worse hand?

With these extra pieces of information, you can determine a better ratio of checking and betting out HU on the river against this opponent. If he folds everything marginal on the river to your bets, you should bet often with okay hands if the chance he'll fold is decent and you aren't sure you can win by checking and calling. This way, you risk the same ammount of bets (if you will fold to a raise), but add fold equity, making this a clear EV play.

Plus, you need to take advantage of his strategy by bluffing often. But if you bet out with great hands and are called only a few times, opponent will not know what your bets mean, and you keep your disguise.

Hope some of this helps. And as for sacrificing value on one hand being profitable in later yes, the answer is an absolute yes. But remember, if you bet out with a good hand, you aren't giving up an entire bet, because villain will often call you. When he does, he'll see a good hand and know you are not always bluffing.