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The bet is intended to make them fold, not call.
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No. This is a value bet you make with what you believe to be the best non-flush hand. Folding hands that beat you is a nice additional benefit.
See, for example,
this post.
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I hope you're not talking about my example hand. I know that example may very well be a value bet. But what about a situation like you have 8 [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/spade.gif[/img] on a A [img]/images/graemlins/diamond.gif[/img] J [img]/images/graemlins/diamond.gif[/img] 7 [img]/images/graemlins/diamond.gif[/img] flop and the turn brings a 2 [img]/images/graemlins/diamond.gif[/img] and you bet OOP, then there is a wide range of better hands that may fold.
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2 things:
(1) That's not an application of Clarkmeister's Theorem. The requirements are: (i) HU; (ii) OOP; (iii) 4th flush card falls on the river.
(2) The underlying function of the Clarkmeister is to make a value bet -- you think you have the best hand at showdown unless Villain hit a one-card flush on the the river. We bet because the many hands that we beat are far, far more likely to check through when the 4th flush card hits, and many hands we lose to (including the one-card flush) will not raise our bet (if they do, depending on the opponent, we might call the raise or fold to it). The post I linked to makes this clear (I think) -- many, many more people that we are beating are calling our bet than are betting when checked to. By failing to bet the river, we are missing a bet; if we think we probably have the best non-flush hand, we are risking the same 1 BB we would risk by check-calling, and the likelihood of being raised is both somewhat small and/or depending on our read pretty easy to deal with.
My point is that the Theorem is about betting our hand for value - it is not about bluffing to make a better hand fold. In the hand you describe, do you really think your 88 is better than opponent's hand with AJxx four-flush? If not, you're bluffing, hoping he folds. May be a fine play, but not an application of the Theorem.