[Jerrod Ankenman]

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ok I see what you guys are saying. But why can't you look at B's bluff raise similarly to A's by way of B's limping hands. B has a range of hands he will limp with. Once in that range he is not folding, similiar to A having the check option. Why shouldn't B bluff raise with his worst limping hands?

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Because he does better by limping with those hands than by bluff-raising with them.

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And how should I apply this to Poker? I'm on the river and bet into. I have a range of hands to fold,call,and raise. Should I bluff Raise with my worst folding hands, my best folding hands, or my worst calling hands?

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Well, in real poker, you should bluff-raise hands that you would otherwise fold that block your opponent from having very strong hands, like hands that contain the ace of the three-flush suit.

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It seems to me that it depends on my assesment of my opponents likely holdings. Am I more likely to push out a better hand by bluff raising with my worst, or to get a worst hand to call by bluff raising with better hands. Also, I'm usually going to gain a lot more with a successful bluff than inducing a bad call. Maybe that's the point Aisthesis was getting at in #4 when he talked about A getting more Bang from his Buck when he bluffs.

PairTheBoard

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What's important to understand are a couple of things:

--When you bluff-raise, you expect to lose the pot 100% of the time when you are called. You bluff-raise your best hands in preference to your worst ones in case your opponent does something stupid, but against an optimal-strategy-playing opponent, your EV is not changed at all by which hands you bluff-raise with. You bluff raise because you want your opponent to call when you value raise. If you never bluff-raise, he can simply fold hands worse than 5/6 to your raises and do better.
--You bluff-raise with hands that you would otherwise fold. You're not trying to induce worse hands to call you. That would be a value raise.