[Xhad]

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What I want to know is that since he is making a positive expectation play by calling your bet, you must be making a negative expectation play by betting into him.

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This is a fallacy. Your opponent can only profitably call because of the dead money already in the pot. He still loses money due to your betting (as opposed to checking), even though he gets to call your bet.

Look at it this way:

For the favorite: a bet your opponent can't correctly call > a bet that your opponent can call > no bet at all.

For the underdog: no bet at all > a bet you can call > a bet you can't call.

Since this is limit, as the favorite you can't give yourself the best-case scenario because you can't bet enough, but you can get your opponent out of HIS best-case scenario by betting.