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I think you would be deadly in this situation from the BB. Asuming the original raiser in the only one in the hand, you could just push all-in everytime your opponent had a bad hand in a steal situation. This would take away the chance of your opponent calling with their J-8 and hitting a flop. Of course you always run the small risk of someone calling with garbage, but that is very unlikely. Consistently pushing from the BB against weak/marginal hand(s) would allow you to accumulate the chips necessary to dominate knowing the hole cards.

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This makes sense, but BB against one opponent on a steal with trash is sort of a special case because you are absolutely guaranteed to have only one opponent who doesn't like his hand at all. Usually, things are complicated a bit by the unpredictability of players yet to act and the possibility that a raiser might decide he really likes a marginal hand. Even so, give your opponent jack-high, throw in a double-up-early-or-go-home mindset and after the second or third time you make this sort of move you might get called.