What is your push range here?

[illegit]

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Because I bet the BB folds here...1:200.

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The BB... the imaginary player with a big stack who we have a read on, a read you're purposely ignoring.. why? Apparently you find it impossible to have this read and I just don't know why.

Say 1 orbit prior the SB pushed into the BB on a stack smaller than ours and we saw the BB fold getting 3-1. Then we know we currently have plenty of fold equity. I shouldn't have to concretize ways in which we can have a particular read in order for you to understand the hypothetical in the abstract, but say you were equipped with this information, are you STILL not pushing any 2? If you are then you were pushing any 2 in the first place you just didn't realize you had a read (which you clearly did have according to the info given by the OP).