[Sherman]

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Also, Sherman, when you check behind flop, and the turn is an offsuit 2, and whatever random pair he has open shoves the turn.

What do you do?

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You call. And no you haven't lost the odds to do so because you don't know that he has a pair. I've said this many many times already. 1) He shouldn't have a pair. 2) His range becomes wider on the turn after your flop check, so you do have the odds to call.

Edit: I've also mentioned many times that it makes no difference if you get it in on the flop or on the turn. If you don't plan on folding the flop or the turn, how does it make any difference when you get the $ in? The only time checking hurts us here is when villain hits his 2 or 4 outer (if he has unpaired cards) and then shoves the turn. Otherwise, checking the flop never hurts us.