2nd pair on monotone flop

[MrBig30]

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I would start by checking.

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Yeah, that sounds like a plan. So let's say that:

a) BB bets, UTG calls, Hero...
b) BB bets, UTG folds, Hero...
c) BB checks, UTG bets, Hero...

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This is a very tricky situation. This is what I would probably do:
a) fold (although calling might be ok)
b) call, reevaluating all options on the turn.
c) raise, hoping to fold out BB, as we are very likely ahead.