Quick edit
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But far more often against these opponents you'll be behind both of them and will be drawing to 0-2 outs and will not be able to win without showing down.
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Oops. Make that 0 to 3.3 outs. (I do think there's a decent chance any 2 will give you a 3-way chop.)
But that's still not enough. Anyway, on the turn I think chances are MP1 is optimistically trying out the top pair he just hit, and Button is most likely preparing to raise with his own top pair. (Your read of the flop action seems good to me.)
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