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bet/fold can NOT equal check/fold as you just demonstrated.

bet/fold has an opportunity to take the pot even while holding a worse hand than your opponent (and check/fold obviously does not).


as far as "what hand are we possibly ahead of here?"
I've seen opponents who cap 77 PF just because they are WAY over-zealous. Obviously they would fold if bet to...but checking to them gives an opportunity for them to take it with a worse hand.
It's possible...though obviously not likely.

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O RLY?