easy value bet on the end or check to induce bluff? 30 bellagio

[MNpoker]

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check to induce a bluff?

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I don't get this part. It makes it sound like you are sure you have the hand won (which based on the title I'm guessing you did win)

If the Button has a flush draw he shouldn't be raising here. (Especially if he plays 'moderately well')
I wouldn't expect him to being playing any 4 here either (except 44).

The only thing that makes sense is an ace.
You should fold the flop. IMO