[Nate tha\\\' Great]

I don't like #2 at all. It's a big pot and he may well have just been taking one off with overs, in which case he may have paired up and you have a decent chance of getting a 3-bet in, or he has some kind of straight draw and you'd rather not give out a free card. If he value-bets aggressively however you can consider check-raising the river.

#1 I would not check this flop but having done so I guess it's *probably* worth the shot to try and represent a big hand and hope that he's a nit or a bad hand-reader. Another nice aspect to #1 is that your hand does have some showdown value and generally speaking this line gets you do showdown, meaning that if you don't get a fold right away you can check-fold the river and be pretty sure that you're beat if he bets. But I wouldn't check the flop.

#3 is fine.