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Live I play $0.50/$1.00 and $1.00/$2.00, but online I only play small stakes, so take this with a grain of salt.
Moves like this always baffle me no matter what the stakes. Over betting the pot seems like such a donkey move, but the problem is the reaction to it may end up being more donkish. In theory, you lose so much value on your monsters to inferior hands and without the nuts, you only get called by hands that have you beat. It's like, if you want to be clever, why not just over bet the pot? Why massively over bet it? On the other hand, I've seen enough players do it and get paid and sometimes curiosity gets the better of us when WE have a good hand and we want to call to see which end of the stupid scale this player is on for next time.
Maybe it's a leak in my game or maybe it's good strategy, but I generally have a really tough time folding a set when an ace hits because most players like to play aces. I think AK, AQ, and AJ are all in his range and I think villain's post flop check is reasonable since he's OOP to players he expects bets from. Another consideration to make: is 220 big blinds really deep enough to fold a set without a really good read? Obviously, you wouldn't just always blindly commit, but with no flushes, no paired board, and two unlikely two card combinations to make a straight, and not a good read to the contrary, I probably call against most average or loose players, although, if huge over pot all-in check/raises are usually indicative of a monster that has you beat at these stakes, I don't think a fold is unreasonable.
The real problem for me here is that this player is tight and his range for making a play like this seems very narrow UNLESS you have a good read to the contrary or have a good handle on where you stand with his perception of your table image.
Really, with a play like this, I think it all boils down to table image and psychology. He has probably made this huge all-in over bet for one of three reasons:
1) He has a good hand like two pair that he thinks you will pay him off with an inferior hand like TPTK
2) He has a monster like AA and thinks you'll pay him off with a great hand like 44 or even two pair
3) He has an average to mediocre to air hand and he thinks you'll fold
If you think it's 1 or 3, call and fold if 2.
Personally, although I would want to call, my instinct would be to fold. Most of the time when players go all-in like that, they have a monster - even @ $2NL.
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