[spresso81]

How would YOU play this AA hand?

Here's the situation. Please read before voting...
You are dealt pocket aces in late position at a full ring cash game ($100 no-limit table). About 6 limpers in the pot when it gets to you. You raise a nominal $10 to keep a couple people in and not scare everyone away. (Yes, I know some of you would raise more than this, but this table isn't that loose.)

You get 3 callers. Flop comes Ks and 2 suited rags (clubs). Everyone checks to you, you bet the size of the pot ($50) to get rid of any flush draws. One guy then check raises you and goes all-in, everyone else now folds. The guy who goes all-in has $900 in front of him. You have $600 in front of you. Does he have a set? Two pair? Flush draw and he's a bad player who's an idiot to risk $600 on a flush draw? You don't know. Your read is that you still have him beat with your Aces. You talk to him, ask him to show you one card. Incredibly, he does(!) and shows you the 4c. You now know he does not have a set OR two pair. Your read says he now only has paired the King, but does have 2 clubs for the flush draw as well.

Here's where it gets tricky. You've watched him play for hours. He's not a really good player, but has been lucky. You count his outs. He has 14 outs: 9 clubs for a flush, the 2 remaining Kings to catch trips, or the 3 remaining Fours to catch 2 pair. Roughly a 56% chance to beat you. You are ahead, but he is now a favorite to win the hand. (And, neither of your Aces is the club, so you cannot catch runner runner for a flush.)

Do you call his all-in for your entire stack when he's at 56% to win the hand? Or do you lay down your Aces and let it go? After all, you've only invested $60 into the pot at this point. What would you do?