My Second Nuts Beats Your Second Nuts

I won a nice pot today on an interesting hand after I started thinking about it. BTW, I needed this hand, as I have been taking some pretty brutal beats on PokerStars lately. This one was for a $258 pot at .50/1 nl.

I pick up JJ and am facing a raise to $4. I reraise to $7 to see where I am at. Initial better calls here, and I may think my JJ is good as an over pair on the flop. A small reraise back, and I play for a set. A big raise back, and I am probably folding. Anyway, two others and the original raiser call. Ok not very likely I am against AA or KK here. QQ is also slightly ruled out. I am likely in the lead, but JJ don't play well 4 handed. Lets see a flop.

JAA

I think I may have just messed myself. Initial better leads out for $20, and I reraise to $40. Fold, Fold, All-in. I call, $258 pot.

Now for some interesting nut analysis here. I have the second nuts, with AA only beating me. AA is pretty unlikely, as we are talking about flopped quad As and nobody represented AA preflop, except maybe me. Now the other guy? It's pretty obvious. AK is what he had. To him this is second nuts as well. Only JJ beats him. There is no way he can get away from this hand, and I don't think anyone else could either.

In case you think you might be able to fold the second nuts on the flop here are some considerations:

1) Does the nut hand make sense based on the preflop betting

AA not really in my case. JJ, was a min reraise preflop so definitely possible

2) What are the odds of the nut hand having just hit.

AA flopping quads are extremely rare. JJ flopping a set, not so rare.