for clarity purposes...i am not saying you have to have a royal flush before committing all your chips to the pile, just a strongly reasonable assurance beyond actually having the nuts before you dive in.
last night i was in a tourney at
Bodog...one away from the money...i pulled AA and raised about 4xBB...got one caller...flop came A K 8...i raised pot and my opponent pushed all in and i called...he is holding 88...fourth street was a J and fifth street was, you guessed it, his fourth 8. rather than doubling up i am the bubbleboy.
would i have played it any differently...NO.
my point is i had a strong reasonable assurance that my A set would very likely hold up. i would not have felt that high level of confidence with JJ because now there are two more hands that can potentially beat me in addition to all the other possibilities.
lastly, at a BandM casino, ALL MY MONEY WOULD GO IN WHEN I HIT THE J set from your scenario above.