Push AJo here?

[TheDrone]

It's been a crazy $10 NL game, with 4 left in the 1st level (T20 BB). Huge stack (T6800) has been calling everything and gotten repeatedly lucky. T500 stack calls UTG, and with T250 left on the button I get AJo and raise to T70 - more or less standard for me in the 1st level. SB has T450, huge stack is the BB and will call anything here. I think a push would have been better, but how much better?

[willperkins]

This sounds like a crazy game with only 4 left and blinds at t20.
I would have limped in and seen the flop as cheaply as possible.
I tend to be very selective agressive and even when down to t250 in chips, I would not raise or push with this hand for two reasons. You would be raising or pushing into the big stack, who you state will call with anything. Also, you already have one limper in the game with the big stack left to act. If I am going to push or raise, I would look for a spot where I am the first one in the pot and if I can, a spot where big stack has folded.
I still think the blinds are low enough you could look for a better spot to raise or push.

[dethgrind]

Against a random hand (the giant stack who will call your push), your AJo wins about 63.5%

Your expected share of the prize pool before this hand (using the independent chip model) is 12.4%.

If you push, get called by only the big stack, and win, the stacks will be as follows:
UTG 480
You 530
SB 440
BB 6550

530 chips here is worth about 19.2% of the prize pool. But since you only win 63.5% of the time, your $EV is 12.2% of the prize pool if you push.

This is very close. Considering that you have about 12 blinds left, and the game is loose and wild, I think you can wait for a better spot than this to push. AJo isn't that great a hand. Your standard raise was probably the right play. Maybe limping is better, but probably not pushing.