Can I get away from AQ here?

[BarryLyndon]

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I wouldn't fold to the push.

I wouldn't raise 4xBB with AQo UTG with no antes.

More standard to just cbet the flop.

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Bad raise preflop, 2.5 - 3xBB better.

Continuation bet that flop, because CRing here commits you in sticky situations and you are deep enough to play multistreet poker here (especially if you bet 2.5xBB).

He bet 800 into a huge pot, which to me is the sign of weakness. I probably thinks you are betting that flop with an A, and he's kinduv a idiot on a heater, so expect to see a flush draw here more times than not. He may just think you are FOS and have a weak ace, which is not entirely wishful thinking. The pot is too big and you are getting reasonable odds. I'd expect to see Ksxs a really good chunk of the time here.

Barry