I'd consider betting the flop without the Ah as giving free cards is less concerning when we have it. Betting could open us up to more bluffing though as well so not sure how much I like it on this particular flop.
River seems like a call. Getting a good price, can be value betting worse, could be bluffing missed flushes.
Stacks are a little awkward for raising, but your hand is strong enough to bump it up a anywhere to 400-800 total. The question is what to do vs a jam.
Folding is completely out of the question here. He’s a maniac so by definition he has a wide range and capable of bluffing when you show weakness. Once you check the flop you’ve committed yourself to calling the turn and river if the board doesn’t get too scary. The 9 pairing the turn and king river don’t make the board scary enough to fold. As for raising, this depends on your image and what type of maniac you are dealing with. If you 2 have a history where you’ve been playing a bunch of pots with him in a very aggressive way and you’ve made him food the river to your raises then he may make a crying call with a king or call with kq but this is a very unlikely scenario. I would just call here and expect him to show up with some bluffs or a 1 pair hand.
As for the flop check, I think it’s fine, especially agains this type of opponent. It’s a 3 bet pot heads up so giving a free card isn’t a disaster and given his agression he will likely bluff a large amount of his range on the turn and river. You also avoid getting check raised by his semibluffs and putting yourself in an awful spot
Call. His value range in this spot is heavy weighted against you and you're only beating the very bottom of it when he does call. It's also doubtful the way the hand was played that anything stronger is folding.
I would value raise the minimum to induce a re-raise. that's your best play. If he re-raises small like 800 its for value and you should fold. If he goes all in its more likely to be a bluff so u should call. You could also value call instead of raising.
