QQ, early-middle stages of 300+20

I have two answers to this:
First: I think this requires a good read to do, first of all. Villian's sissy 200 chip bet into a 925 chip pot screams either a draw or a miss, probably a worse PP. I'd bump it up to say 600-700, maybe even calling a push with a good read, because I think a lot of people see an ace on board as a "right" to bet into a pot. I'd do this about 20%-30% of the time with a good read.
Second: You only have 300 invested, just cut your losses and move onto the next hand. I'd go this route about 70%-80% of the time.

[tshak]

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Villian's sissy 200 chip bet into a 925 chip pot screams either a draw or a miss, probably a worse PP.

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At a $300+20 I would probably give a little more credit then that. As you said this is very read dependant. This would be my default read at $50's or maybe $75's and below. This is the perfect spot for a hand like A[img]/images/graemlins/diamond.gif[/img]K[img]/images/graemlins/diamond.gif[/img] because you dominate so many hands that would be tempted to peel another card off or play back because they sense weakness. Even if Villian is making this weak play with a strong drawing hand like K[img]/images/graemlins/diamond.gif[/img]Q[img]/images/graemlins/diamond.gif[/img] or even Q[img]/images/graemlins/diamond.gif[/img]J[img]/images/graemlins/diamond.gif[/img] we're still behind. Actually, I can't put Villian on many hands that we beat other than JJ, in which case the minraise preflop is horrid and I'd have to see Villian making plays like this to put it in his range. Even with JJ and 88 (being generous) in Villians range I think we're way behind often enough to check/fold this flop.

Edit:
Another thought regarding specific reads. If you are very sure (90%+) that Villian is on a draw here then Villian will call a push most likely as a 1.25:1 favorite. However considering Villian's shorter stack you will be getting about 1.6:1 on your money. But you have to be very sure that Villian wouldn't play a set or a strong A this way. Against that range you're at least 3:1 dog which is why your read must be very strong in order to push.