Hi.
Few things to point out first
1) I don't think you should be playing 20BB at this live game. The rake is insanely high at 10% so I think it will be very difficult to make a profit if you are not playing 100bb or more. You will just get raked to death in the long run.
2) Given that your stack is shallow at 40BB, I don't think you need to raise to 4BB. 3BB or even 2.5BB opens are fine. Since I assume your game is probably loose passive like most 1/2 live games, I think 9$ seems great.
3) You should have some sort of bet sizing plan. Given that you are short, maybe you wanna bet smaller on earlier streets so that you still have money left behind on the river. You also want to make your cbet bluffs cheaper. So if you bet so large on the flop with your strong hands and half pot with your weak hands, there may be some sort of imbalance. Of course this guy is a weaker player, so perhaps it's fine just to bet larger with your TPTK hands, so you can put him all-in on the Turn.
4) On the Turn, you received one of the worse cards in the deck. A bunch of straights and flushes got there. If I had a weak Queen I'm probably check/folding.
With AQ I think you should check and hope he turns something into a bluff. I don't think there is too much value in betting since the range of hands with which he can call you with probably beats you on average in my opinion. Then again, against someone playing 50 VPIP, perhaps he can have a lot of worse QX hands like Q9 QJ Q7 Q6 KQ which can call a push. I don't think there's really any point in betting smaller - There is a pot size bet left and it's pretty clear you are committed so just push or check.
So I would check, and when he bets, determine if you are beating enough worse hands and decide whether to c/f or c/c. I probably call, since I want to let him turn 56 57 67 JT 87 into a bluff and try to represent the flush. Maybe he ends up shoving worse Queens for protection when it is checked to him too.
thanks.
