[4_2_it]

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I would maybe float him on the flop and try to take the pot on the turn, but most of the time, i would just give up the hand and look for a better situation.

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It isn't floating if you are OOP. You are describing a Stop and Go, which I really do not like in this situation because no worse hands are coming along.

Jake, Hand 1 looks fine as long as you got the money in the middle.

Hand 2, playing AQ OOP to a raise is very difficult. Reads are very important. I do not like to play large pots in this situation and usaully call pre-flop, but will occasionally take Jam's line as well. It's all about feel. Against a solid TAG I'd have no problem folding AQ.