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This is a great question.
First off, some real things to think about.
As odd as it may seem, AJ is not a great hand when you are out of position in a ring game. I admit I play it every time in a tournament where there is blind pressure. But you really must be careful of this hand from early position in a 10 person ring game.
Next thing to consider is, who is the late caller? Is he a tight player that only calls raises when he has a strong hand? Is he someone that sees 50% of the flops regardless of any previous PF raise, but then folds post flop if he misses?
Next thing to consider, do you think the late caller has any impression of you; and if so, what is that impression? Many times, you will have no table image at low level tables because no one seems to be paying attention. But perhaps you have been at a table for a long time with the same people. Have you been going into less than 20% of the pots? Do you tend to win if there is a showdow? Or have you been raising into more than 30% of the pots, often going to showdown only to have the second best hand?
Next thing to consider, how much strength did your raise represent? You mentioned you raised, but did not say how much (I am assuming NL). Depending on your table image, or lack of one, a large opening bet was a sign of considerable strength; where a min raise is more a sign of having a decent hand and not wanting trash hands to see a free flop from the blinds. If your PF raise was large and you have a tight table image and the caller was not a tight player, then you are going to bet your AA pocket pair because the board is not scary (*wink*).
Next thing to consider, how much money is in the pot compared to the amount you and the caller have left? If your raise was small and both you and the caller have large stacks, then consider if this is really a pot worth pursuing. On the other hand, if you raised large and your stack is small compared to the pot, then you will have pot odds to see the river even if you missed the flop.
If the late caller is a tight player, you are likely beat. Check folding may save you money over a lot of hands. If the late caller is a loose cannon, and you have a decent table image, bet your hand like you made it. Looks like you opened with AQ and now have TPTK on a rainbow, no straight board. If the loose guy calls, then he probably hit something and has you beat. Play the Turn and River carefully, looking for reasons to fold more than reasons to stay.
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