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No reason to bet this flop. Against one opp, it's a good play. two+, just let someone else lead. If you get a free card, great. You need to assume your fold equity here is 0 and you do not currently have the best hand.
You see from the posts above why we have different names for a SET (PP in hand, one on board) and TRIPS (one in hand, two on board). No one has trips on the flop. Someone may have a set.
If you find yourself often making a play because "I put him on a set" it will usually be the wrong play IMO.
Having said that if you put him on a set, you don't have odds to chase and should fold the flop. It's close, but you need at least 5/1 if you are only calling to see then turn and you don't quite have it. Add in that you put him on the set so he has re draws and it's a fold.
If you call the flop you're playing for the the flush draw and assuming it will win you the pot. Folding the turn is therefore not good, since you now have a massive price to chase. Again, if you put him on a set, the time to fold was the flop, not the turn.
a comment about 'I figured it would be best to open raise '... most poker rules are in place not because there are rules in poker you should always follow, but because there are rules you should always follow UNTIL YOU KNOW WHY YOU DON'T.
Folding or raising AJs UTG this early should be standard TAG strategy IMO, with more folds than raises.
Folding - requires nothing more than discipline.
Raising - requires you know:
1) When you c-bet (answer - not when you get 3 calls behind, esp when the flop isn't much help, but you have a big draw)
2) When to fold to a re raise pre flop(pretty much always)
3) How you will react if you get a 'good' flop (A or J high) and get action.
Limping is the most complex - you need to know:
1) Whether you will call a raise behind. How much will you call?
2) When to fold TP.
3) Pot odds, because we're playing as a draw hand now
The more you play, I suspect you'll find that trying to play hands like AQ, AJ, KQ in EP for a raise just causes you pain and agony. But you won't be ready to hear that until you've gone through the thinking process I have (incompletely) outlined.
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