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Believe it or not, this was a fairly easy laydown. You made a pot sized bet on this board...
[3d 9c Ah]
There is absolutely no coordination. Another ace just calls your bet unless it's AK. That hand and two pair or better raises. The only other possibility is another AQ. You would still only split. It's not worth it to get involved. You gotta start believing raises. If someone raises a pot sized bet, then there is cause for concern all day long.
Have you ever heard of reverse implied odds? It's the amount of chips you'll have to spend with a seemingly trapped hand to see showdown. The better players will fold this instantly, because on certain boards, the only reason someone would raise is if they have a better hand.
The favorite hands of top money players are suited connectors and low packet pairs. That's because they're easy to let go of. Top pros don't like big hands as much because they win small pots, and lose big ones. In the scenrio above holding AQ when you flop a Q, you should expect to get a round of folds, or maybe one call of your pot bet. When someone raises, then you should seriously consider a divorce. Know that commitment with one pair is tedious. Ask yourself what kind of hands you will lose your shirt on. The answer will usually be "Big hands I couldn't let go of".
You have to practice asking yourself "Why is this person raising me". If the answer is "Because there's a good chance I'm behind", then it's best not to get involved. Learn to fold big hands that catch one pair when someone gets heavy with you.
Make no mistake about it. The secret to winning poker is laying down at the right times.
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