Having AQ Vs. QQ and having a Q flop

[KJL]

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to put it briefly, I only have to worry about my opponent having a set of
Queens when I have AQ (or a set of Aces when I have AK) only 6.25% of the time..., right?


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No 6.25% is the probability that the flop contains a Queens assuming you hold AQ and your opponent holds QQ. The chance that he holds QQ when the flop is Qxy and you hold AQ is .08%.
However, as ohnotthat was saying this is not useful you have to take into account his range of hands. This is were he got the 1/22 number from. He compared the probability of QQ with the other hands in your opponents range. So this dosent happen between 4.5% and 6.25% they are completely different numbers. I think this is what ohnothtat was saying, but I only skimmed his post.

To answer your other question, it is possible to get away from these hands. Top pair top kicker is not that good of a hand and to be a succesful poker player, you have to be able to get away from it. You should post the hands that you have trouble with in some of the other forumns to help you with this.