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What are the overall chances that a single pocket ace in texas hold'em will be the winning hand, regardless of the other card?

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You can use this page as a quick reference but the exact odds are 0.00452 or 220 : 1.

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Those are the odds of receiving aces (or any specific pair), which is just 6 combinations {AcAd,AcAh,AcAs,AdAh,AdAs,AhAs} divided by 1,326 possible (52 choose 2). Depending on how you read the question, the odds of winning with AA against one random hand are 85.204% and with Ax against one random hand are 61.14%. –  Loc Nguyen Jul 20 '12 at 0:33
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