odds of opponent holding pocket Aces given you holdpocket Kings

[BruceZ]

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The probability of someone being dealt AA is 1/220. It is 1/220 regardless of what you have (maybe slightly less given that 2 cards are known that are not A's)

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When you hold KK, the probability of a particular opponent having AA increases to 6/C(50,2) = 6/1225 =~ 1/204.

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i meant slightly more. whoops

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BTW, the probability of being dealt AA is 1/221, not 1/220. The odds are 220-1.