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I hold an Ace.
There is one Ace on the flop.
10 players (9 + me) in the game.
What is the probability that *at least* one of the other players holds an Ace at that point in the hand? Prior to the Turn.
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1 - C(45,18) / C(47,18) = 62.4%.
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Could you also provide the math to calculate for other number of players in the hand.
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1 - C(45,2N) / C(47,2N)
where N is the number of opponents (not counting yourself). This is 1 minus the probability of no aces being dealt. C(45,2N) is the number of ways to select the 2N non-aces out of 45 non-aces. C(47,2N) is the total number of ways to select 2N cards.
<font class="small">Code:</font><hr /><pre># opp. P(at least 1 ace out)
1 8.4%
2 16.5%
3 24.1%
4 31.5%
5 38.4%
6 45.0%
7 51.2%
8 57.0%
9 62.4%</pre><hr />