After the pre-flop, 3 clubs, 3 diamonds, 4 spades and 2 hearts had been dealt. That's 12 cards total, leaving 40 in the deck. What was the probability of one of these guys getting a flush?
Flush of Hearts (actually happened): (11C4)(36C1) = 11880
Flush of Clubs: (10C4)(36C1) = 7560
Flush of Diamonds: (10C4)(36C1) = 7560
Flush of Spades: (9C4)(36C1) = 4536
Total number of possible flushes = 11880 + 7560 + 7560 + 4536 = 31536
Total number of remaining hands = 40C5 = 658008
Probability = 31536 / 658008 = 0.0479 = 4.8%
Of course, this does not take into account the probability of two players being dealt AA in the first place!
[someone check my work!!]
Flush of Hearts (actually happened): (11C4)(36C1) = 11880
Flush of Clubs: (10C4)(36C1) = 7560
Flush of Diamonds: (10C4)(36C1) = 7560
Flush of Spades: (9C4)(36C1) = 4536
Total number of possible flushes = 11880 + 7560 + 7560 + 4536 = 31536
Total number of remaining hands = 40C5 = 658008
Probability = 31536 / 658008 = 0.0479 = 4.8%
Of course, this does not take into account the probability of two players being dealt AA in the first place!
[someone check my work!!]
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