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Extremophile
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10-12-2009, 07:08 PM
Post subject: Probability help
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#1 (permalink)
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Flush
Join Date: Oct 2008
Location: Stackton
Posts: 451
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How do we calculate the probability of flopping A or K or Q? I used to do this basic math but I forgot. Thanks!
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Belt
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3-of-a-Kind
Join Date: Feb 2007
Location: Istanbul
Posts: 95
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1 - [(40/52) * (39/51) * (38/50)] = 1 - 0,447 = 0,553 = ~55%
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Robb
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4-of-a-Kind
Join Date: Aug 2007
Posts: 3,072
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Quote:
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Originally Posted by Belt
1 - [(40/52) * (39/51) * (38/50)] = 1 - 0,447 = 0,553 = ~55%
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^^^ This is the probability of flopping at least one A or K or Q, but includes flopping 2 or 3 of those cards, as well. It also assumes we don't have one. So if you have JJ, you have a ~55% chance of running into an Axx, KQx, or AQQ type flop.
To calculate the probability of flopping an A or K given that you have AK is:
P = (6 choose 1) * (48 choose 2) / (50 choose 3) = ~30.0%
where "n choose k" = n! / (k! * (n-k)!).
The terms in the calculation above are conceptually:
6 choose 1 ~ from remaining 3 Aces + 3 Kings, draw 1
44 choose 2 ~ from other 44 cards in deck, draw 2
Divide by total flops possible:
50 choose 3 ~ from all 50 cards not in Hero's hand, draw 3 for a flop
We can also calculate the probability of drawing exactly 2 A's or K's, so flops like AAx, AKx, or KKx:
P = (6 choose 2) * (44 choose 1) / (50 choose 3) = 3.4%
6 choose 2 ~ from remaining 3 Aces + 3 Kings, draw 2
44 choose 2 ~ from other 44 cards in deck, draw 3
And so on...
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