jmcdaniel wrote:
If I understand the calculations correctly, on the deal, I will receive dealt trips about once every 46.3 hands.
---I get 47.3 as follows: pick the rank (13 possible), pick 3 of the 4 cards of that rank (4 possible), pick 2 of the 12 other ranks to complete the hand (12 * 11/2 = 66 possible), pick 1 of the 4 cards of one rank (4 possible), and lastly, pick 1 of the 4 cards of the other rank (4 possible)...multiply together to get 54,912 possible dealt hands that contain three of a kind (but not a full house or quads). Divide 2,598,960 by 54,912 to get about 47.3.
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jmcdaniel later wrote:
...I received 1 dealt trip in 1,500 trials.
---You can use the binomial distribution to calculate (Excel has this too). You want to know the probability of 1 success in 1500 trials with the probability p of a success equal to 54,912/2,598,960, and with q = 1-p.
P(1 dealt trip in 1500 hands)
= C(1500, 1) * p^1 * q^(1500-1)
~4 X 10^(-13), or about 1 in 2.5 trillion (back-to-back dealt royals would be 6 times as likely)
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jmcdaniel also wrote:
Is there a website you can point me to help me learn how to perform the calculation myself?
http://en.wikipedia.org/wiki/Binomial_distribution
http://www.stat.yale.edu/Courses/1997-98/101/binom.htm
