Is The Wiz's Answer To: Odds Of Being Dealt A Sequential Royal Flush (forwards or backwards) Wrong?
April 5th, 2014 at 10:34:50 PM
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At Wizard Of Odds/FAQ/Poker, Ric from Torrance, CA posed 2 questions about royal flushes. I believe the first question was answered correctly by the Wiz, but the second was answered incorrectly. The second question was: what are the odds of being dealt a sequential royal flush (forwards or backwards)? This is a permutation problem since As-Ks-Qs-Js-10s is a sequential royal flush while Js-Ks-10s-As-Qs is not (even though it is a royal flush). The Wiz correctly computed the total number of permutations of five card poker hands to be permut (52,5) = 311,875,200, which is much larger than the 2,598,960 five card poker hand combinations. The Wiz's answer was 4 in 311,875,200 (one for each suit) or 1 in 77,968,800. I believe by the phrasing of the question that the correct answer is 8 in 311,875,200 or 1 in 38,984,400. Why? Because Ric specifically stated "(forwards or backwards)". This means that As-Ks-Qs-Js-10s counts, but so does 10s-Js-Qs-Ks-As; therefore each suit has 2 distinct permutations of sequential royal flushes for a total of 8.
April 5th, 2014 at 11:03:37 PM
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Yes, you are correct. Good catch as that question is over 13 years old.
April 6th, 2014 at 2:14:25 AM
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Quote: tringlomaneYes, you are correct.
Maybe so, but be advised the Wizard hates subject lines like that of this thread.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
