Wikipedia:Reference desk/Archives/Mathematics/2016 April 25

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April 25

What's the chance of getting AKQJT suited or AKQJT9 suited in a trick taking game?

I just got a "6 card" "super" royal flush (AKQJT9). What's the chance of that? I wonder if this'd still be worth much if poker was 13 cards not 5. It's an app so there's no guarantee there aren't bugs but assume there aren't any. Sagittarian Milky Way (talk) 22:26, 25 April 2016 (UTC)

There are ${\binom {52}{13}}$ possible hands, of which ${\binom {46}{7}}$ have the AKQJT9 in a particular suit. So your probability is very slightly less than four times the ratio of these numbers, roughly 1/3000. The probability that any of the four players gets such a hand is somewhat larger. --JBL (talk) 02:44, 26 April 2016 (UTC)

So not crazy unlikely then (not that I would've guessed that). Sagittarian Milky Way (talk) 05:22, 26 April 2016 (UTC)

Playing bridge once or twice a week, I've gotten 5-card flushes from time to time and royal flushes once or twice. I got a seven-card straight flush once, I think. Bubba73 ^{You talkin' to me?} 05:30, 26 April 2016 (UTC)

You did mean 5-card straight flushes, right? --69.159.61.172 (talk) 05:50, 26 April 2016 (UTC)

I've had 5-card straight flushes out of 13 cards pretty frequently and I think I had a 7-card straight flush once. Bubba73 ^{You talkin' to me?} 22:56, 26 April 2016 (UTC)

To clarify, Anon's question followed from the fact you wrote "5-card flushes" instead of "5-card straight flushes". Mere flushes are easy, of course. -- Meni Rosenfeld (talk) 16:18, 27 April 2016 (UTC)

Oh, sorry, I missed that point. I get five-card flushes every time I play! Bubba73 ^{You talkin' to me?} 23:50, 27 April 2016 (UTC)