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My sister was playing no limit Texas Hold'Em at a table with six players and after the flop she made a royal flush. Can you tell me the odds on that happening? They must be astronomical.

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  • Can your sister buy me a lottery ticket?
    – David
    Jun 12, 2020 at 8:27

2 Answers 2

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There are 2598960 unique 5-card poker hands (C(n,r) = C(52, 5) = 2598960). 4 of those are royal flushes. So, the odds of one specific player flopping a royal flush would be 4-in-2598960, or 1-in-649740.

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    Yes. Although if a pair of 4's are dealt to you, the odds of making a royal flush after the flop is significantly lower :) If you're dealt two suited cards between 10 and A, then the odds improve to 1-in-19,600. Sep 28, 2015 at 20:47
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    If you ask a somewhat vague question, you tend to get the easiest specific answer. :) Sep 28, 2015 at 21:09
  • ?? @Chris farmer, for your 4//2.5 million hands, I take it that also does include a RSF that is on the board ONLY, meaning you'd split the pot and wouldn't "win" anything. If true, then you'd have to eliminate 1/7th of the 1/650k possibilities to beat the others (and assume they don't get their own RSF at the same time and tie). Correct? [[ Pokerstars result a few days ago, which is why I care:) "Hand #193344547027: DaaBoss wins pot (2,646) with a Royal Flush" ]]
    – DaaBoss
    Nov 22, 2018 at 6:39
  • @DaaBoss the question is on flopping the royal flush, not rivering it. So only the first 5 cards matter. Altho i agree with Drfbag, the assumption is you hold 2 of the 5 RF cards.
    – sakon
    Jan 22, 2019 at 8:20
  • @sakon no, there is no assumption made in the question. There is nothing written about hole cards already being dealt. The question simply is if you sit down at a Texas hold'em poker table, what are the odds that you have a royal flush after the hole cards and the flop are dealt. Above is the correct answer to that question.
    – azimut
    Jan 22, 2019 at 19:46
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I would disagree Chris with your probabilities. There is only possibility of one royal flush occurring in any one round. So it be 1 in 2.6 million of that occurring. But the odds slightly increase on turn and river. Unlike 5/7 card stud poker, then it be 1 in 650,000 of it occurring.

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    Op specifically asked about flopping a Royal Flush, so the answer provided by Chris is accurate.
    – Herb
    Jan 22, 2019 at 4:12

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