What are the odds of a royal flush being dealt from one deck of cards to one person?

Question

and does it change if multiple people are being dealt hands from the same deck?

Answer 1

There are (52 choose 5) ways to deal 5 cards from a deck of 52 cards, which is equal to [52!/(5!(52-5)!]. There are four possible royal flushes (one for each suit). So, the probability of being delt a royal flush is 4/(52 choose 5), which is 1 in 649740. If other people are delt cards from the same deck, but you can't see any of their cards, the odds don't change. But if you can see some of their cards, the odds do change.

Richard, your answer is not quite correct. There are 4 out of 51 ways to choose the second card, not 1 out of 51. There are 3 out of 51 ways to choose the third card, and 2 out of 51 ways to choose the 4th card. So you need to multiply your probability by 4 factorial.

Answer 2

The number of possible 5-card hands dealt from a deck of 52 cards is 52 C 5 = (52 * 51 * 50 * 49 * 48) / 5! = 2598960.

The number of possible royal flush hands of all those possible combinations is 4 (one for each suit).

Therefore, the probability that a single person will be dealt a royal flush from a deck of 52 is 4 / 2598960 = 1 / 649740.

Adding more players would not change the probability because either way, you're still picking 5 random cards out of a deck of 52.

Answer 3

earth_wind_poker's answer is incorrect.

For your first card, you need the ace, k, q, j, or 10 of any suit. The odds of that are 20/52 or 5/13. After that, you need the remaining 4 cards of the flush, so the odds on subsequent deals are 1/51, then 1/50, then 1/49, finally 1/48. So the answer is 1 in ( 5 / (13 x 51 x 50 x 49 x 48) ). I'll let you do the math.

Now, one day after I posted this answer, I was thinking about the question some more and realized I made a mistake. The odds for the 2nd card are 4/51 because you need any one of the remaing 4 cards for the flush. Similarly, the odds for the third card are 3/50, then 2/49 for the 4th and 1/48 for the 5th. The answer is ( 20 x 4 x 3 x 2 x 1 ) / ( 52 x 51 x 50 x 49 x 48 ). So earlier, I understated the odds by 24 times.

Then when I signed on to post this correction, I see that warren_buffet_fan in the answer directly below mine caught my mistake and gave the right answer. Good work on his (or her) part!

Answer 4

1 in 649740
The number of players in the hand does not matter. There are only 4 combinations of a royal flush. The probability of being dealt a royal flush may change with the number of players since the cards would have to be spaced differently in the deck.

Answer 5

The odds are supposedly about one in 200,000.
It won't matter if multiple people are dealt because the odds are still calculated out of 52 cards.
It's unusual to be dealt a natural (no wild cards) royal flush. Most people will never see that. I was dealt a natural royal flush, which is unusual enough, but what's really amazing is that I was dealt two natural royal flushes within the span of about two hours in one day.

Answer 6

The odds are around 2.5 X 10 to the 16th power: there are 48 different combinations possible for each 4-card combination to complete the royal flush.

Answer 7

if my stat method is correct ,

it's 52 x 51 x 50 x 49 x 48 = whatever

That huge **** number to 1 odds you will be dealt a full house.

and it wouldn't change if there were more people in the hand since the odds of being dealt a specific card wouldn't change.

Answer 8

I caught it about 3 times in a year.

Answer 9

147384 to 1 happy poker playing