First 5 cards Question

[Kevin J]

I admit it. I'm entirely UN-resourceful. I'm sure there are a million places to look this up and it's also probably not that hard to figure out. But I can't do it.

What are the chances of being dealt a royal flush in the first 5 cards of draw poker? If someone can provide the calculation also, I'd appreciate it. Thanks

[BruceZ]

Game played with 1 joker:
24 possible royal flushes (4 natural + 20 w/joker)
C(53,5) = 2,869,685 possible hands
24/C(53,5) = 1 in 119,570.21

Game played with no joker or wild cards:
4 possible royal flushes
C(52,5) = 2,598,960 possible hands
4/C(52,5) = 1 in 649,740.