Odds of matching a poker hand

Hi Wizard of Odds,
I'm a big fan of you and math in general!
my question is the following:
what are the odds of matching an exact hand (and suit of the cards) choosen by the card room at random at the beginning of the night?

Example: the hand randomly generated is Straight 4s 5d 6d 7h 8s

Also, does the % change related to the type of hand? i.e. Straight vs ROyal FLush vs Quads etc

Thank you in advance for your answer

Luca from Nottingham

The answer to the second part is, no, it does not change depending on the type of hand, if all five cards are specified. For example, "quad Aces and a two of spades."

As for the first part, it depends on how many cards you get.
If you only get five, then the odds are 2,598,959-1 against.
If you get seven, there are (52)C(7) = 133,784,560 seven-card sets, of which (47)C(2) = 1081 will have the five cards specified, so the probability is 1/123,760, and the odds are 123,759-1 against.

Thank you very much for the quick reply.
Actually i didn't think about the fact that different hands make no difference as all the cards are specified.

Btw, I was talking about a hand of NLHE, so 2 hole cards and 5 community ones

Cheers

Quote: ThatDonGuy

The answer to the second part is, no, it does not change depending on the type of hand, if all five cards are specified. For example, "quad Aces and a two of spades."

As for the first part, it depends on how many cards you get.
If you only get five, then the odds are 2,598,959-1 against.
If you get seven, there are (52)C(7) = 133,784,560 seven-card sets, of which (47)C(2) = 1081 will have the five cards specified, so the probability is 1/123,760, and the odds are 123,759-1 against.

It might matter if you have to stay in the hand to the end and it’s a game like Hold’em