LinkerSplit
LinkerSplit
Joined: Mar 10, 2019
  • Threads: 3
  • Posts: 7
March 10th, 2019 at 1:42:01 PM permalink
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
ThatDonGuy
ThatDonGuy
Joined: Jun 22, 2011
  • Threads: 95
  • Posts: 4465
March 10th, 2019 at 2:00:29 PM permalink
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.
LinkerSplit
LinkerSplit
Joined: Mar 10, 2019
  • Threads: 3
  • Posts: 7
March 10th, 2019 at 2:26:14 PM permalink
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
unJon
unJon
Joined: Jul 1, 2018
  • Threads: 13
  • Posts: 2091
March 10th, 2019 at 6:06:42 PM permalink
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
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.

  • Jump to: