March 10th, 2019 at 1:42:01 PM
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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

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

March 10th, 2019 at 2:00:29 PM
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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.

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.

March 10th, 2019 at 2:26:14 PM
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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

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

March 10th, 2019 at 6:06:42 PM
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Quote:ThatDonGuyThe 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.