By poker_boy | 6 Comments
Last updated: Sunday, January 13, 2008 | 449 Views Tags: aces, bridge hand, card deck, cards, poker, probability, royal flush
A tough poker hands question this week. Let’s dive straight in
Question: bridge hand is made up of 13 cards. A royal flush (5 highest cards of a single suit) in poker.
Answer: There are only 4 different ways to have a royal flush.
There are C(52,5) different 5 card hands.
4/C(52,5)
= 4/2598960
= 1/649740
= .000001539077
There are C(52,5) different 5 card hands.
4/C(52,5)
= 4/2598960
= 1/649740
= .000001539077
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Comments
6 comments
Mike Smith
January 13, 2008
royal flush: 52*51*50*49*48 or 311 million to 1
January 13, 2008
It depends what kind of poker you are playing.
5-card = 649,740 : 1
7-card = 30,940 : 1
January 13, 2008
The first card could be any. Probability - 1
2nd card must be same suit, 12 left of 51 cards - 12/51
3rd card must be of same suit, 11 left of 50 cards 11/50
etc.
So the formula is
(12*11*10*9*8*7*6*5*4*3*2*1)/
(51*50*49*48*47*46*45*44*43*42*41*40) =
6.299X10^-12 (checked twice)
January 13, 2008
Captainspizzo is correct.
January 13, 2008
A royal flush is the 10,J,Q,K,A of any suit. If we look at the sequence of the draw, you have a 20 of out 52 chance of hitting your first card. After you hit the first card, the rest of the cards have to be the remaining royal cards of that suit. So we have…
20/52 * 4/51 * 3/50 * 2/49 * 1/48 = 480/311875200 = 1/649740
Thus, your odds of hitting a royal flush are 1 in 649740, or 649739:1.
January 13, 2008
try this site for help on probability
http://www.futureaccountant.com/probability/