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The odds against getting a royal flush in poker on first five cards dealt is 649740 to 1 Find the probability of this event?
I will assume you numbers are correct, and the odds of NOT getting a royal flush is 649740 to 1, then the odd of a royal flush is the reciprocal of that. When we speak of odds in probability it has a very specific meaning. If P is the probability of an even , then the odds in favor of P are P/(1-P). For example, the odds of getting a 6 when we throw a die is not 1/6, it is 1/6 divided by 1-(1/6) or 1/6 divided by 5/6 which is 1/5 or 1 in 5. The odds of not getting a 6 is 1/(1/5)=5 to 1 So your given odds are 649740/1 and the odd of getting the royal flush are 1/649740.
What are the odds of getting a straight flush?
With 5 cards: Straight Flush: approx 72,192 to 1 Royal Flush: 649,740 to 1 With 6 cards: Straight Flush: approx 12293 to 1 Royal Flush: 108289 to 1 With 7 cards: Straight Flush: approx 3590 to 1 Royal Flush: 30939 to 1
What are the odds of getting royal flush in five card stud?
The odds of getting a royal flush in five card stud is the same as in any poker game with five cards involved, i.e. 649,740 to 1.
Which wins in poker flush hand a spade to the ace or a club to the ace?
In poker, suits do not have rank. Two royal flush's would tie. Otherwise with an A high flush you would go to the next highest card.
How do you calculate the probability of a royal flush?
First, we determine the total number of five card hands possible. Since there are 52 cards, we simply pick the first card 52 ways, then the second card 51 ways, then the third card 50 ways, then the fourth card 49 ways, and finally the fifth card 48 ways. This gives a total of 52*51*50*49*48. Since the order that we pick the cards is unimportant, we divide this total by the number of ways of permuting five objects, which is 5! = 120. So, the total becomes 52*51*50*49*48/120 = 2598960. Note this is just (52 choose 5). Now that we know the number of possible hands, we simply divide the number of royal flushes (4) by the above 2598960: 4/2598960 = 0.000001539, the probability of getting a royal flush in the first 5 cards off the deck. Of course, depending on the type of poker being played, the probability will differ from this value. Omaha has a higher probability than Texas Hold'em, which has a higher probability than calculated above. Wild cards can drastically change the probability. If every card in the deck is wild, then the probability is 1 (if 5 of a kind isn't allowed) or 0 (if 5 of a kind is allowed).
