What is the probability of getting a royal flush in poker?

Answer 1

4 different kinds of royal flushes, 5 cards each.

***NOTE this takes into account that no one has any hole cards.. Im doing the math with a full 52 card deck****

The first flop card has to be one of those 20 royal flush cards in the deck of 52 so the probability of that hitting is 20/52

Once that first card hits, The suit of the royal flush is now set and there is only 4 remaining cards in the deck to complete the hand.

Therefore the 2nd and 3rd flop cards probabilities are 4/51 and 3/50

The turn then has to be 2/49 cards and the river the last 1/48

Multiplying these: 20/52 * 4/51 * 3/50 * 2/49 * 1/48 = 480/311,875,200

Or simply just under 1 in 650,000 times :)

Answer 2

Okay, I think I've finally got this one after pondering it for a while. Obviously, there are 13 cards per suit and 4 suits. You are starting with 13 possible cards that will give you a flush on the board and the whole 52 card deck. For this example I will not consider the odds based on the two cards you are already delt. So for the first card you have a 13 out of 52 chance of hitting a card of a specific suit. On the second card, you have a 12 (one is already picked) out of 51 (one card is shown) chance. Third card, 11 out of 50. Fourth, 10 out of 49. Fifth, 9 out of 48. You have to multiply each instance together to get the overall possibility. Here's the math: (13 / 52) * (12 / 51) * (11 / 50) * (10 / 49) * (9 / 48) = .000495 This is about half of one thousandth of a percent. To get the odds, divide one by this number: 1 / .00495 = 2019.4 So there is a 1 in 2019 chance of getting a flush on the board for each suit, but we must now multiply by 4 to get the odds of getting any flush of any suit: .000495 * 4 = .001981 1 / .001981 = 504.8 So overall, pretty close to about 1 in 500. Hope this helps. Go Gators.

Answer 3

A Royal Flush is the highest possible hand in Poker and the odds are 649,739 : 1

The above is true for 5 card poker, but not true for Holdem. Because there are 7 cards, the odds go way down:

Choose suit, choose 5 of 5 cards(10JQKA), choose 2 of remaining 47 (numerator)

out of a total of choose 7 of 52 cards (denominator), so you get

combin(4,1)* combin (5,5) * combin( 47,2)/combin(52,7)

Answer is 1 in 30,940

Answer 4

Choose suit, choose 5 of 5 cards(10JQKA), choose 2 of remaining 47 (numerator)

out of a total of choose 7 of 52 cards (denominator), so you get

combin(4,1)* combin (5,5) * combin( 47,2)/combin(52,7)

Answer is 1 in 30,940

Answer 5

I don't know the exact number, but it's something like 620,000 to 1.

Answer 6

649 740:1 or 0.000154%