The odds are I believe 8000 to 1

I think its more around 600 or 700k but just wanted to know the exact number

technically it'd be 4* 1/52 * 1/51 * 1/50 * 1/49 *1/48

So around the 600 or 700k mark

1 in 649,740. This is the exact answer. To understand better. You need a face card or ten as the first hole card. That's 20/52. The next hole card must be one of the other four cards of the same suit which make the royal straight, so 4/51. The three flop cards are 3/50, 2/49, and 1/48.

I flopped a Royal last night at my home game I guess I am the one, The best part is I had it against the same guy I hit a Royal on the turn against about 4 months ago, what are the odds of having a Royal against the same guy twice in one year......?

Well, for the sake of practicality, let's assume that you have 2 suited cards 10 or higher in your hand. If you don't, the odds of flopping a royal flush are 0% because it just isn't possible. If you do have 2/5 of the royal in your hand, the odds of the other 3 cards coming out on the flop is: (3/50)*(2/49)*(1/48) = 6/117600 = 1/19600 So your odds of flopping the royal are 1 in every 19600 times you're dealt two suited cards ten or higher. If you prefer a percentage, this will happen approximately 0.0051% of the time.

i did it last night on full tilt. thats how i found this question. Matt, alabama

Actually the correct answer is 1 in 610,756 - the formula presented above: 1 in 649,740. This is the exact answer. To understand better. You need a face card or ten as the first hole card. That's 20/52. The next hole card must be one of the other four cards of the same suit which make the royal straight, so 4/51. The three flop cards are 3/50, 2/49, and 1/48. The forumla is correct but the answer is INCORRECT and is as stated above. It can also be obtained using COMBIN(x,x) in Excel as follows: There are 4 Royal Flushes in the deck Each RF uses 5 cards There are combin(5,2)=10 ways to get 2-cards for one RF times 4 RF = 40 ways to get dealt 2 cards that are RF starters. There are combin(52,2)=1,326 2-card combinations in a deck 1,325 / 40 = 33 or 1 in 33 odds of getting dealt a 2-card RF starting hand. Now that leaves you with 3 cards you need to FLOP a Royal Flush and there are abviously 3 cards on the FLOP. There are 49 cards left in the deck so combin(49,3) tells us how many 3-card combinations there are which is 18,424. So take your 40 * 18,424 and that gives you the 1 in 610,756 odds of being dealt a 2-card RF starting hand and then flopping the Royal Flush.