What are the exact odds or percentage of flopping a Royal Flush in Hold'em?
Flop? Flop and Turn? Flop Turn and River?

And what kind of formula can you use for figuring it out?

Any of you Math Geeks want to take on this question.

I dont know, but I flopped one about a month ago, not only was it my first royal, but I flopped that shizzzz

I did get one once on the river in omaha, though.

Flopping a royal flush:

You have to start out with either AKs, AQs, AJs, ATs, KQs, KJs, KTs, QJs, QTs, or JTs. For each of these 10 starting hands, there are 4 two card combinations that give you that hand (one for each suit). This is 40 two card combinations out of 52c2 = 1326 possible two card combinations. So 40/1326 = about a 3% chance of starting with a hand that could flop a royal flush.

Then the flop has to come perfect, you need to hit the unique three card combination that matches up with your starting hand to make a royal flush. For a given starting hand, there are 50c3 = 19,600 possible flops, and only 1 of those flops gives you a royal flush. So overall the probability of flopping a royal flush is (40/1326) * (1/19600) = 40 / 25,989,600 = 1 / 649,740. Play 1 million hands of poker (never folding any of those hands preflop however) and you'll probably flop a royal flush once or twice.

Actually I made it more complicated than it needed to be. Consider the 3 flop cards and your 2 hole cards all together, there are only 4 combinations of 5 cards that make a royal flush (one for each suit). There are 52c5 = 2,598,960 combinations of 5 cards, so the probability of flopping a royal flush is 4 / 2,598,960 = 1 / 649,740.

This is of course correct if we calculate the probability of being dealt two cards to a royal flush and then flopping the three cards we need to complete the hand.

However, if we want to know the chance of flopping a royal flush conditional on being dealt a possible royal flush hand (two suited broadway cards), the probability is instead:

1/(50c3) = 1/19,600

i flopped a royal last night and got paid off three streets, including a river shove (he thought i was bruffing). and now you know?

http://forumserver.twoplustwo.com/25...-flush-326411/

You will flop a royal flush 1 out of 649740 times before knowing what 2 cards you hold, and 1 out of 19600 times after seeing your cards and knowing that it is possible to flop a royal flush.

Here is a royal I flopped not so long ago. I have actually flopped 2 in my limited poker career.

This one the cards also came out in order. Would I be right in saying the chances of that are (4)*(1/52*1/51*1/50*1/49*1/48) = 1/77968800?



This was on FT at the end of a long tourney. One player had raised preflop and I called. When the flop came down I checked and the only other player folded without even checking. Seems odd when he could have checked for free. I finished the MTT in second place.

This is correct if you "assign" the direction from right to left on your cards and the flop. But isn't this observation a little result oriented?
The chance to flop a RF in any order is 120 times that as said in previous posts.
If you want to do the calculation starting from the probability of each permutation which is 1/52*1/51*1/50*1/49*1/48 you multiply by 4 due the possible suits, by 10 = C(5,2) since you can have any 2 of the possible holecards, by 2 since your holecards will appear in 2 ways from right to left and finally by 6 due to the number of ways the flop cards can be ordered from right to left. Don't know if it's easier that way though.

Here is my other flopped flush:

Wow. Both diamonds. What are the odds of that?

Why are you asking for math geeks? Do you mean those top 1% who know well the math that is required to understand exactly how I Pods work? Why them? They are busy working on things that stupid people want but have no hope of understanding. The question you asked can be answered by 13 year olds with 95 IQs who have spent a few days studying elementary probability.

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Just because you wrote an extremely dry and boring book doesn't mean you get to berate people are aren't familiar with elementary statistics. Or maybe it does... WP sir.

What he's saying is: Go study it for a few days, because it's honestly not that hard.

I agree btw.

50/50..either you flop it or you dont

What I oibject to is trhe phrase "math geeks". The fact that they exist shouldn't give people the excuse to not learn stuff far simpler than what math geeks know.

It appears to me that David's threshold for "math geekness" is greater than the OP's. If so, I'd wager that David's personal threshold for one to qualify as a "math geek" is higher than the threshold of most people. I'd further wager that any person's threshold for what qualifies someone as a "math geek" is at least partially a function of their own knowledge of mathematics.

Flops like AKQ, AQK, KQA etc. all count as one combination?

Yes. There are 3! = 6 permutations or orderings of that combination. We could use permutations, in which case there would be PERMUT(50,3) = 50*49*48 = 117600 flops counting order, and the probability would be 6/117600 which is the same as 1/19600. If you use permutations, use them in both numerator and denominator. Same if you use combinations.

you're too smart ><

Top 1% of what? if were going to talk math and statistics here. Yeah, think about it. Maybe you ought incorporate a little logic with your response. Are you that arrogant and ignorant all at the same time to suggest that if you know enough math then that means you will automatically know how an iPod works? What about physics, chemistry, logic, (mechanical, industrial, computer, software) engineering, etc. How much of that do you know? Why dont you try and explain to the masses how knowing enough math will enable you to understand exactly how an ipod works? I know Id love to hear it.

PS - You might wanna try teaching junior high math sometime and realize how many kids cant even multiply. Id love to know how you pulled 13 year olds with a 95 IQ out of the thin air. Did you do all the research and grind out all the statistics to arrive at those #'s?

Is "Math Geek" derogatory? If so, are you inferior to somebody you speak of in a derogatory manner? It's kind of ironic that without Mathematics we'd never have the pleasure of reading your post.

To answer the poorly worded question:

4/52c5. Here - I'll put it in terms of what you might understand ... hopefully you're mathematically inclined enough to understand this.

Here's the odds 1 to 649,739
Here's the probability 1/649,740 or 0.000153908%

Hope that's useful for what you're doing.

Have any of you "Math Geeks" ever considered the possibility that this user or any other that aren’t as mathematically inclined as you, possess talents that neither you nor I nor the overwhelming majority don’t? Maybe they are a musician that creates and performs and their music is being played on YOUR iPod. If there were no musicians we wouldn’t need an iPod to begin with. So just continue to berate others because you can comprehend math on a level higher than they can. I’m sure you’ll make a lot of friends with that philosophy. There IS a life beyond math and i propose you search it out.