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Old 02-20-2008, 08:04 PM   #1
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Exact Odds of flopping a Royal.

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.
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Old 02-20-2008, 09:56 PM   #2
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Re: Exact Odds of flopping a Royal.

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.
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Old 02-20-2008, 11:07 PM   #3
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Re: Exact Odds of flopping a Royal.

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.
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Old 02-21-2008, 11:48 AM   #4
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Re: Exact Odds of flopping a Royal.

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.
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Old 02-25-2008, 11:16 AM   #5
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Re: Exact Odds of flopping a Royal.

Quote:
Originally Posted by EvilSteve View Post
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
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Old 08-27-2009, 08:12 PM   #6
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Re: Exact Odds of flopping a Royal.

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?
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Old 08-28-2009, 03:34 PM   #7
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Re: Exact Odds of flopping a Royal.

Quote:
Originally Posted by AtomBomb View Post
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.
http://forumserver.twoplustwo.com/25...-flush-326411/
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Old 05-03-2011, 08:25 AM   #8
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Re: Exact Odds of flopping a Royal.

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.

Last edited by iceberg222; 05-03-2011 at 08:31 AM.
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Old 05-03-2011, 07:16 PM   #9
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Re: Exact Odds of flopping a Royal.

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.
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Old 05-04-2011, 09:13 AM   #10
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Re: Exact Odds of flopping a Royal.

Quote:
Originally Posted by wykh View Post
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.
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Old 05-04-2011, 03:16 PM   #11
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Re: Exact Odds of flopping a Royal.

Here is my other flopped flush:

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Old 05-04-2011, 04:23 PM   #12
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Re: Exact Odds of flopping a Royal.

Quote:
Originally Posted by wykh View Post
Here is my other flopped flush:

Wow. Both diamonds. What are the odds of that?
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Old 05-05-2011, 01:07 AM   #13
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Re: Exact Odds of flopping a Royal.

Quote:
Originally Posted by AtomBomb View Post
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.
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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Old 05-05-2011, 08:02 AM   #14
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Re: Exact Odds of flopping a Royal.

Quote:
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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Old 05-06-2011, 04:07 AM   #15
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Re: Exact Odds of flopping a Royal.

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.
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