Math Question Royal flush

[jay_shark]

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Not trying to hijack the thread but what are the odds of actually flopping a royal (of any suit)? A buddy flopped a royal at my home game and we've been trying to find what the odds were of him flopping it....not just hitting it by the river etc. I've searched alot online but can't find those odds, most just show what the odds are of hitting a royal by the river.

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In case you're interested in the math , and you should be [img]/images/graemlins/smile.gif[/img]

40/52c2/50c3 = 40/(24 010 000)~ 1/600250 .

There are 40 possible two hole cards that are suited and in the range 10,j,q,j,a . Once this player has his two hole cards fixed , there is only one unique flop that gives him a royal flush out of 50c3 possible flops .

So preflop we have 40/52c2 . Now we take this number and multiply it by 1/50c3 which is 40/52c2/50c3 =1/649740

[BruceZ]

[ QUOTE ]
[ QUOTE ]
Not trying to hijack the thread but what are the odds of actually flopping a royal (of any suit)? A buddy flopped a royal at my home game and we've been trying to find what the odds were of him flopping it....not just hitting it by the river etc. I've searched alot online but can't find those odds, most just show what the odds are of hitting a royal by the river.

[/ QUOTE ]

In case you're interested in the math , and you should be [img]/images/graemlins/smile.gif[/img]

40/52c2/50c3 = 40/(24 010 000)~ 1/600250 .

There are 40 possible two hole cards that are suited and in the range 10,j,q,j,a . Once this player has his two hole cards fixed , there is only one unique flop that gives him a royal flush out of 50c3 possible flops .

So preflop we have 40/52c2 . Now we take this number and multiply it by 1/50c3 which is 40/52c2/50c3 =1/600250

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Or just say 4 possible royals out of all possible 5 card combinations, so 4/C(52,5).

[AaronBrown]

The odds assume a perfectly shuffled deck. I recall a study of freak bridge hands in home games that discovered 1 in 3 of the credible reports occurred with a brand-new deck. Considering that decks are used far more than three times, it shows what happens when you start with a sorted deck and a sloppy shuffle.

Because hold'em doesn't sort the cards, this doesn't affect the odds of a royal flush much (it does affect the odds of things like either all or none of the cards on the previous board showing up in the next hand somewhere). However, if the deck is also used for games that do sort, like draw poker or especially bridge, you'll get more royal flushes than the probabilities suggest.