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[QUOTE="Jack Daniels, post: 852246, member: 1954"]
Wow, several different posts all mixing in a lot of numbers. Maybe a short summary:
 
For the sake of this post, the question is really what are the odds of the board showing any royal flush. There are two answers to this depending on whether you are playing at the table and are given two cards or if you are just watching the table and don't have two cards. Obviously if you're in the hand and have two cards the numbers, then from your perspective the odds of it happening are slightly better because the pool of cards to choose from is two cards smaller.
 
So, also assuming that suit and order of arrival doesn't matter we have:
Just observing the table (with no cards exposed):
20/52*4/51*3/50*2/49*1/48 = 480/311,875,200 = 649,740 to 1
 
Player at the table holding two cards where none are 10-A:
20/50*4/49*3/48*2/47*1/46 = 480/254,251,200 = 529,690 to 1
 
So really, by sitting at the table and holding two cards that won't fit any royal flush make the odds of the board showing a royal flush about 18.5% better than just observing the table. These are the best chances. Add in any other criteria like order the cards come in or what suit and the odd get worse exponentially.
 
Heh, maybe this summary wasn't so short. ;)
[/QUOTE]

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