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Old Apr 19, 2004, 6:16am   #1
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Default Royal Flush Odds In Omaha

Maybe some of you math wizards can help me out. I've been playing Omaha for only about two weeks now. Yet I've already had three Royal Flushes, in what I would estimate to be roughly 3,000 hands played. So am I like a statistical anomelie or is this pretty common?

My latest one (they're fun to look at...admit it )



Thanks

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Old Apr 19, 2004, 7:48am   #2
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Ok, I'm not 100% confident on these calculations, but I'm coming up with a Royal Flush will hit once out of every 43,316 hands. Here's the math:

For your starting hand you must hold two and only two of the five cards that make up a royal flush. There are 5 x 4 x 47 x 46 possible hands that meet this condition. There are 52 x 51 x 50 x 49 total possible starting hands. There are six combinations of ways you can receive your hand that meets this situation (YYnn YnYn YnnY nYYn nYnY nnYY where Y is a card towards the royal flush). So the odds of getting a starting hand that can make a royal flush are (6 x 5 x 4 x 47 x 46) / (52 x 51 x 50 x 49) = ~6.65497E-3.

The board must contain the remaining three cards along with two additional cards. There are 3 x 2 x 1 x 45 x 44 possible boards that meet this condtion. There are 48 x 47 x 46 x 45 x 44 possible boards. There are ten combinations of boards that meet this situation (YYYnn YYnYn YYnnY YnYYn YnYnY YnnYY nYYYn nYYnY nYnYY nnYYY). The odds of the board meeting the situation are (10 x 3 x 2 x 1 x 45 x 44) / (48 x 47 x 46 x 45 x 44) = ~5.78168E-5.

Therefore the overall odds are 6.65497E-3 x 5.78168E-5 = 2.30863E-5. Which translates to 1:43316. Irregardless if I calculated the odds right or not, I would say that your three Royals are a statistical anomelie.
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Old Apr 19, 2004, 11:52am   #3
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Yeah, I've played a lot of Omaha in the past month, and I haven't got a royal flush so far. Those 3 in the past 30,000 hands are simply amazing.
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Old Apr 19, 2004, 12:09pm   #4
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I have played a lot of omaha and during the last month I have seen lots and lots of straightflushes but only one royal. That is also the only royal I have seen so far playing online so having three would mean extreme luck
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Old Dec 07, 2005, 1:20am   #5
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Since there are only four possible royal flushes, and the number of
possible hands is 52*51*50*49*48= 311875200, the odds of
making a royal flush are 1 in 77968800. Of course with such low
odds, casinos can afford to have promotions where hitting a
royal flush. An example of this would be Noble Poker offering
$100 million for a Spades Royal Flush that is made at the
final table of some tournament being held in 2006. I think this
is some freeroll event.
http://www.professional-poker.com/ne...oyal-flush.htm
to find out more. Since the odds are virtually nil, the odds
of Noble Poker not paying out this amount are virtually 100%.
http://noblepoker.com/100m_tournament.html
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Old Nov 23, 2008, 5:14pm   #6
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Default my royal flush

I hit a royal flush on my 4th hand of ever playing Omaha hold em on Full Tilt

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Old Nov 27, 2008, 9:24pm   #7
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OMG this is officially the most incredible ghost bump - both interms of age and irrelevancy!

Edit - the math in this thread (see Peenutz's post) makes me LOL.
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Old Nov 28, 2008, 9:48am   #8
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The math is indeed awesome.

Considering how few straight flushes i've made in my life (probably well under 20), I find it quite amazing that i've made 5 royals, 3 online in NLHE, 1 live in NLHE and 1 live in 5CD. I guess they're more common than other straight flushes due to players playing high cards more than low?
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Old Nov 28, 2008, 10:32am   #9
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Quote:
Originally Posted by TWLLM View Post
OMG this is officially the most incredible ghost bump - both interms of age and irrelevancy!

Edit - the math in this thread (see Peenutz's post) makes me LOL.
+1, wowowow.
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Old Dec 02, 2008, 5:49pm   #10
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Quote:
Originally Posted by TWLLM View Post
OMG this is officially the most incredible ghost bump - both interms of age and irrelevancy!

Edit - the math in this thread (see Peenutz's post) makes me LOL.

I loled
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