Odds on this please????

[utmt40]

Last night I was playing some Pot Limit Omaha for the first time ever. On my 9th hand I hit a royal flush then 5 hands later I hit another royal flush (same table). What are the odds on that happening for you math geniuses out there? Thanks.

[utmt40]

Anyone????

[Siegmund]

I place the odds of you holding a royal on a single hand of Omaha played to the river at 1 in 10829:

You need any of four sets of 5 specific cards, plus any 4 of the other 47, in a set of nine cards: 4 * 47C4 / 52C9 = 1 in 5156 2/3. You further need these split two in your hand and three on the board: 4C2 * 5C2 / 9C4 = 60/126.

Calculating the odds of the event you saw is tricky, and depends exactly what you define as "the event you saw."

One way to look at it is that someday you were going to see a royal flush, and that would start you wondering "how long will it be until I see another?": the chance of it being only a 5-hand wait or shorter are about 1 in 2166.

Another interpretation is "what is the chance of two royals in a given 14-hand period" -- but that's a bit unfair to ask, since a) it wouldn't occur to you to wonder about this until after you'd seen it happen and b) these may well be your only two royals in a thousand-hand period - and that wouldn't be so odd at all.

[utmt40]

Thanks for your reply!