Odds on flopping a Royal Flush?

Question

Playing tourney Omaha hi/lo split last night, I hit a Royal Flush on the flop, we were 9 handed at the time and I'm wondering if anyone out there knows the odds on that happening

Answer 1

In Omaha you must play exactly two cards from you hole cards

First you need the two royal cards in your hole cards. You don't want a 3rd as it blocks the royal.

You could technically have two royal draws in your 4 cards

First look at the case of a single 2 royal in you hand and other two card are not blockers or a draw to another nut flush.

combin(52,4) = 27,0725 possible starting hole cards
combin(5,2) = 10 ways to get 2 of the nut flush
combin(4,1) = 4 suite
combin(47,2) = 1081 other card combination that do not block your royal

Royal hole card draw chance = 8% (higher than I thought it would be)

Now need exactly one board to make the royal on the flop
combin(48,3) = 17,296
Flop a royal = 0.006%

Hole x flop odd = 0.001% = 1 / 108,290 royal flop in Omaha

The chance of two royal draws is 0.44% and then you double the flop odds for a total of 1 / 1,951,025

Flop a royal in hole'em = 1 / 649,740

Answer 2

The number of different poker hands is '52 over 5' which is 2598960. Four of them are royal flushes, so the chance of a poker hand to be a royal flush is 649740. Because you have four holes, you can make six different hands, so the odds of this happening are about equal to 6 in 649740, so 1 in 108290.