What are the odds of being dealt a sequential royal?

I recently was dealt a natural royal flush in sequential order. Can you tell me what the odds of that happening are?

When we do video poker calculations, we usually deal with combinations, in which the order of the cards doesn't matter. In a sequential royal, however, order matters so we have to calculate permutations.

There are 311,875,200 permutations of five cards taken five at a time (52 choices for first card times 51 choices for second times 50 times 49 time 48 choices for the fifth card). Four of those hands are ascending sequential royals, so the odds are 4 out of 311,875,200 or 1 out of 77,968,800. Those are also the odds of being dealt a descending sequential royal. The odds of being dealt any sequential royal are 8 out of 311,875,200 or 1 out of 38,984,400.

Congratulations! You experienced a very rare event.

Best of luck in and out of the casinos,
John

Send your slot and video poker questions to John Robison, Slot Expert, at slotexpert@comcast.net. Because of the volume of mail I receive, I regret that I can't reply to every question.