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What are the odds of being dealt a sequential royal?

9 November 2009

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.

John Robison

John Robison is an expert on slot machines and how to play them. John is a slot and video poker columnist and has written for many of gaming’s leading publications. He holds a master's degree in computer science from the prestigious Stevens Institute of Technology.

You may hear John give his slot and video poker tips live on The Good Times Show, hosted by Rudi Schiffer and Mike Schiffer, which is broadcast from Memphis on KXIQ 1180AM Friday afternoon from from 2PM to 5PM Central Time. John is on the show from 4:30 to 5. You can listen to archives of the show on the web anytime.

Books by John Robison:

The Slot Expert's Guide to Playing Slots
John Robison
John Robison is an expert on slot machines and how to play them. John is a slot and video poker columnist and has written for many of gaming’s leading publications. He holds a master's degree in computer science from the prestigious Stevens Institute of Technology.

You may hear John give his slot and video poker tips live on The Good Times Show, hosted by Rudi Schiffer and Mike Schiffer, which is broadcast from Memphis on KXIQ 1180AM Friday afternoon from from 2PM to 5PM Central Time. John is on the show from 4:30 to 5. You can listen to archives of the show on the web anytime.

Books by John Robison:

The Slot Expert's Guide to Playing Slots