The probability of hitting two royal flushes in a row: If we use the draw-based probability (1 in 40,391 per hand), that’s roughly 1 in 1.63 billion. If we use the dealt-only probability (1 in 649,740 per hand), that’s about 1 in 422 billion. Has Bob Dancer or other VP players in your orbit ever gotten consecutive royal flushes?
[Editor's Note: We queried four veteran video poker players and one said, "I've never even heard of that happening." Another: "Not me or anyone I've played with. I've had other 'streaks,' hitting multiple full houses and even 4-of-a kinds in rapid succession, but never two royals." A third said, "No." The fourth, Bob Dancer himself, wrote the following, which we appreciate, as we always do with his answers.]
Assuming we’re talking about single-line games, my personal record for back-to-back royals is 21 hands apart. I was playing a dollar machine at a casino where the display showed slot-club-points accumulated since the last time the card was pulled. This was a one-point-per-dollar-bet casino, and the display read 105 points. On that day, both of the royals happened to be in diamonds.
I haven’t heard about any player actually hitting back-to-backers and that surprises me. For years, I taught classes and sometimes attendees shared their greatest video poker accomplishments, often with a photo and explanation. “I know I should never have been playing that pay schedule, but I hit the royal and am proud of it anyway.” Surely back-to-backers would be something to share.
The odds against this happening, however, are nowhere near the numbers included in your question. The 1.6 billion-to-one odds you presented are appropriate for the question of: “What are the odds of hitting royal flushes on each of the next two hands I play.” That’s a very different question from: “In your lifetime of play, has this ever happened?”
My best guess is that I’ve hit between 2,000 and 2,500 royal flushes lifetime, but that includes on Triple Play through Hundred Play machines where they show up much more frequently and sometimes more than one per deal. For the sake of having a number to use, let’s assume I’ve hit 500 single-line royals.
As a professional who has averaged more than 20 hours a week of play for more than 30 years, I’ve hit more royals than most other players. But I know other players who’ve played more years and more hands per week than I have, so surely each of them has connected on more royals than I have.
For each of those 500 times, I’ve had a 1-in-40,000 chance to hit another royal on the very next hand. That means for me, as a first approximation, lifetime I’ve had about a 1-in-800 chance of getting single-line back-to-backers. That’s nowhere near 1-in-1.6 billion. I’m still playing, so maybe I’ll accomplish this some day.
I assume that nationwide, more than 40,000 royals are hit every week. If true, that means there will be back-to-backers somewhere across the country more than once a week! Hitting 40,000 royals a week nationwide is just a wild-ass guess. It could be 40,000 per day for all I know.
If we aren’t limiting the discussion to single-line games, I was playing 10-cent Hundred Play 8-5 Bonus Poker years ago at the Silverton and on back-to-back deals received royals. I didn’t think it was all that impressive at the time. I still don’t, so I never wrote about it before now.
