Odds on Natural Royal Flush in Video Poker
Written March 8, 2008 by Jack Jones
You could almost bet someone a large amount that they would never be dealt a natural royal flush on a video poker machine and feel pretty safe that you are never going to have to pay up.
With a 52-card deck there are 2,598,960 possible hands, and what you’re asking for is that one of them to be dealt straight away. Those are long, tall odds. And what about all that time and money spent chasing down a natural Royal flush in hearts? Well, here’s the barnyard math.
At a buck and a quarter a pop, and a house edge of let’s say 4% — I m guessing you won’t play every hand perfectly — you’ll end up losing $129,948 to win $100,000. Plus, playing three hands a minute, it could take you over 600 days playing 24/7 before a natural royal flush in hearts appears. But why be extreme? Using ordinary 8-hour days, it would take just under 5 years to play out the bet (no time off for wedding anniversaries, holidays, sick leave, birthdays or any of that foolishness), and even then it’s not guaranteed, you know, just because the odds say it’s likely. Hmmm. In the same period, the kid that flips burgers, mows lawns and heaves shingles would reel in a cool $147,000. Again, Hmmm.
And yet your Brother’s proposition isn’t even close to being as impenetrable as the one a reader previously wrote in about: a casino offering a poker machine with a payout of $1,000,000 for a sequential royal flush.
For an ascending royal flush in any suit, the odds are 77,968,800. If it is suit specific, such as being in hearts, then the chances are one in 311,875,200.