Question of the Day - 27 February 2021

At 2000 hands a day, wouldn't you expect to get a dealt royal more like once a year, not once every eight years?

Furthermore, isn't the number of possible ways a royal can be dealt 5!, or 5-factorial, which is 120? If you define "sequential" as 10JQKA (and not AKQJ10), then shouldn't you multiply 649,740 by 120 to get the actual number of hands you need to be dealt to get a dealt sequential royal? That's much more than four million! In actuality, it's 77,968,800, which divided by the aforementioned 730,000 hands per year, would take 106.8 years.

Now, I'm anything but a math wizard, but I suspect some of the parameters may have gotten mixed up here. If I've got this wrong, I'd be very curious to know what's the flaw in my math/reasoning. 

I have never been a video poker player and maybe I need to learn but I love my table games.  In any case, in the end, long run it is the same under today's rules the casino wins. But in the short run, we can dream and sometimes walk away up a little or a lot  If I wanted to learn Video Poker where is the place to start are Dancer's books basic enough for me I need to start slow (lol) But I would like to add a game that is not a table game

Once in the past ten years I was dealt a royal and once discarded all five cards and drew a royal. I’ve played four to five days a week. Thanks Bob Dancer and Liam Daily. I was playing at the high limit room at the Palms watching people sign tax forms and getting checks and hand pays thinking I must be doing something wrong. I searched video poker, found Bob’s site, attended a class at then the Silverton, purchased the software and turned my whole game around. I was questioning about quitting or limiting my play. I know that royals don’t make a winner. I may not be the best but I’m a lot better. I shudder now when I see someone discard a pair of high cards and keep three cards to a royal. But I used to do the same thing. And of course VPW led me to LVA, Anthony Curtis,Mike Shackelford and a bunch of others. Thanks Bob and R.I.P. Liam.

Those 2.6 M hands you speak of are every combination of hands irrespective of order of cards dealt.  Let me demonstrate as to Royals.
AKOJ10, 10JOKA, A10QKJ, A10KOJ, A10JKQ, A10QJK, ETC., ETC., ETC.

So each royal is the same in the probability calculations of hands and to calculate a sequential royal you would have to include every possible order of cards for a royal which gives you two sequential orders of a royal. In live poker and video poker both sequences of a sequential royal are valid.

Obviously you are not a poker player as this would be well known.

I was dealt a Royal once at a long gone bank of $1 machines right opposite Cleopatra's barge at Caesar's years ago that I attributed to rubbing Cleo's protuberances for luck before playing. I hit another dealt Royal on a five-play at the Gold Coast minutes before leaving for the airport to return home. Ah, the good old days!

Pre-COVID I used to play one night a week for about six hours.  In 2014 I hit a dealt royal.  The next week at a different casino I hit a dealt royal.  Guess that's it for my lifetime.

I’m going with the Wizard on this one. He knows his shit....

First, you are right, that the 2.6 million is the number of possible hands regardless of the order of the cards (the combination of 52 items chosen 5 at a time, or 52!/5!47!), so your probability is right.  However, I agree with Kevin that if you expect a dealt royal once every 649,740 hands and play 730,000 hands a year you should expect about one dealt royal per year, not one every 8 years.

For a sequential royal, you now need to look at the order of the cards dealt, so there are 52!/47! or 311,875,200 possible hands where order matters.  Exactly 8 of those hands are sequential royals, so the probability of a dealt sequential royal is one in 38,904,400, or about 10 times less likely than the 1 in 4 million probability that you quoted.  I suspect the 1 in 4 million is the probability of getting a sequential royal, period, which would include all of those royals where you are holding one to four cards in the right position.  However, your 55 year number is right!

The casinos define a sequential royal as 10JQKA. If AKQJ10 also counts, then that's a "reversible" royal. Many IGT machines have a reversible or sequential royal jackpot.

If you're talking about the odds of getting dealt a sequential royal, but you're really talking about a reversible royal, then 1 in 60 dealt royals are reversibles and the odds against would be (roughly) 39 million to one.

I have gotten only one dealt royal flush, about 15 years ago. And it was my very first royal flush ever. I was playing dimes so only $400 but still remember it. Can't count the number of times I've been dealt 4 to the royal. 

I'm not sure what happened here, but there were a number of mixed references and miscited sources in the original answer. Michael Shackleford didn't write it, so please don't ascribe the errors to him. Some information came off wizardofodds.com, causing the confusion. We're gonna shore up the answer a bit, but will leave all the comments so it's obvious that it's been amended. Sorry for the problem.

Anthony-
Thanks for fixing the QOD answer. 

But please note, the original answer DID say it was written (partially written?) by Mike.  I’m curious (as Mike might be) to know how that happened. 🤔

Someone saw that some of the information came from wizardofodds.com and assumed Shackleford wrote the whole answer. He wasn't involved at all. The answer was written by an LVA staffer. We do one of these every day, sometimes a mistake is made.

A "meta-fact" about dealt royals (if I remember correctly) is that about 1 out of every 16 royals will be a dealt one.  So, unless you play very little over the years, don't feel doomed to only getting 1 dealt royal during your entire life.  A lot of players have had 50 or 100 or more royals during their life, so they've probably had more than just 1 dealt royal.  I have had exactly 1 dealt royal so far in my life, and I've probably had close to 16 royals overall.  I got the dealt royal at the Pioneer Laughlin in the middle of the 2000s decade on a multi-game 25-cent machine.  I was playing Joker Wild at short coin (I didn't have enough bankroll to play max-coin).  With 2 coins in, I got dealt a diamond royal.  I asked the staff if they would take a picture of it and print it out in color so that I could have it as a memento, and they did so gladly.  The payout was $200.  Of course people have needled me for not having had 5 coins in, but I don't care.  I enjoyed my nice little hit!

AL - I did the same thing.  My very first trip to Vegas, I was playing 25c VP at Vegas World in early 90's.  I'd been in town less than 6 hours.  Playing 3-coins, hit a royal after drawing 3 cards.  Paid $187.50.  I've had several people ask if I was upset that I didn't play full coin and I said no, I was playing within my bankroll.  Last thing I needed to do was play above my head on my first ever trip, and first day, in Vegas.

I have since hit one more and that was full pay.  I don't play VP all that often.  More of a craps and poker player.

The way I explained it to people when playing Caribbean Stud and people were betting the bonus dollar for a shot at the jackpot (when it was really low) was this:

If you were to play one hand a minute, every minute of every day, you'd have to play for 1.2 years in order to expect to hit a dealt royal flush.