dealt 4 cards to the royal flush

[Minn. Fatz]

fwiw most of the royals you complete in the proverbial long run are likely to be to 2- or 3-card draws, because it's that much more common to get 2 or 3 cards to the royal than 4.

[jetermacaw]

Was at Harrahs AC last week playing the only QQ machine left. Been playing a lot of TDB on this site, so started out playing 10 hand, caught four to the royal twice and of 20 hands I don't think I even got my bet money back. Switched to 5 hand JOB, and caught this.

[olds442jetaway]

super!

[wildman49]

I just got back from 4 hours of play and this time I had 7 times 4 off the deal to the royal never hit.   The odds of getting a royal dealt is 1 in 649,740 hands, so if a four card odds are  1 in 2,765  then why is it I am getting them dealt like a full house off the deal as them odds are 1 in 695? I play about 10 hands a minute while that is fast and yes i do make mistakes, the fact remains the odds don't change and don't lie. I understands 1 in 47to get the 5th card in  fact one day I took a deck and took out 4 to the royal shuffled each time and turned the top card it took 96 times before i got it. So not getting it over and over is understandable. Now the problem I have is why so many 4 to the royal off the deal when i should be getting a full house that many times and 4 to the royal much less.I need my luck to change soon!What Are the Odds of Being Dealt a 4-Card Royal?



31 July 2011


By John Robison













My wife and I have played video poker since 1985. When they changed
from coin in / coin out it seems like they don't hit like they used to.
Every visit now seems like I get dealt four to the royal over and
over and it never hits.

What are the odds of being dealt four to the royal?

I have been discussing this with the General Manager of Pinnacle
Entertainment and I am telling him that video poker seems just like
slots now. Always one off from the big jackpot.

Thanks for your time.

Mark


Dear Mark,
There are 940 ways to be dealt a 4-card royal. There are 4 suits.
There are 5 ways to choose the missing card. There are 47 cards
remaining in the deck that do not complete the royal. (4 x 5 x 47 =
940)
There are 2,598,960 ways to be dealt a 5-card hand, so your chances
are 940 in 2,598,960 or roughly 1 in 2,765 to be dealt a 4-card royal.
Your chances of drawing to a 4-card royal depends on your strategy.
Now, if the machines are Class III, changing from coins to tickets
shouldn't affect your chances of hitting any particular hand. The
machines are still dealing from a fair deck. If the machines are Class
II, then they are just slot machines.

Best of luck in and out of the casinos,

[rascal]

I had 6 to the Royal the other day at a casino. Great hand! But then.....I woke up.    

[DKStoner]

Billyjoe, that's wonderful!! Maybe someday I'll get the dealt RF I dream about

[onemoretry]

I just finished playing a few sessions of 25 play in this weeks contest. In two consecutive sessions, I was dealt 4 to the royal - I made zero royals!

[Minn. Fatz]

I have to admit I struggled with this one from a mathematical point of view for quite awhile. The obvious question seems to be, what is the probability of getting some number of dealt 4/RFs in a given number of hands? While there is clearly an answer to that, I'm not at all confident of the solution I come up with (a variant of which I'm using to decide whether to continue with the monthly challenge rather than, say, talking more with Mrs. Minn. or taking the dogs for another walk or, uh, doing the taxes).

But I have to conclude I think that's the wrong question. The real question is, how "streaky" can random events be -- assuming they're truly random?

Getting dealt four to a royal is rather less likely then flipping a fair coin and having it come up heads 11 times in a row; say 11.5 to be more exact. So getting that seven times is about as likely as having seven such streaks in a given coin-flipping session.

The likelihood of that happening at least once depends on how many times you flip your coin; just as the likelihood of getting more than the expected number of 4/RFs in a session depends on the number of hands in that session.

Now, if you indulge in a lot of coin-flipping (or VP) sessions, it becomes more and more likely that you are going to see 80, or 90, or 200 heads all in a row. Multiply that by the number of people who post on this forum...

...and it becomes practically certain that one of them, sometime, is going to get 7 4/RFs in a session; or almost any other unusual VP result you can think of.

Here's hoping I'm the lucky son of a gun who gets 2-3 dealt RFs in a row...

Good Mathematics!

[Vman96]

Streak calculations are harder.

Asking if you get 3 or more 4 to a Royal within a 2000 hand stretch within 40,000 hands total is more difficult.

Asking if you get 3 or more 4 to a Royal within 2000 hands period isn't nearly as hard. It's the binomial distribution. The answer to this is 0.0370166 or 1 in 27.015

[wildman49]

Another trip Sunday, after 8 hours of play 3 times 4 to the royal off the deal no luck. That's 14 times now in the last 3 trips. will keep posting till my ship comes in! lol