vpFREE2 Forums

How rare is it?

#1

On a recent trip to Las Vegas, playing FPDW at Sunset Station, I was
dealt a royal (Hooray!). On the same trip, I also got the 4 ducks
after tossing all five initial cards. Both these events are somewhat
rare, but it got me to thinking, how rare would it be to get a royal
after tossing all five initial cards? This depends of course on which
game you're playing, but let's stick with FPDW.

Michael Shackleford indicates on his Wizard of Odds website (VP App5,
http://wizardofodds.com/videopoker/appendix5.html) that for FPDW the
probability for drawing a royal after holding 0 cards is -- zero. Of
course this is just a roundoff for a very low number, as it is possible
to "draw" a royal.

Has anyone gotten a royal after holding 0 cards? Just how rare is it?

Bill

#2

Bob Dancer in one of his classes stated that that
phenomenon accounts for one of his more or less 300
Royals. Does it not have the same odds as a dealt
Royal?
Alas, I have NEVER even seen, either.......

···

--- weharter <weharter@yahoo.com> wrote:

On a recent trip to Las Vegas, playing FPDW at
Sunset Station, I was
dealt a royal (Hooray!). On the same trip, I also
got the 4 ducks
after tossing all five initial cards. Both these
events are somewhat
rare, but it got me to thinking, how rare would it
be to get a royal
after tossing all five initial cards? This depends
of course on which
game you're playing, but let's stick with FPDW.

Michael Shackleford indicates on his Wizard of Odds
website (VP App5,
http://wizardofodds.com/videopoker/appendix5.html)
that for FPDW the
probability for drawing a royal after holding 0
cards is -- zero. Of
course this is just a roundoff for a very low
number, as it is possible
to "draw" a royal.

Has anyone gotten a royal after holding 0 cards?
Just how rare is it?

Bill

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#3

Joe Pucek wrote:

   Bob Dancer in one of his classes stated that that phenomenon
accounts for one of his more or less 300 Royals. Does it not have the
same odds as a dealt Royal?
Alas, I have NEVER even seen, either.......

A royal on a 5-card draw is less probable than a dealt royal, by FAR.

Consider that you have the potential for a dealt royal at every play.
However, the prospect of a royal on a 5-card draw is dependent upon
having tossed your hand in the first place. In a game like 9/6 Jacks,
a tosser happens only 3.25% of the time. (Note, however, than in FPDW
you discard almost 1 in 5 dealt hands ... stats from Frugal VP.)

While this might suggest that a royal on a 5-card draw is 1/30 as
likely as a dealt royal in 9/6 JB, the odds are a bit slighter than
that. Any time you happen to discard a T as part of those 5 cards,
you lessen the probability of a royal on the redraw.

If we simply assume a 1:30 ratio of 5-card draw royals to each dealt
royal, and roughly 1:16 for dealt royals to royals in general, you
arrive at an approximation that 1 of 480 Jacks royals are on the
re-deal after a tossed hand.

With deuces, it's much more likely that in tossing 5 cards you may
toss one or more cards that might otherwise be part of a royal (T-A),
since you never toss a hand entirely that has a face card in Jacks but
will do so in deuces (and, may in fact, drop 2 cards to a royal).

So, without thinking too hard about it, let's assume that the adjusted
ratio of redraw royals to dealt royals in FPDW is 1:10. With a dealt
to overall royal ratio of about 14, we're talking a much more probable
5-card draw royal frequency of 1 in 140 royals -- about 3 times that
of Jacks.

These numbers leave us to find that Bob's reported 5-card draw royal
experience roughly parallels expectation (although you'd look for
actual experience vs. something with a once in 10+ mil hand frequency
to vary all over the map).

Certainly I've beat the odds by hitting a 5-card draw royal, yet
having less than 2 mil hands under my belt -- it's a hit you simply
sit and stare at dumbly for more than a few seconds before crying out,
"Yeah!!".

- Harry

#4

Bill,

All of the numbers on Michael Shackleford's chart are a max of 6 decimal
places. The probability of a RF on the redraw is 0.000000497. Rounded to 6
decimal places it is 0.

5-card

P.S.

  I had a RF on a 5 card redraw Monday playing NSUD.

···

----------------------------------------------------------------------------
------------

Michael Shackleford indicates on his Wizard of Odds website (VP App5,
http://wizardofodds.com/videopoker/appendix5.html>
.com/videopoker/appendix5.html) that for FPDW the
probability for drawing a royal after holding 0 cards is -- zero. Of
course this is just a roundoff for a very low number, as it is possible
to "draw" a royal.

Has anyone gotten a royal after holding 0 cards? Just how rare is it?

Bill

[Non-text portions of this message have been removed]

#5

Has anyone gotten a royal after holding 0 cards? Just how rare is it?

···

--- In vpFREE@yahoogroups.com, "weharter" <weharter@...> wrote:

My wife had her first royal tossing all five cards at the Trump Boat
in East Chicago. She just had one last week on five play.

My one and only royal after tossing five was at Four Queens back in
the late 90's.

We've both had many royals dealt but only those two royals on the re-deal.

#6

..... Certainly I've beat the odds by hitting a 5-card draw royal, yet

having less than 2 mil hands under my belt -- it's a hit you simply
sit and stare at dumbly for more than a few seconds before crying out,
"Yeah!!".

- Harry

I agree with Harry that it's a much rarer event on games other than
deuces because you toss so many more initial hands in deuces.

After thinking about it a bit more, and after a bit more digging on the
Wizard of Odds website, I think the answer for FPDW is 1 in every
3,759,709 hands or about six times less often than a dealt royal.

For those wondering how I got these numbers, from the Wizard's return
table for FPDW
(http://wizardofodds.com/videopoker/tables/deuceswild.html), he
indicates there are 440,202,756 royal flush hands from a possible
19,933,230,517,200 FPDW hands (note that this is all possible
combinations of deal + draw hands and is one way to calculate the 45282
royal cycle for FPDW). On his previously referenced VP App 5 page, he
indicates that 1.2044% of all royals come after holding 0 cards, so
5,301,802 royals occur after holding 0 cards, or 1 in 3,759,709 hands.
Since a "dealt" royal occurs 1 in 649,740 hands, a "drawn" royal after
holding 0 cards occurs 5.8 times less frequently.

In the end, I agree with Harry. It's a hand that you probably sit
there dumbstruck about. Here's hoping that the next time someone gets
this elusive hand they have a camera with them because it's definitely
worth posting a picture!

Bill

#7

I have gotten two

···

--- In vpFREE@yahoogroups.com, "weharter" <weharter@...> wrote:

Has anyone gotten a royal after holding 0 cards? Just how rare is it?

Bill

#8

--- In vpFREE@yahoogroups.com, "deuceswild1000" <deuceswild1000@...>
wrote:

> Has anyone gotten a royal after holding 0 cards? Just how rare is it?
>
> Bill

The 4th royal of my short vp career was on the redraw playing NSUD.
My initial reaction was -- that's nice a wild royal on the redraw.
It took a moment or two for the reality to break my first
impression/assumption. However, I am still waiting for my first dealt
royal. My royal total is still in the single digits.

I saw a young lady get one last year on the FPDW progressive at the
Palms. Last year on a different trip I was playing once again at the
FPDW progressive at the Palms. The royal was almost up to $1200 when
the lady sitting on my left hit the royal. I stopped playing for a
minute to congratulate her and so did the gentleman on my right side.
Before I even played another hand the same gentleman hits a
sequential royal. I did not ask if it was the first hand he played
after starting back, but it could not have been more than 2 or 3 hands
after.

Variance, Variance, All is Variance

Chris

···

--- In vpFREE@yahoogroups.com, "weharter" <weharter@> wrote:

#9

In over 8 years of playing video poker almost daily (FPDW and NSUD), neither John nor I have ever had a royal on the redraw. However, we've had between us at least 7 or 8 dealt royals.
-- Steve in LV

#10

OK, here is my amateur mathematician attempt at figuring this out...

If (and the devil is always in the "if's") you discard all five cards
and if you don't discard any royal flush cards, the following should
apply:

There are 47 cards remaining in the deck. The odds of getting one of
the 20 royal flush cards on the first card is 20 out of 47 (20
divided by 47). On the second card, the suit is determined by the
first, so there are only 4 possible cards to draw, so the odds are 4
out of 46. Then, continuing along, 3/45, 2/44, and lastly, 1 out of
43. Multiplying these out, you get 0.000002608 as a probability, or 1
in 95871.1875, or a little better than once in 95,872 hands.

Also, if a royal flush card gets dicarded, the odds go up
proportionally. Discarding one would essentially cut the odds on the
first card from 20 out of 47 to 15/47, since one suit would no longer
be available to draw to, changing the odds to once in 127,828. If two
RF cards of different suits were discarded, it becomes 1 in 191,742.
Note discarding two cards of the same suit would not change the odds
from discarding one of that suit (you'd still have 15 cards to draw
to if you discard two of the same suit).

As has been mentioned, the 1 in 95,872 is only when all 5 cards are
discarded. I think someone said in FPDW that is only 20% of the time,
which would mean this would occur in something like once every
479,000 hands.

To me, even once in 479,000 seems high based on some of the
experiences relayed in the postings. However, when you add in that
your assumption is that only non-RF cards are discarded, I think the
number of hands that get thrown away with no non-RF cards is even
lower.

#11

"weharter" <weharter@...> wrote:

Has anyone gotten a royal after holding 0 cards? Just how rare is it?

In 20+ years of recreational play, it's happened to me once. I was
playing NSUD 5x Multi-Strike, and got it on the bottom line.

Stuart (RandomStu)
http://home.comcast.net/~sresnick2/fungames.htm

#12

There are 1,533,939 possible hands to be dealt when throwing away 5.
There are 0-4 possible Royals in that draw depending upon penalty
cards. In other words, if you tossed a jack of clubs, you are not
gonna get the royal in clubs, but you have 3 other siuts to make one
in. So, the odds are 1/1533939 to 4/1533939 (1/383484).

The sticky part of this question, is that it is hard to get 5 cards in
FPDW, without a 2,10, or a face card in the deal, and still have a
hand where the EV is to dump all cards. I could only find '389'45.
Thats 3,8,9 suited, 4 & 5 off suit. I bet the questioner either
dumped a hand where he should have held 4 to a straight, 3 to a SF, or
a garbage hand with a face card and lucked out.

···

--- In vpFREE@yahoogroups.com, "Stuart" <sresnick2@...> wrote:

"weharter" <weharter@> wrote:
> Has anyone gotten a royal after holding 0 cards? Just how rare is it

#13

it?
  I already posted that I have had two redealt royals. I forgot about
the wife. She has had one.

Also, I have had three dealt royals. One sequential (not dealt).

Wife has had two dealt royals, one of which was on a three liner.

So, it can happen even to the worst of us.

···

--- In vpFREE@yahoogroups.com, "Stuart" <sresnick2@...> wrote:

"weharter" <weharter@> wrote:
> Has anyone gotten a royal after holding 0 cards? Just how rare is

#14

In over 8 years of playing video poker almost daily (FPDW and NSUD),
neither John nor I have ever had a royal on the redraw. However,

we've had

between us at least 7 or 8 dealt royals.
-- Steve in LV

You're not alone. My wife and I have had close to 20 dealt royals and
neither one of us has had one on the draw either.

Dick

···

--- In vpFREE@yahoogroups.com, "Steve Del Nero" <artcontrol@...> wrote:

#15

I looked back through my royal flush records just now. I've had 308
total royal flushes (the majority of these on multi-line games). Of
these 308, only 2 were on a five card redraw. One was on a 50 play
NSUD game, and the other was on a single line FPDW game. I can
remember the slot attendant remarking on the single line royal: "Oh, it
dealt it too you", and I told her "no - look again!".

One other thing I noticed in looking through my records; I've only had
one royal with a one card hold. It was on a 50 play JOB game.

EE

···

--- In vpFREE@yahoogroups.com, "weharter" <weharter@...> wrote:

Has anyone gotten a royal after holding 0 cards? Just how rare is it?

#16

Here is the math as I see it.

IF 1) we are talking about a natural royal; and 2) discarding no
Aces, Kings, Queens, Jacks, or Tens before the draw, I believe the
odds are 1 in 383,485 calculated as follows:

1/( (20/47) * (4/46) * (3/45) * (2/44) * (1/43) )

or

1/( (20*4*3*2*1) / (47*46*45*44*43) )

Naturally, this assumes that the five cards discarded don't come back
on the redraw. I'm a VP newbie and can only assume that's the case
here.

The 20/47 establishes the suit for the next 4 draws. The 20 is the 5
cards (AKQJT) that participate in the royal times 4 suits. Once the
suit is established, it's 4/46, 3/45, 2/44, and 1/43.

If however, you discard the Ts, for example, the 20 becomes 16
because spades are no longer in play. That would change the odds of
a royal on the redraw to 1/479,356.

I've been a member for a few months and this is my first posting. I
would like to thank all of you for the great information you
provide. My wife and I will be going to Reno/Tahoe and then Vegas in
a couple of weeks and we will be using all this information to help
us decide where and what to play.

Joe

On a recent trip to Las Vegas, playing FPDW at Sunset Station, I

was

dealt a royal (Hooray!). On the same trip, I also got the 4 ducks
after tossing all five initial cards. Both these events are

somewhat

rare, but it got me to thinking, how rare would it be to get a

royal

after tossing all five initial cards? This depends of course on

which

game you're playing, but let's stick with FPDW.

Michael Shackleford indicates on his Wizard of Odds website (VP

App5,

http://wizardofodds.com/videopoker/appendix5.html) that for FPDW

the

probability for drawing a royal after holding 0 cards is -- zero.

Of

course this is just a roundoff for a very low number, as it is

possible

to "draw" a royal.

Has anyone gotten a royal after holding 0 cards? Just how rare is

it?

···

--- In vpFREE@yahoogroups.com, "weharter" <weharter@...> wrote:

Bill

#17

Then, continuing along, 3/45, 2/44, and lastly, 1 out of

43. Multiplying these out, you get 0.000002608 as a probability, or 1
in 95871.1875, or a little better than once in 95,872 hands.

You appear to have calculated the probability correctly, but the
inverse of that number is not 95871.1875, it is 383484.7501. This is
the same number that a later poster produced by dividing the total
number of possible combinations of 47 cards by 4, the number of
possible royals, assuming no royal cards were disdarded.

···

--- In vpFREE@yahoogroups.com, "jrsemifero" <jrsemifero@...> wrote:

#18

weharter <weharter@yahoo.com> wrote:
Has anyone gotten a royal after holding 0 cards? Just how rare is it?

Bill
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`
   
  Last summer at the South Point I did just that - and it was sequential! Held no cards, and up popped a 10 thru ace sequential royal in hearts! according to some of the math folks I asked it was a "lotto" type hit - somewhere over 300 million to one. I did get the $1000 in credits though......(-;
   
  Jigger

···

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#19

Skip calls a dealt jackpot after dumping 4 or 5 cards a "blind
squirrel", as in "even a blind squirrel can find this nut"

I usually hear them called "Free Willy"

Anybody else got a term for this?

···

--- In vpFREE@yahoogroups.com, "weharter" <weharter@...> wrote:

Has anyone gotten a royal after holding 0 cards? Just how rare is it?

Bill

#20

Skip calls a dealt jackpot after dumping 4 or 5 cards a "blind
squirrel", as in "even a blind squirrel can find this nut"

I usually hear them called "Free Willy"

Anybody else got a term for this?

> Has anyone gotten a royal after holding 0 cards? Just how rare is

it?

>
> Bill
>
I mention the result in 100 play .25 is $99,000 less. Only possible

term is Miss Fortune.

···

--- In vpFREE@yahoogroups.com, "William Canevari" <wcanevari@...> wrote:

--- In vpFREE@yahoogroups.com, "weharter" <weharter@> wrote: