vpFREE2 Forums

Probablility of a Royal on a 5-card re-draw?

#1

Thanks SB! Great point about the difference if a 10 was discarded from the
original 5 cards. The game in the foto was Double Bonus, so we can assume
with proper play there was no high card in the original hand, so the only
question would be if a Ten was discarded or not.

I added your info to the below, if the rest is correct perhaps the royal
flush draw probabilities could be added or updated in the VP_Free FAQ section.

Royal Flush Draw Probabilities:
Holding 4 cards to a Royal: 1 in 47
Holding 3 cards to a Royal: 1 in 1,081
Holding 2 cards to a Royal: 1 in 16, 215
Holding 1 card to a Royal: 1 in 178,365
Re-drawing all 5 cards: 1 in 383,485 (if no Ten thru Ace in original
5 cards)
Re-drawing all 5 cards: 1 in 511,313 (if there was a Ten in original
5 cards)
Dealt royal: 1 in 649,739
Dealt Sequential royal: 1 in 38,984,340

Cheers, Dave

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Subj: [vpFREE_Reno] Re: Probablility of a Royal on a 5-card re-draw? Date:
11/27/2008 5:22:06 P.M. Pacific Standard Time From: _kobj21@aol.com_
(mailto:kob…@…com) (mailto:…@…com) To:
_vpFREE_Reno@yahoogroups.com_ (mailto:vpFREE_R…@…com) (aolmsg://03003f48/inethdr/2)

There are 1,533,939 ways to select 5 cards out of the 47 remaining on
the redraw. Assuming one of the cards thrown out wasn't a 10 then the
odds of getting the Royal are 1 in 383,485. This of course is provided
that you are playing a game where it is proper to hold a high card and
didn't make any mistakes in the discard. If a 10 was discarded then it
goes up to 1 in 511,313. Not quite as rare as the dealt Royal but
still up there.

SB

.

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AOL.com.
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#2

vpFREE has links to 5 card's site which lists most VP odds:

http://www.videopokerhelp.net/odds.htm

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On 28 Nov 2008 at 14:08, davensjose@aol.com wrote:

... I added your info to the below, if the rest is correct perhaps
the royal flush draw probabilities could be added or updated
in the VP_Free FAQ section ...

#3

Thanks SB! Great point about the difference if a 10 was discarded

from the

original 5 cards. The game in the foto was Double Bonus, so we

can assume

with proper play there was no high card in the original hand, so

the only

question would be if a Ten was discarded or not.

I added your info to the below, if the rest is correct perhaps the

royal

flush draw probabilities could be added or updated in the VP_Free

FAQ section.

Royal Flush Draw Probabilities:
Holding 4 cards to a Royal: 1 in 47
Holding 3 cards to a Royal: 1 in 1,081
Holding 2 cards to a Royal: 1 in 16, 215
Holding 1 card to a Royal: 1 in 178,365
Re-drawing all 5 cards: 1 in 383,485 (if no Ten thru Ace

in original

5 cards)
Re-drawing all 5 cards: 1 in 511,313 (if there was a Ten

in original

5 cards)
Dealt royal: 1 in 649,739
Dealt Sequential royal: 1 in 38,984,340

Cheers, Dave

On any particular tossed hand you can figure the probalities this
way, but actually getting a re-draw royal is much rarer than this
because you have to consider how often you toss all 5 cards from the
dealt hand where none of the discards affect a royal possibility.

The Wizard of Odds has a table for FPDW that shows the probabilities
of getting any hand based on the number of cards held. For FPDW he
indicates that the probability of a re-draw royal when holding no
cards is 0. This is of course due to rounding. For all the other
probabilites he goes out to six decimal places, so I would guess this
means that the probability of a re-draw royal in this case is no more
than .00000049999... as a .0000005 would most likely be rounded up
to .000001. If this is correct then it means a re-draw royal occurs
1 in every 2,000,000 dealt hands for FPDW.

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--- In vpFREE_Reno@yahoogroups.com, davensjose@... wrote: