I had 3 royals last year, actually, my first three ever. The first
one was on a gambling ship- The St. Tropez on 25c DDB, the second,
at The Palms on the 25c JOB sequential and the third at The Barbary
Coast on 25c BP. All three were gotten with the 1st $20 I put in
each machine. I see that there are a lot of math whizzes here at
vpFree. What are the chances of my next Royal happening the same way?
Steve
Steve,
It depends on a number of factors. The biggest factor, perhaps, is
how long you play at a machine before switching. To take an extreme
example, if you always switch machines after losing $20, you will
hit 100% of your future Royals on your first $20 for that machine.
The longer you tend to play at a machine before switching, the less
likely you will be to hit your next Royal on your first $20. Again,
to take an extreme example, if you tend to insert a new $20 into the
same machine each time you run out of credits and repeat the process
over and over for several hours, it is more likely that your next
Royal will be hit during one of the $20's that is subsequent to your
first $20.
Slowpoke
All three were gotten with the 1st $20 I put in
each machine. I see that there are a lot of math whizzes here at
vpFree. What are the chances of my next Royal happening the same
way?
Steve
From Jazbo Burn's article on Volatility (accessible from the vpFREE
Links), the half-life for 16 bets ($20 @$1.25 per bet) playing JoB
is 133.67 hands (see also the half-life results for other games).
This is the MEDIAN, so you have a 50-50 chance of playing through
133.67 hands without going bust. The question now is: what is the
chance of hitting a royal during the times that you survive this
133.67 hands?
Since the royal cycle for JoB is 40390.55 hands,
Probability (at least one royal in 133.67 hands)
= 1 Probability (no royal in 133.67 hands)
= 1 (40389.55/40390.55)^133.67
=0.003304, or approximately 1 in 303.
Please note that this 1 in 303 figure is the chance of hitting one
or more royals with the first $20, but the chance of hitting two or
more royals with this allotted $20 is negligibly small.
L. Wluiki
*************************************************************
--- In vpFREE@yahoogroups.com, "effellay216" <stpshaw@a...> wrote:
I had 3 royals last year, actually, my first three ever. The first
one was on a gambling ship- The St. Tropez on 25c DDB, the second,
at The Palms on the 25c JOB sequential and the third at The
Barbary
Coast on 25c BP. All three were gotten with the 1st $20 I put in
each machine. I see that there are a lot of math whizzes here at
vpFree. What are the chances of my next Royal happening the same
way?
Steve
This seems like a pretty decent approximation of the exact value for
the problem as you've interpreted it. In my mind, having taken only a
couple of minutes to look at this, I'm wonder if the MEAN time to a
"bust" (were it available), rather than MEDIAN, might not provide a
better approximation.
MEDIAN does give you the half/half point. But a probability
calculation wants a weighted average, or mean.
- Harry
lwluiki wrote:
From Jazbo Burn's article on Volatility (accessible from the vpFREE
Links), the half-life for 16 bets ($20 @$1.25 per bet) playing JoB
is 133.67 hands (see also the half-life results for other games).
This is the MEDIAN, so you have a 50-50 chance of playing through
133.67 hands without going bust. The question now is: what is the
chance of hitting a royal during the times that you survive this
133.67 hands?Since the royal cycle for JoB is 40390.55 hands,
Probability (at least one royal in 133.67 hands)
= 1 Probability (no royal in 133.67 hands)
= 1 (40389.55/40390.55)^133.67
=0.003304, or approximately 1 in 303.
I see your point Harry. Do you have a figure for the MEAN time? I
thought about dividing the MEDIAN time by natural log (2) to get the
mean but wasn't sure how to interpret this. We can also get the mean
by integrating Jazbo's graph.
BTW, the part about hitting more than one royal; this "almost"
happened to me last December. I hit a royal on my first c-note
playing 9-6-4700 JoB, then 7 hands later, was dealt a suited TJQK
and drew the 9 for a straight flush. Two hours (may be 500 hands)
later, I hit a royal playing NSU, and two days later, another one
playing FPDW. That was after a royal dry spell lasting for 160,000+
hands.
I haven't played since, hoping that Dame Fortune might get forgetful
(LOL).
L. Wluiki
*********************************************************************
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...>
wrote:
This seems like a pretty decent approximation of the exact value
for
the problem as you've interpreted it. In my mind, having taken
only a
couple of minutes to look at this, I'm wonder if the MEAN time to a
"bust" (were it available), rather than MEDIAN, might not provide a
better approximation.MEDIAN does give you the half/half point. But a probability
calculation wants a weighted average, or mean.- Harry
lwluiki wrote:
> From Jazbo Burn's article on Volatility (accessible from the
vpFREE
> Links), the half-life for 16 bets ($20 @$1.25 per bet) playing
JoB
> is 133.67 hands (see also the half-life results for other
games).
> This is the MEDIAN, so you have a 50-50 chance of playing
through
> 133.67 hands without going bust. The question now is: what is
the
> chance of hitting a royal during the times that you survive this
> 133.67 hands?
>
> Since the royal cycle for JoB is 40390.55 hands,
> Probability (at least one royal in 133.67 hands)
> = 1 Probability (no royal in 133.67 hands)
> = 1 (40389.55/40390.55)^133.67
> =0.003304, or approximately 1 in 303.
lwluiki wrote:
I see your point Harry. Do you have a figure for the MEAN time? I
thought about dividing the MEDIAN time by natural log (2) to get the
mean but wasn't sure how to interpret this. We can also get the mean
by integrating Jazbo's graph.
I haven't spent a whole lot more time on this than I had as of last
night. (Think in terms of fraction of an hour, or less 
I know of no workup of a "mean time to failure" for video poker ;).
And, even having benefited now from a cup of coffee, I've found no
mental inspiration that's turned me onto an easy way at it.
------
< Warning: Tedious "Half Life" discussion follows ... skip to next
section or, for that matter, the rest of this post >
Concerning application of natural logs: I assume this idea was
suggested by one of two things: (1) That "short term failure" is
dependent upon not having hit sufficient frequently occurring hands
and therefore might have a natural distribution, or (2) Jazbo's naming
his concept "Half Life".
In the first case, I believe that frequently occuring hands do achieve
a natural distribution within a tangible amount of time, but the time
involved in Jazbo's Half Life concept is far too short to apply here.
As far as the "Half Life" name, I'd have preferred he'd used something
else. The half life concept is a reference to substances that
experience natural decay. They lose half their substance over a
constant period of time, e.g. an element with a 5 minute half life
would be reduced to half it's original mass after 5 minutes, to a
quarter by 10 minutes, an eighth after 15 minutes, etc. This rate of
decay can be quantified in terms of natural logarithms.
Jazbo's name suggests his concept describes the number of hands before
a given bankroll might be halved, not depleted.
At any rate, for his concept, natural logs don't apply.
------
Manually integrating the graph might well be the most expediant
solution if you were driven to solve the original question posed.
That's a fun task for a rainy Saturday afternoon of which I haven't
had the pleasure since my freshman calculus course -- and one which I
don't intend to repeat ... might as well set me down at a pick'em
machine for an 8 hr. session (no offense intended to the pick'em
freaks out there).
- Harry
A couple of years ago, I also noticed this seemingly strange phenomena. I
can honestly say about half my "jackpots" (whether they be RF's or other big
hands like 4A/w2 on DDB) have occurred within the first 20 minutes or so
after sitting down at the machine. I've had a couple occur in the first 5
minutes of play.
But when I checked my notes and did some guesstimating on the number of
hands played in each session, it pretty much works out my royals average
every 40K hands. Same thing for the other big hands and their "expected hit
rates". So I guess nothing unusual is happening after all.
carlos
PS I wonder how many players have experienced this and tell themselves, "If
I don't hit something in the first half hour, that means I'm not going to.
I may as well go home." ?
-----Original Message-----
From: Harry Porter [mailto:harry.por…@…net]
Sent: Saturday, February 21, 2004 10:11 PM
To: vpFREE@yahoogroups.com
Subject: [vpFREE] Re: Royals (I came up with: 1 in 303)
This seems like a pretty decent approximation of the exact value for
the problem as you've interpreted it...[etc]