vpFREE2 Forums

RORBR goal

#1

There has been a lot of discussion about the possibility of playing forever and never going bust or hitting a royal, even though the ER sans RF is less than one.

Jonathan has argued that the probability of this happening is non-zero. I agree that the probability is non-zero, but it is so small that it's insignificant. For all practical purposes, it can be assumed to be zero, so I agree with Steve that it can be ignored.

It has been suggested that a simulation have an arbitrary cutoff point just in case this occurs. If you want to put such a cutoff in a simulation, I suggest setting it at 100,000,000 hands. That's HANDS, not sessions (realizations as Jonathan calls them). A session is defined as starting with a given bankroll and playing until we either lose that bankroll or hit a royal. Since an average session is at most about 25,000 hands, that's about 4,000 sessions.

Why did I pick that number? 100,000,000 is approximately the number of hands a true pro might play in a lifetime. At 1,000 hands per hour, that's 100,000 hours of play. Playing 40 hours a week, and taking two weeks off per year, that's 50 years of full time play. That's close enough to infinity for our purposes.

I have run many simulations of 10,000 sessions for each of 20 starting bankrolls and never had a case of the computer hanging in an infinite loop. (That's what would happen since I do not include a test for a never-ending session.) Note that 10,000 sessions represents at least 2.5 lifetimes of full time professional play.

While discussing all the theoretical mathematics, let's not lose sight of the true goal. So what is our true goal? I can't speak for the others, but for me it's to provide a practical risk number to a real player, and for that purpose two or three significant digits in the answer is sufficient. What player cares whether the RoR or the RORBR in a certain situation is 37% or 37.4592388103% ?

I have incorporated the Sorokin/jazbo method proposed by Steve into Optimum Video Poker 1.0.8a which was e-mailed out last night. I am confident that, although the answer may not be "exact", it's accurate enough for practical use by even the most serious pro.

Dan

···

--
Dan Paymar
Author of best selling book, "Video Poker - Optimum Play"
Editor/Publisher of VP newsletter "Video Poker Times"
Developer of VP analysis/trainer software "Optimum Video Poker"
Visit my web site at www.OptimumPlay.com

"Chance favors the prepared mind." -- Louis Pasteur

#2

There has been a lot of discussion about the possibility of playing
forever and never going bust or hitting a royal, even though the ER
sans RF is less than one.

Jonathan has argued that the probability of this happening is
non-zero. I agree that the probability is non-zero, but it is so
small that it's insignificant. For all practical purposes, it can be
assumed to be zero, so I agree with Steve that it can be ignored.

Just to clarify, my position isn't that this probability is so small that
it can be ignored, my position is that this probability approaches
zero as the number of hands played approaches infinity, and that
it is mathematically impossible to play forever without hitting a royal,
no matter how favorable the non-royal payoffs are made.

It has been suggested that a simulation have an arbitrary cutoff
point just in case this occurs. If you want to put such a cutoff in a
simulation, I suggest setting it at 100,000,000 hands. That's HANDS,
not sessions (realizations as Jonathan calls them). A session is
defined as starting with a given bankroll and playing until we either
lose that bankroll or hit a royal. Since an average session is at
most about 25,000 hands, that's about 4,000 sessions.

Why did I pick that number? 100,000,000 is approximately the number
of hands a true pro might play in a lifetime. At 1,000 hands per
hour, that's 100,000 hours of play. Playing 40 hours a week, and
taking two weeks off per year, that's 50 years of full time play.
That's close enough to infinity for our purposes.

I have run many simulations of 10,000 sessions for each of 20
starting bankrolls and never had a case of the computer hanging in an
infinite loop. (That's what would happen since I do not include a
test for a never-ending session.) Note that 10,000 sessions
represents at least 2.5 lifetimes of full time professional play.

While discussing all the theoretical mathematics, let's not lose
sight of the true goal. So what is our true goal? I can't speak for
the others, but for me it's to provide a practical risk number to a
real player, and for that purpose two or three significant digits in
the answer is sufficient. What player cares whether the RoR or the
RORBR in a certain situation is 37% or 37.4592388103% ?

I have incorporated the Sorokin/jazbo method proposed by Steve into
Optimum Video Poker 1.0.8a which was e-mailed out last night. I am
confident that, although the answer may not be "exact", it's accurate
enough for practical use by even the most serious pro.

I'm confident that it is in fact exact. I believe there are others here who
agree with my claim.

···

On Thursday 17 November 2005 09:22 am, Dan Paymar wrote:

#3

> I have incorporated the Sorokin/jazbo method proposed by Steve

into

> Optimum Video Poker 1.0.8a which was e-mailed out last night. I am
> confident that, although the answer may not be "exact", it's

accurate

> enough for practical use by even the most serious pro.
I'm confident that it is in fact exact. I believe there are others

here who

agree with my claim.

My understanding is that it is in fact exact, which is its advantage
over simulations.

R(N)=R(1)^N
(risk of losing N equals the risk of losing 1 multiplied by itself (N-
1) times)

R(1)=SUM[(prob of Win) x R(Win)]
(risk of losing 1 equals the sum (for each possible outcome) of the
probability of a Win times the risk of losing that Win)

···

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x...> wrote:

On Thursday 17 November 2005 09:22 am, Dan Paymar wrote: