Does anyone know if an "average number of games played per 1 stake
game" has ever been computed for a VP game? Jazbo's VP Volatility
article in the VPfree Bankroll Links states that if the session stake
is 320 bets, the median number of FPDW games that can be played is
16,000. The ratio is 50 to 1 in this case. But this is a median
value, not a mean, and refers only to 320 bet stakes and FPDW. So ...
I wonder what the mean average is over the long run? Does anyone know,
or know how it could be computed? I suppose it's possible it can't be
computed.
A Technical VP Question
Does anyone know if an "average number of games played per 1 stake
game" has ever been computed for a VP game? Jazbo's VP Volatility
article in the VPfree Bankroll Links states that if the session stake
is 320 bets, the median number of FPDW games that can be played is
16,000. The ratio is 50 to 1 in this case. But this is a median
value, not a mean, and refers only to 320 bet stakes and FPDW.
So ...
I wonder what the mean average is over the long run? Does anyone
know,
or know how it could be computed? I suppose it's possible it can't
be
computed.
The mean number of hands for a 1-unit stake in FPDW is infinite. With
a positive expectation game, some lucky devil will get to play forever
on a 1-unit stake. Once you have a single outcome that is infinite,
then the mean cannot be described by anything better than "infinite".
The question is more interesting for a negative expectation game like
JOB. My program, Dunbar's Risk Analyzer for Video Poker, reports
the "average number of hands played". If you set the "Trip Bankroll"
to 1, and let it rip for something like 1,000,000 trials, you can get a
value that ought to be ballpark accurate. (You also have to make the
number of hands large enough so that it always results in ruin. (6
million hands/trial is not enough, I found!)
The values I got for 9/6 JOB under the above settings were 213 the
first time, 239 the next, and 199 the last time. I think we can assume
the mean is somewhere around 220 plus or minus 30 or so. None of
us "expect" to last 200 plays on 1 unit, so you can see why the median
might be a more usueful indicator of what to expect from any given
bankroll!
I'll do a 100,000,000 trial overnight to see if I can zero in on the
real value for JOB.
--Dunbar
···
--- In vpFREE@yahoogroups.com, "brumar_lv" <brumar_lv@...> wrote:
I tried this by Using Winpoker, set on Autoplay, with a cash-in of 320
coins, then letting it run until the money was gone, or 100,000 hands
were played. The results are:
round 1: 610 hands-broke
round 2: 100,000 hands 3500 credits left
round 3: 240 hands-broke
round 4: 13430 hands-broke
round 5: 635 hands-broke
round 6: 100,000 hands 16315 credits left
round 7: 1384 hands-broke
round 8: 520 hands-broke
round 9: 90634 hands-broke
round 10: 1358 hands-broke
You asked about FPDW, which is apositive game, 100.76%. Results would
be different for a negative game, even NSUD at 99.7%
···
--- In vpFREE@yahoogroups.com, "brumar_lv" <brumar_lv@...> wrote:
Does anyone know if an "average number of games played per 1 stake
game" has ever been computed for a VP game? Jazbo's VP Volatility
article in the VPfree Bankroll Links states that if the session stake
is 320 bets, the median number of FPDW games that can be played is
16,000. The ratio is 50 to 1 in this case. But this is a median
value, not a mean, and refers only to 320 bet stakes and FPDW. So ...
I wonder what the mean average is over the long run? Does anyone know,
or know how it could be computed? I suppose it's possible it can't be
computed.
Here's the followup. I let Dunbar's Risk Analyzer-VP start with 1
unit 100 million times playing 9/6 JOB. The mean number of plays was
214. I think that's probably accurate to within a few hands.
Unless I'm missing a nuance, if you know the mean number of plays
from a 1-unit bank, then you would just multiply that by the bankroll
to get the mean number of plays for any bank. So, for a 320-unit
bank in JOB you would get a mean number of plays of 214*320 = 68,480,
compared to Jazbo's JOB median of around 12,500. As expected, the
mean is much higher than the median.
As bankroll increases, the mean becomes a smaller multiple of the
median. For a JOB bankroll of 1 unit, the median number of plays is
around 1.45. So the mean (214) is around 148 times as large as the
median. By the time you get to a 320-unit bankroll, the mean
is "only" around 5 times as large as the median.
--Dunbar
>
> Does anyone know if an "average number of games played per 1
stake
> game" has ever been computed for a VP game? Jazbo's VP
Volatility
> article in the VPfree Bankroll Links states that if the session
stake
> is 320 bets, the median number of FPDW games that can be played
is
> 16,000. The ratio is 50 to 1 in this case. But this is a median
> value, not a mean, and refers only to 320 bet stakes and FPDW.
So ...
> I wonder what the mean average is over the long run? Does anyone
know,
> or know how it could be computed? I suppose it's possible it
can't
be
> computed.
>The mean number of hands for a 1-unit stake in FPDW is infinite.
With
a positive expectation game, some lucky devil will get to play
forever
on a 1-unit stake. Once you have a single outcome that is
infinite,
then the mean cannot be described by anything better
than "infinite".
The question is more interesting for a negative expectation game
like
JOB. My program, Dunbar's Risk Analyzer for Video Poker, reports
the "average number of hands played". If you set the "Trip
Bankroll"
to 1, and let it rip for something like 1,000,000 trials, you can
get a
value that ought to be ballpark accurate. (You also have to make
the
number of hands large enough so that it always results in ruin. (6
million hands/trial is not enough, I found!)The values I got for 9/6 JOB under the above settings were 213 the
first time, 239 the next, and 199 the last time. I think we can
assume
the mean is somewhere around 220 plus or minus 30 or so. None of
us "expect" to last 200 plays on 1 unit, so you can see why the
median
might be a more usueful indicator of what to expect from any given
bankroll!I'll do a 100,000,000 trial overnight to see if I can zero in on
the
···
--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@...> wrote:
--- In vpFREE@yahoogroups.com, "brumar_lv" <brumar_lv@> wrote:
real value for JOB.--Dunbar
Thank you for running the test. 100,000,000 trials using your Risk
Analyzer is truly amazing! I'm surprised the "mean" is such a large
number. While most of the time it won't be anywhere close to 214, on
rare occasions it will be much much larger. So for 9/6JB, a negative
game, the mode is 1, the median about 1.45, and the mean is 214 ...
while for positive games like FPDW the mode is 1, the median also
about 1.45, and the mean infinite. It appears the median and
mean will eventually merge, or nearly merge, for negative games.
Here's the followup. I let Dunbar's Risk Analyzer-VP start with 1
unit 100 million times playing 9/6 JOB. The mean number of plays
was
214. I think that's probably accurate to within a few hands.
Unless I'm missing a nuance, if you know the mean number of plays
from a 1-unit bank, then you would just multiply that by the
bankroll
to get the mean number of plays for any bank. So, for a 320-unit
bank in JOB you would get a mean number of plays of 214*320 =
68,480,
compared to Jazbo's JOB median of around 12,500. As expected, the
mean is much higher than the median.As bankroll increases, the mean becomes a smaller multiple of the
median. For a JOB bankroll of 1 unit, the median number of plays
is
around 1.45. So the mean (214) is around 148 times as large as the
median. By the time you get to a 320-unit bankroll, the mean
is "only" around 5 times as large as the median.--Dunbar
>
> The mean number of hands for a 1-unit stake in FPDW is infinite.
With
> a positive expectation game, some lucky devil will get to play
forever
> on a 1-unit stake. Once you have a single outcome that is
infinite,
> then the mean cannot be described by anything better
than "infinite".
>
> The question is more interesting for a negative expectation game
like
> JOB. My program, Dunbar's Risk Analyzer for Video Poker, reports
> the "average number of hands played". If you set the "Trip
Bankroll"
> to 1, and let it rip for something like 1,000,000 trials, you can
get a
> value that ought to be ballpark accurate. (You also have to make
the
> number of hands large enough so that it always results in ruin.
(6
> million hands/trial is not enough, I found!)
>
> The values I got for 9/6 JOB under the above settings were 213
the
> first time, 239 the next, and 199 the last time. I think we can
assume
> the mean is somewhere around 220 plus or minus 30 or so. None of
> us "expect" to last 200 plays on 1 unit, so you can see why the
median
> might be a more usueful indicator of what to expect from any
given
···
--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@...> wrote:
> bankroll!
>
> I'll do a 100,000,000 trial overnight to see if I can zero in on
the
> real value for JOB.
>
> --Dunbar
>