Half-life and survivability

[Peter]

Hi!

From his web-site, it appears as if Jazbo's last work on Video Poker Volatility was in early
2000. I find his concept of survivability and half-life to be quite interesting and, maybe,
could be useful for the type of Video Poker playing that I like to do.

I especially like the fact that it seems to tell you what to expect in terms of how many
hands you might be able to play for a given stake (not bankroll). The gist of it seems to be
that, for most reasonable VP games, you have a 50/50 chance of playing 10,000-15,000
hands of $1 VP with a stash of $1,600 (i.e., 320 bets), playing perfect strategy, of course.

Has anyone worked out (or can accurately guess) where NSUD or the several 99.99% games
at Wynn's fits into Jazbo's Half-Life Results table. How about the curves for 80 bet or 320
bet survivability? Are the 10,000-15,000 figures in the ballpark for those games?

Does someone have a cook-book way to compute these curves for the various number of
bets?

Thanks

…..bl

[cdfsrule1]

If all you want is ball-park figures, you can use the Java application at:
http://www.lotspiech.com/GamblersRuin.html
(It should run in most web browsers)

I believe the pdf-convolution-based method is the only one that can give RoR for a finite
number of hands. The sorokin/jazbo formula (and I don't mean to give ANY credit to
either of these fine gentlemen for discovery of this formula; afterall, if you look in nearly
any statistics book that covers Markov chains you will find it) only handles an INFINITE
hand limit. If you are really pressed for a more accurate answer (than Lotspeich's code
gives you) I can compute it for you.

BTW, In case anyone is wondering... hidden inside the PDF convolution method is the
Poisson distribution. Yup, you can't escape the poisson distribution (when you are dealing
with rare events that have a fixed likelihood of occurrence (rate) during a particular time
interval-- or number of hands). And, yeah, I am not the first person to say this-- again,
just check your favorite stats textbook.

Oh... some time ago I discussed how some reported results for finite RoR may depend on
the computation method here: http://groups.yahoo.com/group/vpFREE/message/49153

My feeling is, that for VP players (not academics), a rough answer here is likely good
enough (which you get easily from Lotspeich).

Has anyone worked out (or can accurately guess) where NSUD or the several 99.99%

games

at Wynn's fits into Jazbo's Half-Life Results table. How about the curves for 80 bet or

320

bet survivability? Are the 10,000-15,000 figures in the ballpark for those games?

Does someone have a cook-book way to compute these curves for the various number

of

···

--- In vpFREE@yahoogroups.com, "bornloser1537" <bornloser1537@y...> wrote:

bets?

[Michael_Peck]

Hi!

From his web-site, it appears as if Jazbo's last work on Video Poker

Volatility was in early

2000. I find his concept of survivability and half-life to be quite

interesting and, maybe,

could be useful for the type of Video Poker playing that I like to do.

I'm interested in this kind of information too. Enough so that I've
been doing some quick & dirty programming that seems to be producing
reasonable results. Here's what I have:

1) An "exact" calculation of the probability distribution of returns
for any initial stake and number of hands played. A requirement to
make this computationally tractable is you have to set an upper limit
on the total return, which I try to set at a ridiculously high level.

2) A Monte Carlo simulation that at present just calculates risk of
ruin for a given initial stake and number of hands played.

I've previously done

3) An "exact" pdf calculation for any number of hands played ignoring
gambler's ruin.
4) A Monte Carlo simulation of returns for any number of hands played,
also ignoring gambler's ruin.

Here's a couple validation exercises I've done so far. First, here
<http://www.wildlife-pix.com/vpoker/ret10k.png> is a case where risk
of ruin is negligible: 10,000 hands of JOB with an initial stake of
1,000 bets or 5,000 coins. Here the histogram is from the Monte Carlo
simulation ignoring ruin, the solid green line is the exact
calculation accounting for ruin, and the red dashed line is the exact
calculation ignoring ruin. The solid blue line is a Normal
distribution having the same mean and variance as 10,000 hands of jacks.

Second, I tried to reproduce Jazbo's survivability analysis
(http://www.jazbo.com/videopoker/halflife.html) for JOB with an
initial stake of 80 bets. The results are here:
<http://www.wildlife-pix.com/vpoker/surv80.png>. The solid red line is
from the exact calculation, the points are from simulations with a
sample size of 10,000. The dotted blue line is Jazbo's estimate of the
"half life": 1,785 hands. By the way survivability does seem to be
very close to an exponentially decaying function of hands played, so
calling this a half life is appropriate.

So far so good. I have two different ways of doing the exact pdf
calculation; both agree in a case where they should. Monte Carlo
simulations have different, much more straightforward, logic than
exact calculations and they also agree.

Has anyone worked out (or can accurately guess) where NSUD or the

several 99.99% games

at Wynn's fits into Jazbo's Half-Life Results table. How about the

curves for 80 bet or 320

bet survivability? Are the 10,000-15,000 figures in the ballpark

for those games?

I'll work on it when I can.

I'll probably post my source code later, after I've quadruple checked
the logic and done some more computational checks. I'm trying to
decide if I care that this might actually useful enough to have some
modest commercial value.

Mike

···

--- In vpFREE@yahoogroups.com, "bornloser1537" <bornloser1537@y...> wrote:

[Peter]

WOW! That's sounds great. I'll be looking and listening, and going over what you have
posted here. Thanks!

.....bl

···

--- In vpFREE@yahoogroups.com, "Michael Peck" <mpeck1@i...> wrote:

I'm interested in this kind of information too. Enough so that I've
been doing some quick & dirty programming that seems to be producing
reasonable results.

I'll probably post my source code later, after I've quadruple checked
the logic and done some more computational checks. I'm trying to
decide if I care that this might actually useful enough to have some
modest commercial value.

Mike

[nightoftheiguana2000]

Has anyone worked out (or can accurately guess) where NSUD or the

several 99.99% games

at Wynn's fits into Jazbo's Half-Life Results table.

NSUD is about the same as FP except it costs you about 1% per hand to
play ($.0125/hand for 5-coin quarters relative to FP). Similar
approximations apply to other short pay games (i.e. figure the cost of
the short).

···

--- In vpFREE@yahoogroups.com, "bornloser1537" <bornloser1537@y...> wrote:

[Dunbar]

Has anyone worked out (or can accurately guess) where NSUD or the

several 99.99% games

at Wynn's fits into Jazbo's Half-Life Results table. How about

the
curves for 80 bet or 320

bet survivability? Are the 10,000-15,000 figures in the ballpark

for those games?

I found the half-life survivability for NSUD using my program,
Dunbar's Risk Analyzer for Video Poker:

For an 80-bet starting bank, the half-life is within 5 plays of
1140.
For a 320-bet starting bank, the half-life is within 20 plays of
9975.

The numbers for NSUD are pretty different from those for FPDW. I get
the same 1322 plays that Jazbo gets for an 80-bet starting bank of
FPDW.

Does someone have a cook-book way to compute these curves for the

various number of

bets?

I don't have one. Getting the numbers out of my program requires
making a few initial guesses until you zero in on the number of
hands to have a 50% RoR. Doing this for a single starting bankroll
is easy. But generating a curve with my method would be very slow.

If there is another game you're interested in, I'll be glad to give
you the 50% survivability. Same thing goes for a different starting
bank.

--Dunbar

···

Thanks

…..bl

[Harry_Porter]

Tune out immediately if hair-splitting makes you grind your teeth (of
course, we don't have anything of that sort here otherwise

Ideally I'd have preferred Jazbo applied some other term to his
analysis of the number of hands at which it's expected half of the
players starting with a given bankroll would break.

Formally, "half-life" refers to the natural decay of a substance (e.g.
uranium-238) into another substance. It's the time over which half of
the substance is converted. For example, starting with 100 grams of
an element having a half-life of 100 years, after 100 years you'd have
50 g remaining, after another 100 years you'd have 25, another 100
leaves 12.5, etc.

The closest analogy to half-life in reference to a bankroll would be
the number of hands at which it would be expected only half of the
bnakroll would remain. However, this type of "decay" would only apply
to negative play and the decay is linear, not geometric, i.e. after 2
of such half-lives it's expected a bankroll would be fully exhausted.

I'd propose another term that I think fits far better: LD-50. This
is the amount of a toxic substance at which half of the subjects
exposed to it "bite the dust". It's used in the study of both poisons
and medications. As put forth in this case, the "dose" would be the
number of hands played.

I would think that "LD-50" would find particular favor with pros
playing a competitive opportunity, such as a limited availability
progressive

- Harry

[Peter]

Thank you, NOTI!

Let me mull this over. It usually takes a lot of thinking and
some "mulling" for things like this to sink in and really be
understood by my slow-working brain (that seems to get slower and
slower with age...I never do appreciate those "senior moments...LOL)

.....bl

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@y...> wrote:

--- In vpFREE@yahoogroups.com, "bornloser1537" <bornloser1537@y...>

wrote:

> Has anyone worked out (or can accurately guess) where NSUD or the
several 99.99% games
> at Wynn's fits into Jazbo's Half-Life Results table.

NSUD is about the same as FP except it costs you about 1% per hand to
play ($.0125/hand for 5-coin quarters relative to FP). Similar
approximations apply to other short pay games (i.e. figure the cost

of

···

the short).

[Peter]

WOW! What else can I say, but thank you, thank, you, thank you,
thank you?

I think that the most significant statement, in addition to the
result itself, is: "The numbers for NSUD are pretty different from
those for FPDW."

In terms of your offer to do other computations, the two that I
think that I would ask for first would be:

      APDW: 1-2-3-4-4-11-15-25-200-800 (99.96%)
9/6/90 JoB: 1-2-3-4-6-9-25-90-800 (99.996%)

My own main curiosity would be where APDW fits in to the other two
DW games. Would it be right square in the middle between NSUD and
FPDW, or what?

Perhaps a table similar to Jazbo's could be built up and stored
somewhere on VPFREE, as the survivability for additional games were
computed. Of course, appropriate credit would be listed,
acknowledging the specific contributors. (Hint to the
administrator...LOL)

Thanks, again.

.....bl

> Has anyone worked out (or can accurately guess) where NSUD or

the

several 99.99% games
> at Wynn's fits into Jazbo's Half-Life Results table. How about
the
curves for 80 bet or 320
> bet survivability? Are the 10,000-15,000 figures in the

ballpark

for those games?

I found the half-life survivability for NSUD using my program,
Dunbar's Risk Analyzer for Video Poker:

For an 80-bet starting bank, the half-life is within 5 plays of
1140.
For a 320-bet starting bank, the half-life is within 20 plays of
9975.

The numbers for NSUD are pretty different from those for FPDW. I

get

the same 1322 plays that Jazbo gets for an 80-bet starting bank of
FPDW.

> Does someone have a cook-book way to compute these curves for

the

various number of
> bets?

I don't have one. Getting the numbers out of my program requires
making a few initial guesses until you zero in on the number of
hands to have a 50% RoR. Doing this for a single starting bankroll
is easy. But generating a curve with my method would be very slow.

If there is another game you're interested in, I'll be glad to

give

you the 50% survivability. Same thing goes for a different

starting

···

--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@h...> wrote:

bank.

--Dunbar

>
> Thanks
>
> …..bl
>

[Peter]

Perhaps it should be called: "TNOHAWIEHOTPSWAGBWB". NASA, the best
acronym generator of all time, would undoubtedly have picked this
one. LOL.

Of course, as always, I have my tongue firmly implanted in my cheek.

.....bl

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...>
wrote:

···

Ideally I'd have preferred Jazbo applied some other term to his
analysis of the number of hands at which it's expected half of the
players starting with a given bankroll would break.

- Harry

[Peter]

Hi!

I found a product called "Dunbar's Risk Analyzer" available at several places on the web for
$15.

The write-up, however, apparently described a Blackjack product. Is there a specific Video
Poker version available? What is the most current version? Where would you recommend
it be purchased if one were interested. I am assuming that, with it, I could work out some
of these numbers myself?

Is there still not a Macintosh version available?

.....bl

···

--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@h...> wrote:

Dunbar's Risk Analyzer for Video Poker:

[Dunbar]

In terms of your offer to do other computations, the two that I
think that I would ask for first would be:

      APDW: 1-2-3-4-4-11-15-25-200-800 (99.96%)
9/6/90 JoB: 1-2-3-4-6-9-25-90-800 (99.996%)

APDW:
For an 80-play starting bank, the 50% RoR point comes at 1198 bets
(± 5)
For a 320-play starting bank, the 50% RoR point comes at 10,950 bets
(± 20)

JOB 9/6/90
For an 80-play starting bank, the 50% RoR point comes at 1825 bets
(± 5)
For a 320-play starting bank, the 50% RoR point comes at 14,650 bets
(± 25)

My own main curiosity would be where APDW fits in to the other two
DW games. Would it be right square in the middle between NSUD and
FPDW, or what?

APDW is much closer to NSUD. For the 320-play banks, you get this
many bets before having a 50% RoR:

NSUD: 9975 bets
APDW: 10950 bets
FPDW: 15700 bets

--Dunbar

--- In vpFREE@yahoogroups.com, "bornloser1537" <bornloser1537@y...>
wrote:

WOW! What else can I say, but thank you, thank, you, thank you,
thank you?

I think that the most significant statement, in addition to the
result itself, is: "The numbers for NSUD are pretty different from
those for FPDW."

In terms of your offer to do other computations, the two that I
think that I would ask for first would be:

      APDW: 1-2-3-4-4-11-15-25-200-800 (99.96%)
9/6/90 JoB: 1-2-3-4-6-9-25-90-800 (99.996%)

My own main curiosity would be where APDW fits in to the other two
DW games. Would it be right square in the middle between NSUD and
FPDW, or what?

Perhaps a table similar to Jazbo's could be built up and stored
somewhere on VPFREE, as the survivability for additional games

were

computed. Of course, appropriate credit would be listed,
acknowledging the specific contributors. (Hint to the
administrator...LOL)

Thanks, again.

.....bl

>
> > Has anyone worked out (or can accurately guess) where NSUD or
the
> several 99.99% games
> > at Wynn's fits into Jazbo's Half-Life Results table. How

about

> the
> curves for 80 bet or 320
> > bet survivability? Are the 10,000-15,000 figures in the
ballpark
> for those games?
>
> I found the half-life survivability for NSUD using my program,
> Dunbar's Risk Analyzer for Video Poker:
>
> For an 80-bet starting bank, the half-life is within 5 plays of
> 1140.
> For a 320-bet starting bank, the half-life is within 20 plays of
> 9975.
>
> The numbers for NSUD are pretty different from those for FPDW. I
get
> the same 1322 plays that Jazbo gets for an 80-bet starting bank

of

> FPDW.
>
> > Does someone have a cook-book way to compute these curves for
the
> various number of
> > bets?
>
> I don't have one. Getting the numbers out of my program

requires

> making a few initial guesses until you zero in on the number of
> hands to have a 50% RoR. Doing this for a single starting

bankroll

> is easy. But generating a curve with my method would be very

slow.

···

--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@h...> wrote:
>
> If there is another game you're interested in, I'll be glad to
give
> you the 50% survivability. Same thing goes for a different
starting
> bank.
>
> --Dunbar
>
>
>
>
> >
> > Thanks
> >
> > …..bl
> >
>

[Dunbar]

--- In vpFREE@yahoogroups.com, "bornloser1537" <bornloser1537@y...>
wrote:

Hi!

I found a product called "Dunbar's Risk Analyzer" available at

several places on the web for

$15.

The write-up, however, apparently described a Blackjack product.

Is there a specific Video

Poker version available? What is the most current version? Where

would you recommend

it be purchased if one were interested.

Thanks for your interest, bl. The original "Dunbar's Risk Analyzer"
is indeed a blackjack risk analyzer, and has been available since
1999. It is appropriate for games that have payouts that are near
1:1. Video poker is, of course, not one of those games!

"Dunbar's Risk Analyzer for Video Poker" is a new program that will
be available in December. I believe you will be able to order it
from the Las Vegas Advisor (GreatStuff4Gamblers.com) website. The
program will do both longterm and session ("Trip") RoR analysis,
incorporating the effects of cashback, tips, player errors, and
withheld taxes.

I am assuming that, with it, I could work out some
of these numbers myself?

Yes, that's correct. The way I am getting the numbers is
doing "Trip" analysis of different lengths, until I get a length
that has 50% RoR.

Is there still not a Macintosh version available?

The program should work on any PC with Excel. Unfortunately, all
the features will not work on a Mac, even if the Mac has Excel.

--Dunbar

[Peter]

Thank you. I will be looking.

.....bl

···

--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@h...> wrote:

"Dunbar's Risk Analyzer for Video Poker" is a new program that will
be available in December. I believe you will be able to order it
from the Las Vegas Advisor (GreatStuff4Gamblers.com) website. The
program will do both longterm and session ("Trip") RoR analysis,
incorporating the effects of cashback, tips, player errors, and
withheld taxes.

--Dunbar

[Harry_Porter]

bornloser1537 wrote:

I find his concept of survivability and half-life to be quite
interesting and, maybe, could be useful for the type of Video Poker
playing that I like to do.

Perhaps. For myself, I look to Dunbar's "Risk Analyzer for Video
Poker" to be of far greater practical value.

A half-life (LD-50 table of games with session lengths that are
shortedned to half the stated values if I look for 70% confidence of
lasting through a desired length of play is far too variable to be
useful in my play ... I look to reliably maintain consistent trip play
to optimize benefits and promotions.

I find Jazbo's numbers a passing curiosity (interesting, none the less).

- H.

[Peter]

Again, for those of you who cringe at splitting hairs, move on
quickly.

There is no "perhaps" about it. Note that the statement was "I find
his concept of survivability and half-life to be quite interesting
and, maybe, could be useful for the type of Video Poker playing that
I like to do".

I almost always try to put my emphasis on "I", namely, that it is my
opinion. And, of course, as such, there is no "perhaps".

I try not to impose my thoughts and inclinations onto anyone else.
My apologies if that seemed to be the case.

.....bl

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...>
wrote:

···

Perhaps.

- H.

[Harry_Porter]

bornloser1537 wrote:

I try not to impose my thoughts and inclinations onto anyone else.
My apologies if that seemed to be the case.

You wrote, "Perhaps ..." I responded, "Maybe ..."

Both were observations and neither were judgmental. In each case we
followed with our own impressions of how the data might/might not be
of use in our play.

- H.