I feel that 3-5 royals as a bankroll is insufficient.
If you lose 2 royals, you are inadequately funded and need more money to
continue with any confidence
Digest Number 1370
--- In vpFREE@yahoogroups.com, Elliott L Shapiro <videopoker@j...>
wrote:
I feel that 3-5 royals as a bankroll is insufficient.
If you lose 2 royals, you are inadequately funded and need more
money to
continue with any confidence
according to:
http://www.gamblingtools.net/vp/vpanalyzer.html
full pay deuces wild with 0.25% cashback and 10% risk of ruin
requires a bankroll of 2562 bets (3.2 royals)
this assumes perfect play and an honest (random) machine and uses the
sorokin risk of ruin formula
(posted on vpFree with a copy also sent directly to aaquad250)
pal16r8 wrote:
--- In vpFREE@yahoogroups.com, Elliott L Shapiro <videopoker@j...>
wrote:
> I feel that 3-5 royals as a bankroll is insufficient.
> If you lose 2 royals, you are inadequately funded and need more
money to
> continue with any confidenceaccording to:
http://www.gamblingtools.net/vp/vpanalyzer.htmlfull pay deuces wild with 0.25% cashback and 10% risk of ruin
requires a bankroll of 2562 bets (3.2 royals)this assumes perfect play and an honest (random) machine and uses the
sorokin risk of ruin formula
This raised some important questions for me, and so I tried to get a better grasp on this by reviewing some past posts, but that just seemed to just bring up more questions, so I will address the ones pertaining to this post first, and then revisit an old post.
First, just out of curiosity, how can a person tell that the vpanalyzer that has been linked-to, above, uses the sorokin RoR formula? I looked over the page and can't find any reference to sorokin, so I presume that you have obtained that information independently from another source.
Second, and more importantly, I just presumed (probably wrongly) that the above statement means that the above vpanalyzer is "sorokin OPTIMIZED", and I further thought (but am not so sure now) that this _necessarily_ meant that the strategy employed for "sorokin optimized risk of ruin" would _always_ have an ER of something less than what results from max-ER strategy. I thought the whole idea from Sorokin was that by sacrificing at least a small portion of ER, you can significantly extend play. If this all happens to be actually true, then does anyone know of a bankroll/RoR calculator that uses max-ER strategy instead, since that's what I play? I know about Jeff Lotspiech's "Gambler's Ruin" calculator -- http://www.lotspiech.com/GamblersRuin.html -- which I like very much, and which is based on "optimum" play, citing an ER of 99.5 for JoB; I guess that's close enough unless someone can suggest something better.
Now, in doing a little research of my own (as I almost always do before burdening the group), I looked back at the previous recent discussion of sorokin numbers, and post number 24848 by aaquad250 -- http://groups.yahoo.com/group/vpFREE/message/24848 -- when viewed in the light of this most recent post, now presents new questions for me, so I'm also taking the liberty of sending a copy of this post directly to aaquad250 to be sure that s/he sees this and hopefully might respond.
In post 24848, aaquad250 said:
> ... my strategies are sorokin optimized
> a good calculator is here:
> http://www.gamblingtools.net/vp/vpanalyzer.html
> these are max-ev strategy 10% ror numbers:
> deuces (+.76%,var26): 3525
> all american (+.72%,var27): 3909
> joker (+.65%,var26): 4289
>
> how many strategies are there now?
> max-ev, low-risk, short-coin, min-rf-cost, sorokin-optimized ...
>
> min-risk doesn't sound right, cause min-risk would be to not play at
> all, correct?
Now, aaquad250 refers to the same vpanalyzer that you have suggested, but also lists some sorokin numbers along with ER's that look exactly like max-ER values, and then mentions at the end that "max-ev" and "sorokin-optimized" are two different strategies (among 5 he listed). It is his statement immediately following the link to the vpanalyzer which is throwing me off a bit: "these are max-ev strategy 10% ror numbers:".
This is how I had interpreted his original post:
1. _HIS_ (aaquad250's) strategies are sorokin optimized! This does not automatically imply that those from the _vpanalyzer_ are as well.
2. Then immediately after the link to the vpanalyzer he provides a short list and his statement about "max-ev", and then proceeds to include in parenthesis the actual "max-ev" percentages for the corresponding games, followed by numbers which, because they lacked a decimal point and had too few digits, did not appear to me to be 'sorokin' numbers to me -- so I just assumed that they were the bankrolls needed to ensure a 10% risk of ruin for those particular games. I was able to confirm that by using the referenced vpanalyzer, with cashback set to zero.
So now, in light of pal16r8's post which emphatically states that vpanalyzer uses the sorokin ror formula, I'm left wondering whether there is any contradiction with aaquad250, or if aaquad merely included the percentages (max-er) merely as a way of indicating that the games that are analyzed happen to be full-pay.
If the vpanalyzer does, in fact, use a less profitable strategy than max-er, does anyone know what the revised ER is for those sorokin optimized strategies? As I thought about this, it occurred to me that this last question might depend upon the size of the beginning bankroll that is entered, because that might affect the actual strategy that is employed, but since this does, IIRC, compute RoR in terms of infinite play (... especially in light of Dan Paymar's article: "Risk of Ruin -- Video Poker for Fun and Profit" which includes a chart showing "Risk of ruin playing forever"), it seems that perhaps the strategy is actually independent of beginning bankroll, which after all must become infinitely small relative to infinite play (i.e., relative to infinity, a bankroll of 100000 is just as infinitely small as a bankroll of 1 bet) -- and the only thing that would ever change would be percentage that are likely to succeed.
I know I've probably bored the pants off of anyone crazy enough to read to this point, but I can't sleep at night thinking about such things. 
Cheers.
Bill Velek
Second, and more importantly, I just presumed (probably wrongly)
that
the above statement means that the above vpanalyzer is "sorokin
OPTIMIZED", and I further thought (but am not so sure now) that
this
_necessarily_ meant that the strategy employed for "sorokin
optimized
risk of ruin" would _always_ have an ER of something less than what
results from max-ER strategy
The vpanalyzer works much the same as WinPoker, you select a game and
adjust the paytable and it calculates the average return and variance
using a computer perfect strategy. The easiest way to verify this is
to check the results, vpanalyzer says full pay deuces wild has a
payback of 100.76% and a variance of 25.84 . WinPoker says full pay
deuces wild has a payback of 100.7620% and a variance of 25.83462 .
Reduced risk strategies produce lower numbers for both payback and
variance. (the variance is lower hence the risk is less but the
tradeoff is that the payback is also less) A reduced risk strategy
requires a slightly smaller bankroll, however this advanced topic is
not covered by vpanalyzer or WinPoker.
Another source of bankroll information is:
http://wizardofodds.com/games/videopoker/vidpokapx1.html
···
--- In vpFREE@yahoogroups.com, Bill Velek <billvelek@a...> wrote:
(posted on vpFree with a copy also sent directly to aaquad250)
pal16r8 wrote:
> --- In vpFREE@yahoogroups.com, Elliott L Shapiro <videopoker@j...>
>
> wrote:
> > I feel that 3-5 royals as a bankroll is insufficient.
> > If you lose 2 royals, you are inadequately funded and need more
>
> money to
>
> > continue with any confidence
>
> according to:
> http://www.gamblingtools.net/vp/vpanalyzer.html
>
> full pay deuces wild with 0.25% cashback and 10% risk of ruin
> requires a bankroll of 2562 bets (3.2 royals)
>
> this assumes perfect play and an honest (random) machine and uses the
> sorokin risk of ruin formulaThis raised some important questions for me, and so I tried to get a
better grasp on this by reviewing some past posts, but that just seemed
to just bring up more questions, so I will address the ones pertaining
to this post first, and then revisit an old post.First, just out of curiosity, how can a person tell that the vpanalyzer
that has been linked-to, above, uses the sorokin RoR formula? I looked
over the page and can't find any reference to sorokin, so I presume that
you have obtained that information independently from another source.Second, and more importantly, I just presumed (probably wrongly) that
the above statement means that the above vpanalyzer is "sorokin
OPTIMIZED",
The RoR formula is based on the probability distribution, which is
obviously dependent on the strategy. You supply the probabilities
for the vpanalyzer, and it computes RoR values for whatever
strategy was used to produce the probability numbers. To get
min-risk numbers from this tool, it would be necessary to first
determine the min-risk strategy in order to obtain the corresponding
probabilities.
and I further thought (but am not so sure now) that this
_necessarily_ meant that the strategy employed for "sorokin optimized
risk of ruin" would _always_ have an ER of something less than what
results from max-ER strategy.
The min-risk strategy _usually_ has a lower ER. If the game happens
to be exactly breakeven with max-EV play, then the min-risk strategy
becomes identical to the max-EV strategy and both will return 100%.
If the games is not exactly breakeven but is extremely close to breakeven,
then it is possible for the min-risk strategy to remain identical to the
max-EV strategy.
If the max-EV strategy is "sufficiently" favorable or unfavorable, then the
min-risk strategy will differ from the max-EV strategy. For favorable games,
the min-risk strategy is less agressive, and for unfavorable games the
min-risk strategy is more agressive, than the max-EV strategy. I've
discussed this in more detail in some recent posts.
I thought the whole idea from Sorokin was
that by sacrificing at least a small portion of ER, you can
significantly extend play.
I'm not sure "extend" is the right way to think about min-risk strategies.
Comparing min-risk to max-EV is an apples/oranges comparison. They
are inherently different ways of measuring performance. EV measures
progress in terms of "dollars per game played" while risk measures
performance in terms of "probability of reaching (or failing to risk) a
specified target".
If you play for some fixed number of rounds, then average the resulting
bankrolls, then the max-EV strategy will always appear to perform better.
However, max-EV makes an implicit assumption that your bankroll can
go negative, even infinitely negative if necessary in order to play the
specified number of rounds.
Assuming a favorable game, the min-risk strategy minimizes the probability
that you will go broke. Another way of stating this is that the min-risk
strategy maximizes the probability that you will play indefinitely without
losing your bankroll. Risk based strategies to not permit the bankroll to
ever become negative during the course of play
The min-risk strategy is also useful for maximizing the likelihood of
reaching a fixed target bankroll before going broke. When the target
is finite, min-risk strategies can be employed even when the game
is negative EV.
So, in a real sense, EV and risk measure performance in ways that
are inherently incompatible, making it somewhat meaningless to
compare them to each other. Maximizing EV requires you to increase
your risk of going broke. Minimizing risk requires you to sacrifice EV.
I claim that neither is inherently "better" than the other.
If this all happens to be actually true,
then does anyone know of a bankroll/RoR calculator that uses max-ER
strategy instead, since that's what I play?
I'd bet lunch that the numbers quoted above were based on a max-ER
strategy. It takes extra effort to compute min-risk strategies.
Now, in doing a little research of my own (as I almost always do before
burdening the group), I looked back at the previous recent discussion of
sorokin numbers, and post number 24848 by aaquad250 --
http://groups.yahoo.com/group/vpFREE/message/24848 -- when viewed in the
light of this most recent post, now presents new questions for me, so
I'm also taking the liberty of sending a copy of this post directly to
aaquad250 to be sure that s/he sees this and hopefully might respond.In post 24848, aaquad250 said:
> ... my strategies are sorokin optimized
> a good calculator is here:
> http://www.gamblingtools.net/vp/vpanalyzer.html
> these are max-ev strategy 10% ror numbers:
> deuces (+.76%,var26): 3525
> all american (+.72%,var27): 3909
> joker (+.65%,var26): 4289
>
> how many strategies are there now?
> max-ev, low-risk, short-coin, min-rf-cost, sorokin-optimized ...
>
> min-risk doesn't sound right, cause min-risk would be to not play at
> all, correct?Now, aaquad250 refers to the same vpanalyzer that you have suggested,
but also lists some sorokin numbers along with ER's that look exactly
like max-ER values, and then mentions at the end that "max-ev" and
"sorokin-optimized" are two different strategies (among 5 he listed).
It is his statement immediately following the link to the vpanalyzer
which is throwing me off a bit: "these are max-ev strategy 10% ror
numbers:".This is how I had interpreted his original post:
1. _HIS_ (aaquad250's) strategies are sorokin optimized! This does not
automatically imply that those from the _vpanalyzer_ are as well.2. Then immediately after the link to the vpanalyzer he provides a
short list and his statement about "max-ev", and then proceeds to
include in parenthesis the actual "max-ev" percentages for the
corresponding games, followed by numbers which, because they lacked a
decimal point and had too few digits, did not appear to me to be
'sorokin' numbers to me -- so I just assumed that they were the
bankrolls needed to ensure a 10% risk of ruin for those particular
games. I was able to confirm that by using the referenced vpanalyzer,
with cashback set to zero.
Correct me if I'm wrong, but didn't you have to enter the payoffs and
the probabilities for those payoffs into vpanalyzer? If it was computing
a strategy for you, you'd have to tell it what kind of hand was
associated with the payoff, and that wasn't part of the process.
The analyzer simply applies the RoR formula to the data you provide,
it doesn't create a strategy, nor does it have sufficient information to
enable it to compute a strategy.
So now, in light of pal16r8's post which emphatically states that
vpanalyzer uses the sorokin ror formula, I'm left wondering whether
there is any contradiction with aaquad250, or if aaquad merely included
the percentages (max-er) merely as a way of indicating that the games
that are analyzed happen to be full-pay.
In the cases where I was able to produce RoR numbers (non-wild games)
I got the same numbers as aaquad250 by using max-EV strategies.
If the vpanalyzer does, in fact, use a less profitable strategy than
max-er, does anyone know what the revised ER is for those sorokin
optimized strategies?
I've described the process for computing min-risk strategies in a
recent post, where I talked about "virtual payoffs". Once you get
the min-risk strategy, you can use the probabilities and the real
payoffs to compute ER for the min-risk strategy. Another related
post from a few months back, titles "Equivalent Games" shows how
to model risk in terms of an endless series of coin flips using a
single biased coin. That may or may not be helpful as well.
As I thought about this, it occurred to me that
this last question might depend upon the size of the beginning bankroll
that is entered,
Nope. The min-risk strategy is independent of the bankroll.
because that might affect the actual strategy that is
employed, but since this does, IIRC, compute RoR in terms of infinite
play (... especially in light of Dan Paymar's article: "Risk of Ruin --
Video Poker for Fun and Profit" which includes a chart showing "Risk of
ruin playing forever"), it seems that perhaps the strategy is actually
independent of beginning bankroll, which after all must become
infinitely small relative to infinite play (i.e., relative to infinity,
a bankroll of 100000 is just as infinitely small as a bankroll of 1 bet)
-- and the only thing that would ever change would be percentage that
are likely to succeed.
Risk does not require infinite play in order to be interpreted in useful ways.
The same RoR value can be use to compute the probability of reaching
any fixed goal G from a starting bankroll B. This is technically an
approximation, but the approximation should be very good whenever
B and G are "far apart".
I know I've probably bored the pants off of anyone crazy enough to read
to this point, but I can't sleep at night thinking about such things.
Yes, this stuff haunts me in my sleep too 
···
On Wednesday 28 January 2004 11:01 am, Bill Velek wrote:
Steve Jacobs wrote:
snip
snip
> First, just out of curiosity, how can a person tell that the vpanalyzer
> that has been linked-to, above, uses the sorokin RoR formula? I looked
> over the page and can't find any reference to sorokin, so I presume that
> you have obtained that information independently from another source.
>
> Second, and more importantly, I just presumed (probably wrongly) that
> the above statement means that the above vpanalyzer is "sorokin
> OPTIMIZED",The RoR formula is based on the probability distribution, which is
obviously dependent on the strategy. You supply the probabilities
for the vpanalyzer, ...
snip
Perhaps on other analyzers, but I can't see a way to do that on the one linked above unless you are saying that the strategy used by the analyzer is altered by the changing of the paytables, which a user _can_ do. I can understand that this could be a method to do that, but then how would the analyzer know what the true paytable values are for purposes of making its RoR calculations once the strategy has been determined?
... and it computes RoR values for whatever
strategy was used to produce the probability numbers. To get
min-risk numbers from this tool, it would be necessary to first
determine the min-risk strategy in order to obtain the corresponding
probabilities.
Thanks for the info on the other points which I am snipping.
... Risk based strategies to not permit the bankroll to
ever become negative during the course of play
Understood. A negative bankroll is "ruin" by definition, and just becomes part of the stats ... one of the 10%, if the setting is for a 10% Risk of Ruin, correct?
snip -- including snipping of aaquad250's post
> ... I was able to confirm that by using the referenced vpanalyzer,
> with cashback set to zero.
[confirm that aaquad's numbers were bankroll values rather than sorokin numbers]
Correct me if I'm wrong, but didn't you have to enter the payoffs and
the probabilities for those payoffs into vpanalyzer? If it was computing
a strategy for you, you'd have to tell it what kind of hand was
associated with the payoff, and that wasn't part of the process.
The analyzer simply applies the RoR formula to the data you provide,
it doesn't create a strategy, nor does it have sufficient information to
enable it to compute a strategy.
I used the default values that are already set in the machine for the games aaquad had referred to in his post. Yes, it is possible to change the values in the paytable, but I don't know what you mean by "enter ... the probabilities for those payoffs ...", and there doesn't appear to be any place on that particular analyzer to do that. But maybe I'm missing something. Have you taken a look at the above-link (I found it through vpFREE's website).
> So now, in light of pal16r8's post which emphatically states that
> vpanalyzer uses the sorokin ror formula, I'm left wondering whether
> there is any contradiction with aaquad250, or if aaquad merely included
> the percentages (max-er) merely as a way of indicating that the games
> that are analyzed happen to be full-pay.In the cases where I was able to produce RoR numbers (non-wild games)
I got the same numbers as aaquad250 by using max-EV strategies.> If the vpanalyzer does, in fact, use a less profitable strategy than
> max-er, does anyone know what the revised ER is for those sorokin
> optimized strategies?I've described the process for computing min-risk strategies in a
recent post, where I talked about "virtual payoffs".
Understood. I believe I used the same concept while analyzing Multi Strike.
Once you get
the min-risk strategy, you can use the probabilities and the real
payoffs to compute ER for the min-risk strategy. Another related
post from a few months back, titles "Equivalent Games" shows how
to model risk in terms of an endless series of coin flips using a
single biased coin. That may or may not be helpful as well.> As I thought about this, it occurred to me that
> this last question might depend upon the size of the beginning bankroll
> that is entered,Nope. The min-risk strategy is independent of the bankroll.
Okay. I see that now, because we are speaking now about the RoR if playing for infinity, right? Because if we were trying to make a calculation in reference to a target amount, at which we would stop, which is what another analyzer does -- the one called "Gambler's Ruin", then I can't see how they could be independent. I mean, if two people had a goal of stopping at one million dollars, and one of them had a beginning bankroll of $1.00 and the other a beginning bankroll of $999,999.00, I find it hard to believe that a RoR strategy would be the same for both of them, and therefore have the same ER for each. Or are we just speaking about tremendously different percentages of those who make it and those who suffer ruin?? I can see how that might be the answer. If they both utlilze the same strategy, with perhaps a .000001% chance of survival and a 99.99999% chance of ruin for the $1.00 bankroll, and something more or less vice versa for the $999,999.00 bankroll. Maybe I'm starting to catch on. I'm a bit slower in my old age. 
> because that might affect the actual strategy that is
> employed, but since this does, IIRC, compute RoR in terms of infinite
> play (... especially in light of Dan Paymar's article: "Risk of Ruin --
> Video Poker for Fun and Profit" which includes a chart showing "Risk of
> ruin playing forever"), it seems that perhaps the strategy is actually
> independent of beginning bankroll, which after all must become
> infinitely small relative to infinite play (i.e., relative to infinity,
> a bankroll of 100000 is just as infinitely small as a bankroll of 1 bet)
> -- and the only thing that would ever change would be percentage that
> are likely to succeed.Risk does not require infinite play in order to be interpreted in useful ways.
The same RoR value can be use to compute the probability of reaching
any fixed goal G from a starting bankroll B. This is technically an
approximation, but the approximation should be very good whenever
B and G are "far apart".
Okay. I understand, and I want to thank you very much for your time and patience.
Cheers.
Bill Velek
···
On Wednesday 28 January 2004 11:01 am, Bill Velek wrote:
Steve Jacobs wrote:
snip
> > > http://www.gamblingtools.net/vp/vpanalyzer.html
snip
> > First, just out of curiosity, how can a person tell that the vpanalyzer
> > that has been linked-to, above, uses the sorokin RoR formula? I looked
> > over the page and can't find any reference to sorokin, so I presume
> > that you have obtained that information independently from another
> > source.
> >
> > Second, and more importantly, I just presumed (probably wrongly) that
> > the above statement means that the above vpanalyzer is "sorokin
> > OPTIMIZED",
>
> The RoR formula is based on the probability distribution, which is
> obviously dependent on the strategy. You supply the probabilities
> for the vpanalyzer, ...snip
Perhaps on other analyzers, but I can't see a way to do that on the one
linked above unless you are saying that the strategy used by the
analyzer is altered by the changing of the paytables, which a user _can_
do. I can understand that this could be a method to do that, but then
how would the analyzer know what the true paytable values are for
purposes of making its RoR calculations once the strategy has been
determined?
Don't go too much by my description, because I've never been able
to get Cindy's analyser to work correctly from a Linux browser, so
I'm speculating on how it works. I could be way off base here.
That aside, I have a program of my own for doing RoR calculations.
All it needs are payoff values and the probabilities that go with them.
RoR is a function of the probability distribution, the math doesn't
care at all about the underlying structure of whatever game/strategy
produced the numbers.
> ... and it computes RoR values for whatever
> strategy was used to produce the probability numbers. To get
> min-risk numbers from this tool, it would be necessary to first
> determine the min-risk strategy in order to obtain the corresponding
> probabilities.Thanks for the info on the other points which I am snipping.
> ... Risk based strategies to not permit the bankroll to
> ever become negative during the course of playUnderstood. A negative bankroll is "ruin" by definition, and just
becomes part of the stats ... one of the 10%, if the setting is for a
10% Risk of Ruin, correct?
Correct.
snip -- including snipping of aaquad250's post
> > ... I was able to confirm that by using the referenced vpanalyzer,
> > with cashback set to zero.[confirm that aaquad's numbers were bankroll values rather than sorokin
numbers]> Correct me if I'm wrong, but didn't you have to enter the payoffs and
> the probabilities for those payoffs into vpanalyzer? If it was computing
> a strategy for you, you'd have to tell it what kind of hand was
> associated with the payoff, and that wasn't part of the process.
> The analyzer simply applies the RoR formula to the data you provide,
> it doesn't create a strategy, nor does it have sufficient information to
> enable it to compute a strategy.I used the default values that are already set in the machine for the
games aaquad had referred to in his post. Yes, it is possible to change
the values in the paytable, but I don't know what you mean by "enter ...
the probabilities for those payoffs ...", and there doesn't appear to be
any place on that particular analyzer to do that. But maybe I'm missing
something. Have you taken a look at the above-link (I found it through
vpFREE's website).
Rats. This is a different tool than the one I was talking about. Sorry
for the confusion.
> > So now, in light of pal16r8's post which emphatically states that
> > vpanalyzer uses the sorokin ror formula, I'm left wondering whether
> > there is any contradiction with aaquad250, or if aaquad merely included
> > the percentages (max-er) merely as a way of indicating that the games
> > that are analyzed happen to be full-pay.
>
> In the cases where I was able to produce RoR numbers (non-wild games)
> I got the same numbers as aaquad250 by using max-EV strategies.
>
> > If the vpanalyzer does, in fact, use a less profitable strategy than
> > max-er, does anyone know what the revised ER is for those sorokin
> > optimized strategies?
>
> I've described the process for computing min-risk strategies in a
> recent post, where I talked about "virtual payoffs".Understood. I believe I used the same concept while analyzing Multi Strike.
> Once you get
> the min-risk strategy, you can use the probabilities and the real
> payoffs to compute ER for the min-risk strategy. Another related
> post from a few months back, titles "Equivalent Games" shows how
> to model risk in terms of an endless series of coin flips using a
> single biased coin. That may or may not be helpful as well.
>
> > As I thought about this, it occurred to me that
> > this last question might depend upon the size of the beginning bankroll
> > that is entered,
>
> Nope. The min-risk strategy is independent of the bankroll.Okay. I see that now, because we are speaking now about the RoR if
playing for infinity, right?
The value computed by solving the RoR equation is the risk or losing
a single unit bankroll. If this value is R, then the risk of losing a B
unit bankroll is simply R^B.
Because if we were trying to make a
calculation in reference to a target amount, at which we would stop,
which is what another analyzer does -- the one called "Gambler's Ruin",
then I can't see how they could be independent. I mean, if two people
had a goal of stopping at one million dollars, and one of them had a
beginning bankroll of $1.00 and the other a beginning bankroll of
$999,999.00, I find it hard to believe that a RoR strategy would be the
same for both of them, and therefore have the same ER for each.
They are the same, to a good approximation. If you want the absolute
minimum risk, then you need to alter strategy based on how close you
are to the goal. For example, if your goal is 20,000 unit and you already
have 19,975 units, then hitting a royal is no better than hitting quads.
However, solving this kind of problem is very difficult and also produces
an extremely complex strategy. So, to simplify matters, it makes sense
to find a fixed strategy that minimizes RoR and is independent of distance
from the goal. The effect of this approximation is easy to understand
once you understand how to model risk with equivalent coin flips
(my "Equivalent Games" post describes that), but without that background
I don't know an easy way to describe the approximation.
With a current bankroll of B units and a target of G units, the probability
of _success_ is given by:
p(win) = (1 - R^B) / (1 - R^G)
I find that a little easier to remember than the overall probabiity of ruin,
which is given by:
p(lose) = 1 - p(win) = (R^B - R^G) / (1 - R^G)
Or are
we just speaking about tremendously different percentages of those who
make it and those who suffer ruin?? I can see how that might be the
answer. If they both utlilze the same strategy, with perhaps a .000001%
chance of survival and a 99.99999% chance of ruin for the $1.00
bankroll, and something more or less vice versa for the $999,999.00
bankroll. Maybe I'm starting to catch on. I'm a bit slower in my old
age.
Having a large bankroll simply means that you have more changes to
play one unit indefinitely. You fail only if you fail with all B units, one
after the other, so probability of success is (1 - R^B).
> > because that might affect the actual strategy that is
> > employed, but since this does, IIRC, compute RoR in terms of infinite
> > play (... especially in light of Dan Paymar's article: "Risk of Ruin --
> > Video Poker for Fun and Profit" which includes a chart showing "Risk of
> > ruin playing forever"), it seems that perhaps the strategy is actually
> > independent of beginning bankroll, which after all must become
> > infinitely small relative to infinite play (i.e., relative to infinity,
> > a bankroll of 100000 is just as infinitely small as a bankroll of 1
> > bet) -- and the only thing that would ever change would be percentage
> > that are likely to succeed.
>
> Risk does not require infinite play in order to be interpreted in
> useful ways.
> The same RoR value can be use to compute the probability of reaching
> any fixed goal G from a starting bankroll B. This is technically an
> approximation, but the approximation should be very good whenever
> B and G are "far apart".Okay. I understand, and I want to thank you very much for your time and
patience.
You're welcome. Glad I could help.
···
On Thursday 29 January 2004 01:38 am, Bill Velek wrote:
> On Wednesday 28 January 2004 11:01 am, Bill Velek wrote: