vpFREE2 Forums

Risk of Ruin Formulas: A Possible New Use?

#1

If the ER (Expected Return) of a game is 101%, and I gamble $10,000,
then the expected profit is $100 (.01 x $10,000 = $100). This is a
small amount, but only because the "profit" in the calculation is
based on the amount gambled rather than my bankroll. Suppose my
bankroll was $1000, and I used it to gamble $10,000. I gambled the
winnings as I played until I eventually gambled $10,000. When I
finish, in this example, I cash out with $1100, so my actual profit
is 10% of my bankroll. This is a pretty good return on my
investment, and I can keep doing it over and over. Keep in mind I
used small numbers to keep the example simple.

So the question becomes whether it's reasonable to assume I can
gamble $10,000 with a $1000 bankroll. Whether it's reasonable must
depend on the ER and variance of the game I'm playing. So I'm
wondering if Risk of Ruin formulas can be used to determine if it is
reasonable. That is, a RofR formula can have two uses ... (1) to
estimate the odds I'll lose my $1000 and (2) to compute an estimate
of the "multiple" I can expect between my bankroll and how much I
gamble, and thus the percentage return of the game in relation to my
bankroll. So, might this be a new way to compare games using RofR
formulas?

I'm not familiar with the details of RofR formulas, and their
possible uses. It may be this use is already known to people who use
these formulas. For me, personally, I'm only familiar with RofR as
used in the sense of (1) above.

#2

brumar_lv wrote:

So the question becomes whether it's reasonable to assume I can
gamble $10,000 with a $1000 bankroll. Whether it's reasonable must
depend on the ER and variance of the game I'm playing. So I'm
wondering if Risk of Ruin formulas can be used to determine if it is
reasonable. That is, a RofR formula can have two uses ... (1) to
estimate the odds I'll lose my $1000 and (2) to compute an estimate
of the "multiple" I can expect between my bankroll and how much I
gamble, and thus the percentage return of the game in relation to my
bankroll. So, might this be a new way to compare games using RofR
formulas?

Ok, bear in mind that a RoR value indicates the probability that you
will go broke in playing through a given amount of bets, with a given
confidence.

For example, a 5% ROR for this example is an indication that, given a
bankroll of $1000, you will break before playing through $10,000
coin-in 5% of the time.

So, in response to your question, once you set a threshold that is a
reasonable probability of success, you calculate RoR under the
corresponding failure rate. E.g., you consider a 90% chance of
playing through $10K coin-in to be a "reasonable chance of success".
You calculate the 10% ROR for that bankroll. If it's 98%, you
calculate the 2% ROR value.

The "multiple" you suggest above is the ratio of coin-in to bankroll,
and you set the coin-in/bankroll numbers appropriatesly to test for a
targeted "multiple".

- Harry

#3

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

Ok, bear in mind that a RoR value indicates the probability that you
will go broke in playing through a given amount of bets, with a

given

confidence.

For example, a 5% ROR for this example is an indication that, given

a

bankroll of $1000, you will break before playing through $10,000
coin-in 5% of the time.

So, in response to your question, once you set a threshold that is a
reasonable probability of success, you calculate RoR under the
corresponding failure rate. E.g., you consider a 90% chance of
playing through $10K coin-in to be a "reasonable chance of

success".

You calculate the 10% ROR for that bankroll. If it's 98%, you
calculate the 2% ROR value.

The "multiple" you suggest above is the ratio of coin-in to

bankroll,

and you set the coin-in/bankroll numbers appropriatesly to test for

a

targeted "multiple".

- Harry

Thanks for the explanation. I clearly erred in referring to RofR
formulas as currently used. I doubt they can be used to answer the
question I posed. My question is whether there is a way to calculate
the "average bankroll" needed to wager $10,000 (for example) on a
25-cent game such as 9/6JB? Put differently, what is the average
ratio between the amount wagered and the bankroll required to make
those wagers? I would imagine this ratio varies from game to game,
because of ER differences.

#4

brumar_lv wrote:

Thanks for the explanation. I clearly erred in referring to RofR
formulas as currently used. I doubt they can be used to answer the
question I posed. My question is whether there is a way to calculate
the "average bankroll" needed to wager $10,000 (for example) on a
25-cent game such as 9/6JB? Put differently, what is the average
ratio between the amount wagered and the bankroll required to make
those wagers? I would imagine this ratio varies from game to game,
because of ER differences.

Well, you can pose the question in terms of "average bankroll", if you
desire. And you're right, ROR won't get you an answer. For that
matter, I don't have a suggestion for arriving at an answer aside from
building your own session simulator and putting it through the
necessary number of runs for a decent approximation of this value.

That said, I consider "average bankroll", as defined by you, to be an
academic quantity -- for it's not one I personally would concern
myself. That's simply a reflection of what I, personally, carry into
play as a concern.

My first concern is what bankroll I need to carry into the play to
have a given confidence of completing my desired number of hands (I
generally target a value between 1% and 5%, depending on the play ...
on occasion, I might be satisfied with 10%). This question is
satisfied via ROR.

The second concern, when I care to find it, is my average loss on
those occasions where play goes south, and my average win on sessions
that are profitable. It's simply nice to have a sense of the range in
which results have a decent expectation of falling (not exactly the
middle 50% of the probability distribution, but close enough for
government work). This can be found by interperlating values from the
graphs produced in previously mentioned products such as VPW and Dunbar's.

- Harry

#5

FWIW, I usually do a fair amount of "simulations" with the Dunbar and VPW bankroll
calculators before a trip. With games and denominations chosen, and some idea as to
how much I wish to play (i.e., total number of hands), cumulatively, through the whle trip, I
get a good idea about the minimum amount of money that I need to bring to accomplish
my goals.

The nice thing about being conservative in one's simulations (i.e., like keeping ROR quite
low, oftentimes below 1%) one usually comes nowhere near going broke and, at times,
come home with a nice windfall (when one hits a nice winning streak).

I have thus found that the "shorterm" bankroll calculators are what one wants from trip to
trip, and not the lifetime bankroll for knowing how much you need over a lifetime.

.....bl

ยทยทยท

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

It's simply nice to have a sense of the range in
which results have a decent expectation of falling (not exactly the
middle 50% of the probability distribution, but close enough for
government work). This can be found by interperlating values from the
graphs produced in previously mentioned products such as VPW and Dunbar's.

- Harry

#6

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...>
wrote:
That said, I consider "average bankroll", as defined by you, to be an
academic quantity -- for it's not one I personally would concern
myself. That's simply a reflection of what I, personally, carry into
play as a concern.

I was trying to be a tad original, unsuccessfully upon further
reflection. I mentioned RofR formulas because they correlate
bankroll with the ER and variance of a game. But my objective had
nothing to do with RofR as currently used. Here's the example I gave
in my original post:

"If the ER (Expected Return) of a game is 101%, and I gamble $10,000,
then the expected profit is $100 (.01 x $10,000 = $100). Suppose my
bankroll was $1000, and I used it to gamble $10,000. I gambled the
winnings as I played until I eventually gambled $10,000. When I
finish, in this example, I cash out with $1100, so my actual profit
is 10% of my bankroll."

This example made me wonder if finding the ratio between bankroll and
games played might be useful to know. Useful because it would tell
me the expected return on my bankroll (10% in my example). Knowing
this might enable one to choose which game to play ... the one with
the highest expected return (since I assumed each game would have its
own ratio).

But, unfortunately, I don't think an "average" exists in any
meaningful way, because I think the average increases as the bankroll
size increases. If the bankroll is large enough the average
becomes infinite and one can play forever with it (assuming the ER is
positive).

As you said, the average seems to be only an academic quantity. For
the purpose I had in mind, the NO table seems to be the best
tool for choosing which game to play.