Risk of Ruin and Required Return/Bankroll Requirement

[Dan2]

Harry D. Porter wrote:

In past months I've entered a couple of posts to the various vp groups
concerning the risk associated with video poker and the statistics that
are commonly presented in video poker software.

I'm going to discuss further evaluation of this and, frankly, if you
couldn't give a damn it's time to tune out :). (That's for your
benefit, Marsha!)

The most common statistic displayed is the variance of a game. I've
maintained that standard deviation, the square root of variance, is a
more accurate measure of a game's risk. However, at least one source
who I greatly respect has maintained that variance is the more pertinent
measure.

In the wee hours of a sleepless night I've had a chance to examine this
question more closely. A key aid in my review has been a Risk of Ruin
Spreadsheet that was developed by Dunbar (first name a mystery). The
source of his work is a short-term risk of ruin formula detailed in Don
Schlesinger's BJ Attack (1997), p. 162. The spreadsheet allows you to
determine the ROR for any specified bankroll given the standard
deviation and effective return of a game. While the formula was devised
for the specific purpose of evaluating blackjack, it is readily put to
use in looking at video poker.

Dunbar, along with Jeff B., later wrote an article published in the
Fall, 1999 issue of Blackjack Forum entitled "Risk of ruin for video
poker and other skewed-up games." The main thrust of that article was
to give the derivation of the now-famous Sorokin formula, named for
its developer, Russian mathematician Evgeny Sorokin, and to show why
that formula is much more suited to video poker than any other
method. (Jazbo published essentially the same formula a few months
earlier, as reported in the March/April 1999 issue of Video Poker
Times. It is not clear whether Jazbo got the formula from Sorokin or
derived it himself.)

Yuri Sorkin, our local VP genius, developed a spreadsheet based upon
the Sorokin formula which he has used for several of his articles in
Video Poker Times. (The similarity of names is purely coincidental.
Both are common family names in Russia.)

The Sorokin formula is used for the Risk of Ruin feature in the
soon-to-be-released program for both Macintosh and Windows, Optimum
Video Poker.

Dan

···

--

Dan Paymar, author of the book, "Video Poker - Optimum Play"
Editor and Publisher of "Video Poker Times" newsletter
Web site at http://www.OptimumPlay.com

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

[Non-text portions of this message have been removed]

[Harry_Porter]

Dan Paymar wrote:
It should confess that I chose to look at the problem of the
applicability of variance and std. dev. to video poker using the 1997
Dunbar formula because it was more expedient than the subsequent
Sorokin formula which Dan detailed in an article which can be found on
his website.

The latter formula requires an interative method to be used to
determine risk of ruin and I lacked access to a spreadsheet that would
facilitate this (I'll own up to being a little too lazy to take the
time to set one up myself). I've reasoned, with a fair degree of
confidence, that under the rationale I discussed that standard
deviation was more likely to be a directly proportional to the Risk of
Ruin of two games, and that variance was likely to be directly
proportional to the bankroll requirements of two games. (Note that
this is under the condition that returns are equivalent. Obviously
that is generally not the case, however, using a two-step method these
relationships for s.d. and var can be demonstrated.)

I'll add a disclaimer that I hardly consider myself to be as qualified
in this examination as those who have more experience in this matter,
which is why I've sought their input.

- Harry

···

Dunbar, along with Jeff B., later wrote an article published in the
Fall, 1999 issue of Blackjack Forum entitled "Risk of ruin for video
poker and other skewed-up games." The main thrust of that article
was to give the derivation of the now-famous Sorokin formula, named
for its developer, Russian mathematician Evgeny Sorokin, and to show
why that formula is much more suited to video poker than any other
method. (Jazbo published essentially the same formula a few months
earlier, as reported in the March/April 1999 issue of Video Poker
Times. It is not clear whether Jazbo got the formula from Sorokin or
derived it himself.)

Yuri Sorkin, our local VP genius, developed a spreadsheet based upon
the Sorokin formula which he has used for several of his articles in
Video Poker Times. (The similarity of names is purely coincidental.
Both are common family names in Russia.)

The Sorokin formula is used for the Risk of Ruin feature in the
soon-to-be-released program for both Macintosh and Windows, Optimum
Video Poker.