 
| ||
|
|
|
DON JOHNSON: COULD HE HAVE WON MORE?–PART 3
by Eliot Jacobson, Ph.D.
For 25 years, Dr. Jacobson has held positions as professor of mathematics and professor of computer science. With dozens of research articles, publications, and media appearances, Dr. Jacobson is widely recognized as one of the world's top experts on casino table games and casino game mathematics. His web site is
www.apheat.net, which contains the latest information on beatable casino table games, side bets, and promotions.Editor’s Note: In a series of articles in the BJI (issues 138 and 139), our contributing writers analyzed how Don Johnson exploited several Atlantic City casinos’ loss-rebate programs to win millions. The following is Part 3 of a three-part series of articles reprinted with permission from Dr. Jacobson, showing his recent analysis of how Johnson accomplished this. Part 1 appeared in BJI #161 and Part 2 in BJI $162.
When Don Johnson (DJ) beat several East Coast casinos in late 2011 through early 2012 by exploiting their loss rebate programs, few understood the scope of his triumph. After his success, there were a number of articles (for example,
this article in Atlantic Magazine) that tried to explain his success as a mix of luck and experience. Several other articles produced mathematical analyses that did not directly address the main questions. As I described in this post, DJ succeeded because there was an off-the-top profit to be made simply by playing within the constraints he negotiated and strategically choosing quit points. The question I pose in this post is if DJ could have done even better?At the
World Game Protection Conference, DJ stated that there were three constraints on his play.- He had to place one million ($1,000,000) dollars cash in the cage.
- He was allowed to wager a maximum of $100,000 per hand.
- If he lost $500,000 or more in a day, he could stop playing and get a 20% rebate on the totality of his losses for the day.
The common wisdom in the aftermath of DJ’s success was that DJ should play until he either lost or won $500,000, then quit for the day. As I showed in my previous post, this "wisdom" about optimal stopping points is patently false. With a one million dollar starting bankroll, DJ’s optimal quit points were to stop when his current bankroll was either less than $200,000 (quit-loss) or after winning $2,000,000 (quit-win).
With these stopping points:
- DJ’s average edge over the house was 0.63%.
- DJ’s expected total win per day was $85,800.
- DJ’s expected number of hands per day was 137.
Yesterday, I realized that there was a hidden assumption in my analysis: that Don Johnson must deposit exactly $1,000,000, no more, no less. As I researched this assumption online, I could find no evidence in any of the multitude of media articles about DJ that he ever deposited more than $1,000,000. Did he? I don’t know. Regardless, the question is if he could have won even more by strategically sizing his deposits to reflect specific market conditions.
To be precise, suppose that in addition to the two strategic decisions (quit-win, quit-loss) DJ could make about when to stop for the day, there was a third decision he could make as well: the size of his starting bankroll. What if the requirement for DJ was not that he place exactly one million dollars in the cage, but instead the requirement was that DJ place at least one million dollars in the cage? Was his deposit amount a variable under his control? Could DJ have made even more by depositing an optimal amount in the cage?
Here is the setup for DJ’s optimization problem:
- DJ’s starting bankroll per day was at least $1,000,000.
- DJ was allowed to wager $100,000 per hand.
- DJ was given a 20% rebate on his full losses if he lost at least $500,000 in a day.
Given these constraints, what are the appropriate bankroll, quit-loss and quit-win points to maximize DJ’s daily net income?
To answer this question, I ran a bunch of simulations...
...enter your member login information below to read this article/newsletter...
Paid Members-Only Article
You have clicked on a link to a Blackjack Insider web page or article for paid subscribers. You must have a paid membership to the Blackjack Insider newsletter to view this content. About 1/2 of the articles in each issue of the Blackjack Insider are for paid members only, while the rest are viewable by everyone. Your purchased membership will allow you to read all Blackjack Insider articles for 12 months.
Enter your user name and password below (they were listed and e-mailed to you after you purchased your Blackjack Insider membership):
Forgot your membership id or password? Click here.
How do I get a membership?
A membership can be purchased online at our secure store with your credit card for only $19.95 per year. You will receive a user name and password immediately by e-mail which you can use to read the all past and future members-only articles for 12 months, as well as the regular free articles.
CLICK HERE TO PURCHASE A ONE YEAR MEMBERSHIP NOW... only $19.95
Do I have to buy a membership?
No. Blackjack Insider will continue to be published as a free monthly e-newsletter. But about 1/2 of the articles each month will be for paid members only. Subscribers without a membership can still view and read the non-members articles for free.
What happens after I buy a membership?
Immediately after you complete your purchase, you will receive a unique login user name and password. These are displayed on the final purchase page, and are e-mailed to you. When you click on a members-only article in our web site, you will be prompted for this user name and password (as shown above). Simply enter them, and enjoy the article! Note: make sure you turn on the checkbox above when you login, to save the user name and password so that you don't have to re-enter them every time you view members-only articles.
Why did you switch to paid memberships?
Blackjack Insider is a professional monthly publication with top-notch articles by world-reknown gaming experts. In addition, we have regular reporters that monitor game conditions and tournament schedules throughout North America. We use a partially paid subscriber model to enable us to continue getting the best content for our readers from leading authors on blackjack and gaming.
|
|
©2015, DeepNet Technologies. No material to be copied without express permission of DeepNet Technologies.
This site developed by
DeepNet Technologies, Ontario, Canada. Contact webmaster @ bjinsider . com
if you have problems.
This site is best viewed in a 800x600 graphics mode, or higher.