Blackjack newsletter and blackjack strategySubscribe to the Blackjack Insider newsletter

How to Win EVEN MORE Blackjack Tournaments - Volume II... only $14.95. Ken Smith's second e-book on tournament blackjack contains more of his winning strategies that have made him one of the best tournament blackjack players in the world.

Or, purchase both Volume I and Volume II together for $24.95... over 15% off!

NEW! Read how Ken used skill to win a recent blackjack tournament. Get his books and you could too!

How To Win EVEN MORE Blackjack Tournaments - Volume II
(web ads above removed with paid membership. Click here for advertisement rates)


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, 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 three-part article, reprinted with permission from Dr. Jacobson, is his recent analysis of how Johnson accomplished this.


When I heard Don Johnson (DJ) speak at the World Game Protection Conference last Tuesday, I expected him to dismiss his blackjack winnings as the result of a little bit of advantage play and a lot of luck. That’s how he portrayed events in this article in Atlantic Magazine. However, after his explanation of how he beat horse racing (see this post), there was little doubt about his skill as one of the world’s top advantage players. When DJ smoothly quoted the exact house advantage of one of the blackjack games he played (0.263%), he removed all doubt.

As DJ explained, the deal he negotiated in Atlantic City had the following terms:

  • DJ placed $1,000,000 in credit with the casino.
  • Any time DJ lost $500,000 in a day, he could stop playing and receive a 20% rebate on his loss.
  • He could place a maximum wager of $100,000. Some places, this maximum was $50,000.

In the casino-world, it is often the case that people state something "obvious" which is in no way "obvious" and is often just wrong. Such was the case in the aftermath of DJ’s slaughter. Almost everyone took it for granted that the best strategy was for DJ to play until he either won $500,000 or lost $500,000, then leave for the day. This "strategy" appears logically sound (if you’re not using any logic). But, strangely, it didn’t represent the actual course of events in DJ’s play. In fact, DJ played much longer on the days he was winning than this "strategy" dictated.  On losing days, DJ often endured a loss of more than $500,000. I decided to model the circumstances of DJ’s play to determine the optimal stopping points. What I found showed that DJ was right to continue playing well beyond the mythical  "stopping points" of +/- $500,000.

First, I fixed the game played. For top players, the following rules are standard on a shoe game:

  • Six decks
  • Dealer stands on soft 17
  • Player can double on any first two cards
  • Player can double after split
  • Player can re-split aces
  • Player can re-split to four hands
  • Late surrender

DJ certainly played this game. He may have played against other rule-sets, but he did not disclose those.

Next, I wrote a computer program that allowed me to do a Monte Carlo simulation of possible stopping strategies used by DJ.  I then ran 16 simulations for various stopping strategies (from a $500,000 win up to a $2,000,000 win) to determine the optimal stopping point (rounded to $100,000). Each of the 16 simulations consisted of modeling one hundred million (100,000,000) players using that stopping strategy, and averaging their results. The program’s output included the player’s edge over the house, the expected win for the player, and the average number of hands played by the player.

The following table gives the results of the analysis of the stopping points for DJ with a $100,000 flat wager:

These results show that the optimal stopping point for DJ was a win of $1,600,000 (not $500,000, as is popularly believed). DJ was playing with an overall edge of 0.93% over the house. DJ’s expected win was $61,786. The expected number of hands played was 66.1.

The following table gives the results of the analysis of the stopping points for DJ with a $50,000 flat wager:

In this case, the optimal stopping point for DJ was a win of $1,000,000. DJ was playing with an overall edge of 0.58% over the house. DJ’s expected win was $46,852. The expected number of hands played was 160.2.

At this point you may also wonder at the credibility of stopping with a loss of $500,000, and you would be right. Once again, popular belief is misguided. After DJ lost $500,000, he is essentially playing with a discount of 20% on every bet he makes, since he no longer has to qualify for his loss discount. The only constraint is that DJ should keep enough to make a double down or split ($200,000 with a $100,000 bet and $100,000 with a $50,000 bet). DJ clearly stated in the talk that on several occasions he lost more than $500,000 before quitting for the day. Do you think DJ knew what he was doing?

With two degrees of freedom (high and low stopping points), I re-did the analysis given in the tables above. Essentially, I fiddled with a lot of simulations. Here are the optimal stopping points and other pertinent data when wagering $100,000 per hand...

...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):

User name:
Password: (case sensitive)
Save user name and password in your browser so you don't have to type them again later

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.


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.