A card counting system is a valuable weapon in an advantage player’s bag of tricks. But a true advantage player understands EV and how to capitalize on a positive EV situation.
For a much more thorough breakdown, we have the following breakdown by Dr. Eliot Jacobson! Dr. Jacobson also provides a calculator that you can use to calculate the value of Loss Rebate opportunities.
“How Don Johnson Beat Blackjack Without Card Counting”
by Eliot Jacobson, Ph.D.
Don Johnson is arguably one of the most famous names in modern advantage play, with his triumphant slaughter of three Atlantic City casinos in late 2011 into early 2012. I was fortunate to hear Don Johnson speak at the
World Game Protection Conference in February, 2013. Though Johnson was short on details, it became apparent that the popular media got it completely wrong. Johnson was not some lucky high roller. He was not a party animal who rode good rules to a big profit. In his talk, Johnson smoothly quoted the house edge on the blackjack game he played (0.263%). What “lucky gambler” knows that information? He stated that he had used Ph.D. mathematicians (plural) to help develop his strategy. He discussed a job history that included running a profitable horse racing syndicate. That was enough for me. He was the real deal.
I thought, “I’m a Ph.D. mathematician; I can do that!” I got to work to figure out how Don Johnson did it. The main advantage that Johnson negotiated was a “loss rebate.” Simply put, if he lost money during a trip, then a percentage of his losses would be returned. This is a common incentive for high-rollers, but it is usually accompanied by a requirement for a minimum amount of play. Typically the high-roller is required to play at least 12 hours to qualify for his rebate. This play requirement allows the casino to earn enough “theoretical win” to compensate for the cost of the rebates when they are given. What gave Johnson the edge was that his loss rebate incentive had no minimum play requirement. Here are the details:
The blackjack rules were 6 decks, DOA, DAS, S17, LSR, RSA, with a house edge of 0.263%.
The table maximum wager was $100,000.
Don Johnson could claim a 20% rebate on his losses any time he lost $500,000 or more.
There was no minimum play requirement.
The loss rebate reset every day.
It’s easy to see that this structure can be beaten. If Johnson simply quit for the day after either winning $500,000 or losing $500,000, then on his winning days he would keep the full amount, but on the losing days he would only lose $400,000 (after his 20% rebate). With a $100,000 wager, these quit points (winning or losing 5 units) would likely occur after just a few hands. But blackjack is so close to an even game that playing a few hands is about the same as a coin-flip. It follows that with this trivial strategy Johnson would win, on average, slightly less than $50,000 per day. But could he do better? The key to optimizing Johnson’s winnings was to determine his best “win/loss quit points.” These are the profit-maximizing win/loss dollar values at which Don Johnson would leave for the day and either keep his winnings or collect his rebate. I dusted off my old “Stochastic Processes” book from graduate school and soon proved a sequence of three theorems I call the “Loss Rebate Theorems” (see
this post for a summary). These theorems led to an easy to use spreadsheet solution that you can download. This spread sheet can be used to analyze any loss rebate program, but is most accurate for those casino games with low volatility, for example, baccarat and blackjack. When the “Loss Rebate Theorem” spreadsheet was used to analyze Don Johnson’s 20% loss rebate program, assuming a $100,000 wager, it yielded the following:
Don Johnson should quit after winning $2,411,000.
Don Johnson should quit after losing $2,597,000.
The probability of hitting the win-quit point in any given session was 49.07%.
Don Johnson was playing with an effective edge over the house of about 0.26%.
On average, the number of expected rounds to reach a quit point was 481.
On average, the expected win per day for Don Johnson was $125,000.
In simpler terms, Don Johnson’s optimal strategy was to quit after either winning $2.4M or losing 2.6M. At an average pace of 100 hands per hour, his expected play time was just under 5 hours per day. His average daily win over the long run was about $125,000. To double check these theoretical results, I also ran a large number of Monte Carlo simulations. I considered various win/loss quit points and for each I simulated about a hundred million “Don Johnson’s.” After these simulations completed, I felt confident that the theoretical results given above were accurate.
I wrote an e-mail to Don Johnson, sharing my results. I was delighted when he responded to my e-mail, saying that my results were in agreement with those provided by his mathematicians. In addition to the loss rebate program above, Don Johnson piled on more positive expected value. First, Johnson negotiated $50,000 per day in “show-up” money. That is, by simply walking into the casino to play each day, he was given $50,000 cash. Taken together, the loss rebate program and show-up money yielded an expected cash profit of about $175,000 per day.
In a recent Bloomberg documentary, Johnson admitted to intentionally creating havoc at the tables to induce frequent dealer errors in his favor. At $100,000 per error, even two errors per day was another $200,000 in his favor. In a later personal email, Johnson admitted to me that he did “other things” (that I can’t disclose) as well.
Since completing my work on loss rebate advantage play, I have learned that beating loss rebates is at the top of ongoing advantage play opportunities. There are syndicates that fund temporary “high-rollers” to play against these programs. There are US-based players who use their overseas passports and pretend to be high-rollers coming to America to gamble. There are teams who scout incentive programs worldwide looking for any edge. If it is worth it, they will beat it. Indeed, on this very web page, Colin Jones stated, “He (Don Johnson) actually used a technique that we used to grow our first team’s bankroll massively in a short period.” My initial impression of Don Johnson at the World Game Protection Conference was that he was one of the best. In completing this research, the full scope of what Johnson achieved vastly exceeded my initial impression of him. Don Johnson is truly one of the top
advantage players of all time.
For more information on Don Johnson, loss rebates and other advantage play information, visit Dr. Jacobson’s blog, www.apheat.net. .