Man wins 15 million in AC over 6 months

[Sinatra1]

There was a story on most of the Philly news last nite about a man who has won over 15 million playing BJ in AC. The Trop reported that he has won $1.8 million from them. Here is a link. http://www.kmov.com/news/off-beat/Man-wins-millions-after-years-of-gambling-122433389.html

So much for the theory by all the nit wits that they can't be beat. Maybe Dweezel wants to wait another 6 months, before he believes it can be done. Once you win $15 million whats left, just retire.

[Guest]

There was a story on most of the Philly news last nite about a man who has won over 15 million playing BJ in AC. The Trop reported that he has won $1.8 million from them. Here is a link. http://www.kmov.com/news/off-beat/Man-wins-millions-after-years-of-gambling-122433389.html

So much for the theory by all the nit wits that they can't be beat. Maybe Dweezel wants to wait another 6 months, before he believes it can be done. Once you win $15 million whats left, just retire.

Ha, "a run of good luck". That is what I used to tell them. This guy has got the formula. That reminds me: I was going to give you some tips on keeping from getting barred:

Once you are winning consistently whether BJ, Bac or both:

1. Move around a lot. Don't pick on the same casinos like Johnson did.

2. Stick to small units, Don't excede $100 or $200 units.

3. Always act and talk like you are amazed at your good luck. "This is the best run of luck I've ever had!"

This will hold them off for a while. But to keep from getting barred forever try to get a newspaper article printed about your successes.

See, NOW they can NEVER bar Johnson no matter what his unit size. It would make too big a splash in the newspapers.

Oh, and by the way, there is no such thing as a run of luck THAT good. This guy KNOWS what he is doing. And yes, it proves it CAN be done!

Edited May 24, 2011 by Guest

[TomM]

Here is a link too another story on that guy from the press of Atlantic City. com including a picture that is more comprehensive, courtesy of someone at BF.

http://www.pressofatlanticcity.com/news/breaking/meet-the-blackjack-player-who-beat-the-trop-for-million/article_86f42838-83c8-11e0-92d7-001cc4c03286.html

Didn't blow it all on clothes and bling-bling I guess.

[Guest]

Well unfortunately many casinos barred him BEFORE he became newspaper savvy. Just goes to show you they will bar anyone who consistently beats them, card counter or not. Best is to play under the radar as much as possible and for small units.

But right, it sure blows a 15 million dollar hole right through Dweezrl's theories doesn't it. Do you suppose Johnson ran a few 100,000 shoe tests first?

Edited May 24, 2011 by Guest

[epstein]

Don Johnson won nearly $6 million playing blackjack in one night, single-handedly decimating the monthly revenue of Atlantic City’s Tropicana casino. Not long before that, he’d taken the Borgata for $5 million and Caesars for $4 million. Here’s how he did it.

DON JOHNSON FINDS IT HARD to remember the exact cards. Who could? At the height of his 12-hour blitz of the Tropicana casino in Atlantic City, New Jersey, last April, he was playing a hand of blackjack nearly every minute.

Dozens of spectators pressed against the glass of the high-roller pit. Inside, playing at a green-felt table opposite a black-vested dealer, a burly middle-aged man in a red cap and black Oregon State hoodie was wagering $100,000 a hand. Word spreads when the betting is that big. Johnson was on an amazing streak. The towers of chips stacked in front of him formed a colorful miniature skyline. His winning run had been picked up by the casino’s watchful overhead cameras and drawn the close scrutiny of the pit bosses. In just one hand, he remembers, he won $800,000. In a three-hand sequence, he took $1.2 million.

The basics of blackjack are simple. Almost everyone knows them. You play against the house. Two cards are placed faceup before the player, and two more cards, one down, one up, before the dealer. A card’s suit doesn’t matter, only its numerical value—each face card is worth 10, and an ace can be either a one or an 11. The goal is to get to 21, or as close to it as possible without going over. Scanning the cards on the table before him, the player can either stand or keep taking cards in an effort to approach 21. Since the house’s hand has one card facedown, the player can’t know exactly what the hand is, which is what makes this a game.

As Johnson remembers it, the $800,000 hand started with him betting $100,000 and being dealt two eights. If a player is dealt two of a kind, he can choose to “split†the hand, which means he can play each of the cards as a separate hand and ask for two more cards, in effect doubling his bet. That’s what Johnson did. His next two cards, surprisingly, were also both eights, so he split each again. Getting four cards of the same number in a row doesn’t happen often, but it does happen. Johnson says he was once dealt six consecutive aces at the Mohegan Sun casino in Connecticut. He was now playing four hands, each consisting of a single eight-card, with $400,000 in the balance.

He was neither nervous nor excited. Johnson plays a long game, so the ups and downs of individual hands, even big swings like this one, don’t matter that much to him. He is a veteran player. Little interferes with his concentration. He doesn’t get rattled. With him, it’s all about the math, and he knows it cold. Whenever the racily clad cocktail waitress wandered in with a fresh whiskey and Diet Coke, he took it from the tray.

The house’s hand showed an upturned five. Arrayed on the table before him were the four eights. He was allowed to double down—to double his bet—on any hand, so when he was dealt a three on the first of his hands, he doubled his bet on that one, to $200,000. When his second hand was dealt a two, he doubled down on that, too. When he was dealt a three and a two on the next two hands, he says, he doubled down on those, for a total wager of $800,000.

It was the dealer’s turn. He drew a 10, so the two cards he was showing totaled 15. Johnson called the game—in essence, betting that the dealer’s down card was a seven or higher, which would push his hand over 21. This was a good bet: since all face cards are worth 10, the deck holds more high cards than low. When the dealer turned over the house’s down card, it was a 10, busting him. Johnson won all four hands.

Johnson didn’t celebrate. He didn’t even pause. As another skyscraper of chips was pushed into his skyline, he signaled for the next hand. He was just getting started.

The headline in The Press of Atlantic City was enough to gladden the heart of anyone who has ever made a wager or rooted for the underdog:

BLACKJACK PLAYER TAKES TROPICANA

FOR NEARLY $6 MILLION,

SINGLE-HANDEDLY RUINS CASINO’S MONTH

But the story was even bigger than that. Johnson’s assault on the Tropicana was merely the latest in a series of blitzes he’d made on Atlantic City’s gambling establishments. In the four previous months, he’d taken $5 million from the Borgata casino and another $4 million from Caesars. Caesars had cut him off, he says, and then effectively banned him from its casinos worldwide.

Fifteen million dollars in winnings from three different casinos? Nobody gets that lucky. How did he do it?

The first and most obvious suspicion was card counting. Card counters seek to gain a strong advantage by keeping a mental tally of every card dealt, and then adjusting the wager according to the value of the cards that remain in the deck. (The tactic requires both great memory and superior math skills.) Made famous in books and movies, card counting is considered cheating, at least by casinos. In most states (but not New Jersey), known practitioners are banned. The wagering of card counters assumes a clearly recognizable pattern over time, and Johnson was being watched very carefully. The verdict: card counting was not Don Johnson’s game. He had beaten the casinos fair and square.

It hurt. Largely as a result of Johnson’s streak, the Trop’s table-game revenues for April 2011 were the second-lowest among the 11 casinos in Atlantic City. Mark Giannantonio, the president and CEO of the Trop, who had authorized the $100,000-a-hand limit for Johnson, was given the boot weeks later. Johnson’s winnings had administered a similar jolt to the Borgata and to Caesars. All of these gambling houses were already hurting, what with the spread of legalized gambling in surrounding states. By April, combined monthly gaming revenue had been declining on a year-over-year basis for 32 months.

For most people, though, the newspaper headline told a happy story. An ordinary guy in a red cap and black hoodie had struck it rich, had beaten the casinos black-and-blue. It seemed a fantasy come true, the very dream that draws suckers to the gaming tables.

But that’s not the whole story either.

DESPITE HIS PEDESTRIAN ATTIRE, Don Johnson is no average Joe. For one thing, he is an extraordinarily skilled blackjack player. Tony Rodio, who succeeded Giannantonio as the Trop’s CEO, says, “He plays perfect cards.†In every blackjack scenario, Johnson knows the right decision to make. But that’s true of plenty of good players. What gives Johnson his edge is his knowledge of the gaming industry. As good as he is at playing cards, he turns out to be even better at playing the casinos.

Hard times do not favor the house. The signs of a five-year slump are evident all over Atlantic City, in rundown façades, empty parking lots, and the faded glitz of its casinos’ garish interiors. Pennsylvania is likely to supplant New Jersey this year as the second-largest gaming state in the nation. The new Parx racetrack and casino in Bensalem, Pennsylvania, a gigantic gambling complex, is less than 80 miles away from the Atlantic City boardwalk. Revenue from Atlantic City’s 11 casinos fell from a high of $5.2 billion in 2006 to just $3.3 billion last year. The local gaming industry hopes the opening of a 12th casino, Revel, this spring may finally reverse that downward trend, but that’s unlikely.

“It doesn’t matter how many casinos there are,†Israel Posner, a gaming-industry expert at nearby Stockton College, told me. When you add gaming tables or slots at a fancy new venue like Revel, or like the Borgata, which opened in 2003, the novelty may initially draw crowds, but adding gaming supply without enlarging the number of customers ultimately hurts everyone.

When revenues slump, casinos must rely more heavily on their most prized customers, the high rollers who wager huge amounts—tens of thousands or even hundreds of thousands of dollars a hand. Hooking and reeling in these “whales,†as they are known in the industry, can become essential. High rollers are lured with free meals and drinks, free luxury suites, free rides on private jets, and … more. (There’s a reason most casino ads feature beautiful, scantily clad young women.) The marketers present casinos as glamorous playgrounds where workaday worries and things like morality, sobriety, and prudence are on holiday. When you’re rich, normal rules don’t apply! The idea, like the oldest of pickpocket tricks, is to distract the mark with such frolic that he doesn’t notice he’s losing far more than his free amenities actually cost. For what doth it profit a man to gain a $20,000 ride on a private jet if he drops $200,000 playing poker? The right “elite player†can lose enough in a weekend to balance a casino’s books for a month.

Of course, high rollers “are not all created equally,†says Rodio, the Tropicana’s CEO. (He was the only Atlantic City casino executive who agreed to talk to me about Johnson.) “When someone makes all the right decisions, the house advantage is relatively small; maybe we will win, on average, one or two hands more than him for every hundred decisions. There are other blackjack players, or craps players, who don’t use perfect strategy, and with them there is a big swing in the house advantage. So there is more competition among casinos for players who aren’t as skilled.â€

For the casino, the art is in telling the skilled whales from the unskilled ones, then discouraging the former and seducing the latter. The industry pays close attention to high-level players; once a player earns a reputation for winning, the courtship ends. The last thing a skilled player wants is a big reputation. Some wear disguises when they play.

But even though he has been around the gambling industry for all of his 49 years, Johnson snuck up on Atlantic City. To look at him, over six feet tall and thickly built, you would never guess that he was once a jockey. He grew up tending his uncle’s racehorses in Salem, Oregon, and began riding them competitively at age 15. In his best years as a professional jockey, he was practically skeletal. He stood 6 foot 1 and weighed only 108 pounds. He worked with a physician to keep weight off, fighting his natural growth rate with thyroid medication that amped up his metabolism and subsisting on vitamin supplements. The regimen was so demanding that he eventually had to give it up. His body quickly assumed more normal proportions, and he went to work helping manage racetracks, a career that brought him to Philadelphia when he was about 30. He was hired to manage Philadelphia Park, the track that evolved into the Parx casino, in Bensalem, where he lives today. Johnson was in charge of day-to-day operations, including the betting operation. He started to learn a lot about gambling.

It was a growth industry. Today, according to the American Gaming Association, commercial casino gambling—not including Native American casinos or the hundreds of racetracks and government-sponsored lotteries—is a $34 billion business in America, with commercial casinos in 22 states, employing about 340,000 people. Pari-mutuel betting (on horse racing, dog racing, and jai alai) is now legal in 43 states, and online gaming netted more than $4 billion from U.S. bettors in 2010. Over the past 20 years, Johnson’s career has moved from managing racetracks to helping regulate this burgeoning industry. He has served as a state regulator in Oregon, Idaho, Texas, and Wyoming. About a decade ago, he founded a business that does computer-assisted wagering on horses. The software his company employs analyzes more data than an ordinary handicapper will see in a thousand lifetimes, and defines risk to a degree that was impossible just five years ago.

Johnson is not, as he puts it, “naive in math.â€

He began playing cards seriously about 10 years ago, calculating his odds versus the house’s.

Compared with horse racing, the odds in blackjack are fairly straightforward to calculate. Many casinos sell laminated charts in their guest shops that reveal the optimal strategy for any situation the game presents. But these odds are calculated by simulating millions of hands, and as Johnson says, “I will never see 400 million hands.â€

More useful, for his purposes, is running a smaller number of hands and paying attention to variation. The way averages work, the larger the sample, the narrower the range of variation. A session of, say, 600 hands will display wider swings, with steeper winning and losing streaks, than the standard casino charts. That insight becomes important when the betting terms and special ground rules for the game are set—and Don Johnson’s skill at establishing these terms is what sets him apart from your average casino visitor.

Johnson is very good at gambling, mainly because he’s less willing to gamble than most. He does not just walk into a casino and start playing, which is what roughly 99 percent of customers do. This is, in his words, tantamount to “blindly throwing away money.†The rules of the game are set to give the house a significant advantage. That doesn’t mean you can’t win playing by the standard house rules; people do win on occasion. But the vast majority of players lose, and the longer they play, the more they lose.

Sophisticated gamblers won’t play by the standard rules. They negotiate. Because the casino values high rollers more than the average customer, it is willing to lessen its edge for them. It does this primarily by offering discounts, or “loss rebates.†When a casino offers a discount of, say, 10 percent, that means if the player loses $100,000 at the blackjack table, he has to pay only $90,000. Beyond the usual high-roller perks, the casino might also sweeten the deal by staking the player a significant amount up front, offering thousands of dollars in free chips, just to get the ball rolling. But even in that scenario, Johnson won’t play. By his reckoning, a few thousand in free chips plus a standard 10 percent discount just means that the casino is going to end up with slightly less of the player’s money after a few hours of play. The player still loses.

But two years ago, Johnson says, the casinos started getting desperate. With their table-game revenues tanking and the number of whales diminishing, casino marketers began to compete more aggressively for the big spenders. After all, one high roller who has a bad night can determine whether a casino’s table games finish a month in the red or in the black. Inside the casinos, this heightened the natural tension between the marketers, who are always pushing to sweeten the discounts, and the gaming managers, who want to maximize the house’s statistical edge. But month after month of declining revenues strengthened the marketers’ position. By late 2010, the discounts at some of the strapped Atlantic City casinos began creeping upward, as high as 20 percent.

“The casinos started accepting more risk, looking for a possible larger return,†says Posner, the gaming-industry expert. “They tended to start swinging for the fences.â€

Johnson noticed.

“They began offering deals that nobody’s ever seen in New Jersey history,†he told me. “I’d never heard of anything like it in the world, not even for a player like [the late Australian media tycoon] Kerry Packer, who came in with a $20 million bank and was worth billions and billions.â€

When casinos started getting desperate, Johnson was perfectly poised to take advantage of them. He had the money to wager big, he had the skill to win, and he did not have enough of a reputation for the casinos to be wary of him. He was also, as the Trop’s Tony Rodio puts it, “a cheap date.†He wasn’t interested in the high-end perks; he was interested in maximizing his odds of winning. For Johnson, the game began before he ever set foot in the casino.

ATLANTIC CITY DID KNOW who Johnson was. The casinos’ own research told them he was a skilled player capable of betting large amounts. But he was not considered good enough to discourage or avoid.

In fact, in late 2010, he says, they called him.

Johnson had not played a game at the Borgata in more than a year. He had been trying to figure out its blackjack game for years but had never been able to win big. At one point, he accepted a “lifetime discount,†but when he had a winning trip he effectively lost the benefit of the discount. The way any discount works, you have to lose a certain amount to capitalize on it. If you had a lifetime discount of, say, 20 percent on $500,000, you would have to lose whatever money you’d made on previous trips plus another $500,000 before the discount kicked in. When this happened to Johnson, he knew the ground rules had skewed against him. So it was no longer worth his while to play there.

He explained this when the Borgata tried to entice him back.

“Well, what if we change that?†he recalls a casino executive saying. “What if we put you on a trip-to-trip discount basis?â€

Johnson started negotiating.

Once the Borgata closed the deal, he says, Caesars and the Trop, competing for Johnson’s business, offered similar terms. That’s what enabled him to systematically beat them, one by one.

In theory, this shouldn’t happen. The casinos use computer models that calculate the odds down to the last penny so they can craft terms to entice high rollers without forfeiting the house advantage. “We have a very elaborate model,†Rodio says. “Once a customer comes in, regardless of the game they may play, we plug them into the model so that we know what the house advantage is, based upon the game that they are playing and the way they play the game. And then from that, we can make a determination of what is the appropriate [discount] we can make for the person, based on their skill level. I can’t speak for how other properties do it, but that is how we do it.â€

So how did all these casinos end up giving Johnson what he himself describes as a “huge edge� “I just think somebody missed the math when they did the numbers on it,†he told an interviewer.

Johnson did not miss the math. For example, at the Trop, he was willing to play with a 20 percent discount after his losses hit $500,000, but only if the casino structured the rules of the game to shave away some of the house advantage. Johnson could calculate exactly how much of an advantage he would gain with each small adjustment in the rules of play. He won’t say what all the adjustments were in the final e-mailed agreement with the Trop, but they included playing with a hand-shuffled six-deck shoe; the right to split and double down on up to four hands at once; and a “soft 17†(the player can draw another card on a hand totaling six plus an ace, counting the ace as either a one or an 11, while the dealer must stand, counting the ace as an 11). When Johnson and the Trop finally agreed, he had whittled the house edge down to one-fourth of 1 percent, by his figuring. In effect, he was playing a 50-50 game against the house, and with the discount, he was risking only 80 cents of every dollar he played. He had to pony up $1 million of his own money to start, but, as he would say later: “You’d never lose the million. If you got to [$500,000 in losses], you would stop and take your 20 percent discount. You’d owe them only $400,000.â€

In a 50-50 game, you’re taking basically the same risk as the house, but if you get lucky and start out winning, you have little incentive to stop.

So when Johnson got far enough ahead in his winning sprees, he reasoned that he might as well keep playing. “I was already ahead of the property,†he says. “So my philosophy at that point was that I can afford to take an additional risk here, because I’m battling with their money, using their discount against them.â€

According to Johnson, the Trop pulled the deal after he won a total of $5.8 million, the Borgata cut him off at $5 million, and the dealer at Caesars refused to fill the chip tray once his earnings topped $4 million.

“I was ready to play on,†Johnson said. “And I looked around, and I said, ‘Are you going to do a fill?’ I’ve got every chip in the tray. I think I even had the $100 chips. ‘Are you guys going to do a fill?’ And they just said, ‘No, we’re out.’â€

He says he learned later that someone at the casino had called the manager, who was in London, and told him that Don Johnson was ahead of them “by four.â€

“Four hundred thousand?†the manager asked.

“No, 4 million.â€

So Caesars, too, pulled the plug. When Johnson insisted that he wanted to keep playing, he says, the pit boss pointed out of the high-roller pit to the general betting floor, where the game was governed by normal house rules.

“You can go out there and play,†he said.

Johnson went upstairs and fell asleep.

These winning streaks have made Johnson one of the best-known gamblers in the world. He was shocked when his story made the front page of The Press of Atlantic City. Donald Wittkowski, a reporter at the newspaper, landed the story when the casinos filed their monthly revenue reports.

“I guess for the first time in 30 years, a group of casinos actually had a huge setback on account of one player,†Johnson told me. “Somebody connected all the dots and said it must be one guy.â€

The Trop has embraced Johnson, inviting him back to host a tournament—but its management isn’t about to offer him the same terms again. (Even so—playing by the same rules he had negotiated earlier, according to Johnson, but without a discount—he managed to win another $2 million from the Tropicana in October.)

“Most properties in Atlantic City at this point won’t even deal to him,†Rodio says. “The Tropicana will continue to deal to him, we will continue to give aggressive limits, take care of his rooms and his accounts when he is here. But because he is so far in front of us, we have modified his discounts.â€

JOHNSON SAYS HIS LIFE hasn’t really changed all that much. He hasn’t bought himself anything big, and still lives in the same house in Bensalem. But in the past year, he has hung out with Jon Bon Jovi and Charlie Sheen, sprayed the world’s most expensive bottle of champagne on a crowd of clubgoers in London, and hosted a Las Vegas birthday bash for Pamela Anderson. He is enjoying his fame in gambling circles, and has gotten used to flying around the world on comped jets. Everybody wants to play against the most famous blackjack player in the world.

But from now on, the casinos will make sure the odds remain comfortably stacked against him.

[epstein]

Don Johnson #2: How He Beat Blackjack

When DJ smoothly quoted the exact house advantage of one of the blackjack games he played (0.263%), he removed all doubt.

If you have not yet seen it, I recommend this video produced by Bloomberg [added 01/14]. It gives a good feeling for who Don Johnson is, as a person. Factually, it is better than most mass consumption articles on gambling, but still falls very short from giving any real explanation for what happened.

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. This simulation actually modeled a shoe-game that used a cut card with the rules listed above. It is a bit of arcane science, but when the dealer uses a cut card, the edge moves slightly towards the house side (the so-called “cut card effectâ€). In the case of this game, the edge is about 0.29% using a cut card. For more details, I refer you to

http://wizardofodds.com/games/blackjack/appendix/4/

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. In the results below, I assumed $1,000,000 put in the cage, no more, no less. In my next article on Don Johnson (see this post), I waive this requirement as well to find Johnson’s optimal win-rate based on unrestricted win/loss-quit points.

Here are the optimal stopping points and other pertinent data when wagering $100,000 per hand, assuming $1,000,000 in the cage:

Stop when the current bankroll is less than $200,000 (losing more than $800,000).

Stop after winning $2,000,000.

The player edge is 0.63%.

The average total win is $85,800.

The average number of hands is 136.9.

Here are the optimal stopping points and other pertinent data when wagering $50,000 per hand:

Stop when the current bankroll is less than $100,000 (losing more than $900,000).

Stop after winning $1,200,000.

The player edge is 0.34%.

The average total win is $59,900.

The average number of hands is 350.3.

There is another approach to this analysis. Suppose DJ plays without stopping points, but instead pre-determines the number of hands he is going to play per day and sticks to that number, no matter what. Subject to a fixed number of hands, what number of hands would maximize DJ’s winnings?

In this case, the analysis is nearly exact. The methodology is described in the book “Casino Operations Management,†chapter 15. I previously wrote a version of this analysis for my own consulting work and that’s what I used to model DJ here. I simply input his loss rebate parameters and manually tried various numbers of hands until I found his maximum win.

The following table gives the optimal “number of hands†stopping point for a $100,000 wager:

With a $100,000 flat-bet and a “number of hands†stopping point, DJ should play exactly 393 hands per day. In this case, DJ would average winning $83,101 per day, with an average edge of 0.211% over the house.

The following table gives the optimal “number of hands†stopping point for a $50,000 wager:

With a $50,000 flat-bet and a “number of hands†stopping point, DJ should play exactly 432 hands per day. In this case, DJ would average winning $35,356 per day, with an average edge of 0.164% over the house.

This data is not the end of the story to explain how DJ crushed the house. During his talk, DJ explained that he got $50,000 show-up money per day. He also stated that he crafted an extremely belligerent and obnoxious personality that pushed dealers and staff to the edge. He stated that this contributed to dealer errors and judgement calls made by floor staff. He estimated that he won an extra three units per day by virtue of his “act.†That amounted to either $150,000 or $300,000 based on his wager size (I take DJ at his word on this, I cannot verify these numbers).

Finally, DJ revealed that he had secret teammates. He said that the table limits were from a table minimum of $100 to his flat bet (either $50,000 or $100,000). Whenever the shoe went sufficiently negative, he would throw some sort of “fit†consistent with his act and stop playing. His teammates would then eat the remainder of the negative shoe. In this way, his play was the same as a card counter who effectively spread his bets from $100 to DJ’s maximum bet of either $50,000 or $100,000. I estimated DJ’s additional earnings per day from blackjack card counting by using the values given in this post. Using that analysis,

With a $50,000 bet, DJ had a theoretical win of about $26,000 per day from card counting.

With a $100,000 bet, DJ had a theoretical win of about $21,000 per day from card counting.

Taking all these sources of income into consideration, DJ’s expected earnings per day with a $50,000 flat-bet was approximately:

$60,000 + $50,000 + 3x$50,000 + $27,000 = $287,000.

DJ’s expected earnings per day with a $100,000 flat-bet was approximately:

$86,000 + $50,000 + 3x$100,000 +$21,000 = $457,000.

In the article in Atlantic Magazine, it appeared that DJ had been incredibly lucky to win as fast as he did. It is now clear that there was very little luck involved. DJ manipulated the “market conditions†he was provided to create conditions he could beat. DJ then consulted with his mathematical advisers to help create a strategy to optimize his return given all the available parameters of play. DJ then implemented his plan with an extraordinarily high level of talent that spanned every strategic and tactical nuance.

It is humbling, no matter which side of the tables you play, to witness this level of skill, planning and execution. The casinos in Atlantic City didn’t stand a chance.

http://http://apheat.net/2013/05/02/don-johnson-2-how-he-beat-blackjack/

[epstein]

the video from bloomberg

http://www.bloomberg.com/video/the-player-secrets-of-a-vegas-whale-p5Yp8AANTVeqa1_MXspl5A.html

[Guest]

Well interesting but.....

DJ does not count cards. He is therefore an NBJ player.

A good NBJ player KNOWS within the first few hands if his table is beatable or not.

If not, Johnson can simply leave the table. The casino is going to partially cover his losses at such tables anyway.

But, at the stakes he plays, unlike us, he can also ask for new cards rather than leave.

This usually turns his losing table into a winning table because Basic Strategy works best in random cards and new cards are the most random they will ever be.

So it is all about only playing the tables you can beat which, in turn, is all about sticking to new cards. Get it?

Edited November 29, 2014 by Ellis