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This distribution gives a house edge of 0. In the actual blackjack game that Johnson played, outcomes cover the entire range from winning 8 units to losing 8 units, after splits, doubles and surrender are taken into consideration.

The correct house edge is 0. It follows that the authors used a distribution whose standard deviation was substantially smaller than the actual standard deviation for blackjack. It appears the authors did not investigate the exact blackjack rules that Don Johnson played against.

Had they made this effort, the authors could have gotten the correct distribution for their blackjack simulations with a simple Google search, which would have led them to the wizardofodds. com website. This search would have led them to use an accurate blackjack model.

In fact, by doing so, the casino effectively relinquished what little house edge they had over a player who made the right choices. In blackjack, it actually serves the casino more to have higher betting limits because when players lose big, they would eventually stop playing in order to at least shore up their losses.

But with discounts on losses, players will keep on playing. Today, Don Johnson has been banned from almost all of the casinos in Atlantic City and Las Vegas.

The small number of casinos that agrees to let him play has put betting limitations on games. Discounts are likewise no longer offered to him.

Now it is time to visit one of the best online casinos for blackjack. There are two black jack cards, spades and clubs. In card room circles or home games, the jack of spades is nicknamed Ogier. And the jack of clubs is called Pam. Welcome to Blackjack Pam, your online blackjack resource.

The content of this website is only for information about blackjack.

Some content is only viewable by ASA Members. Please login or become an ASA member to gain access. I saw the title of this article when I did a recent Google search and I immediately wrote to the authors to request a copy.

They were very kind to quickly write back and forward a copy. Many thanks to the authors for their speedy generosity. Unfortunately, I discovered that their article is seriously flawed in both fact and methodology.

These are highly non-optimal boundary conditions. In personal communications, Johnson stated that my results above are consistent with those obtained by his mathematicians. In an interview with The Atlantic , Johnson described how the casinos gave him a 20 percent discount on his losses and slightly more favorable house rules that let him break the bank.

Perks for high rollers, like free hotel stays and trips on jets, are not new to gambling houses. But two years ago with revenues tanking in an unstable market, casinos became desperate to attract big spenders, to the point that they began calling to invite Johnson, a known player, to play in late with special deals.

Johnson admitted to The Press of Atlantic City , taking some losses along the way. The year-old resident of Bensalem, Pa. His profession is gambling-related as chief executive officer of Heritage Development LLC, which develops computer-assisted wagering systems for horseracing.

His prowess in blackjack, he says, has gotten him banned from some casinos. Johnson said he did not count cards, which is considered cheating and will get you banned from some casinos, but not illegal.

Blackjack players with a trained memory and enough acuity can keep track of which cards have been played and which are still in the deck, thereby maximizing their chances for beating the house. Explains Richard, a former card counter who today works on Wall Street and who asks that his last name not be used , "As the composition of the cards in the deck fluctuates, the player's advantage fluctuates.

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 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. bettors in 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. 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. 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, hands will display wider swings, with steeper winning and losing streaks, than the standard casino charts.

He does not just walk into a casino and start playing, which is what roughly 99 percent of customers do. But the vast majority of players lose, and the longer they play, the more they lose. They negotiate. Because the casino values high rollers more than the average customer, it is willing to lessen its edge for them.

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. 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.

By late , the discounts at some of the strapped Atlantic City casinos began creeping upward, as high as 20 percent. 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.

For Johnson, the game began before he ever set foot in the casino. A tlantic City did know who Johnson was. But he was not considered good enough to discourage or avoid.

In fact, in late , 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. The way any discount works, you have to lose a certain amount to capitalize on it.

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. 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.

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.

Johnson did not miss the math. Johnson could calculate exactly how much of an advantage he would gain with each small adjustment in the rules of play. 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 game against the house, and with the discount, he was risking only 80 cents of every dollar he played. So when Johnson got far enough ahead in his winning sprees, he reasoned that he might as well keep playing.

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.

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.