Blackjack Math

It’s fun to watch how Hollywood treats the card counters. Back in the 1950’s and 60’s, all the movie studios and TV stations applied a code. No-one could be shown getting away with a crime, ignoring the fact that counting cards never has been a crime. Everything had to reinforce the myth that crime does not pay. This meant that everyone who “cheated” had to be punished in some way. (more…)

Travel back in time a few decades and you will find the source of many modern myths. The most interesting swirl around the group of professional gamblers who devised the so-called basic strategy and those people, blessed with a good memory, that can beat the House by counting cards. Today’s wisdom says that putting the two together gives you the best chance of beating the house edge. There is some truth to this for those of you who go to real-world casinos. Indeed, many casinos actually sell small cards with the basic strategy printed in neat tables and charts. The original math wonks who crunched the numbers used to guard their knowledge and sell it only at high price. Today, the casinos effectively give it away. Why are the casinos so confident you will not break the bank? (more…)

For the majority going through school, the math classes are a form of slow torture. All these tiresome problems to solve and never any obvious relevance to real-world situations. Except, of course, that the theory of probabilities gives you everything you need to know about how to bet effectively. Once you can work out the odds on any given event occurring, you are ahead of the game when it comes to winning. In a sense, gambling is the application of science. But this slightly breaks down because knowing the odds does not guarantee you will win. The actual result of the event is still determined by events outside your ability to control. Whether you win is a matter of luck. So we might conclude that gambling in general is a mixture of science and intangibles like intuition. (more…)

There’s a sad fact about playing in a casino, whether real or virtual. The operators have worked out how to play the games on offer and set the odds to favor themselves. After all, if the majority did not lose, there would be no money to pay out all the money you win. Needless to say, the casinos have invested time and money into working out every possible variation on the rules and the ways to play under them. (more…)

There is a lot of argument on mathematical gambling systems. They seem to be illegal, but it’s really hard to identify them. One of the most popular methods used is card counting particularly in card games. It’s not a rule. Not everyone might understand and apply it. But as for those, who can - it may become a nice profit. Seems, like there are a couple of movies about mathematical gaming systems like this. (more…)

There’s a large variety of card counting techniques employed by professional players all over the world. And while some are very easy and can be learned within a few minutes, other strategies may take weeks or even months of real game practice to be mastered. For those of you who just want to beat the casino’s house edge while playing blackjack there’s no better strategy than the KO card counting technique.
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In 1975, Stanford Wong came out with Professional Blackjack. Wong had a Ph.D. in economics from Stanford University, hence his pseudonym. This book was the next big advance for card counters. Wong described his playing style, which included table-hopping shoe games to avoid playing at negative counts. As four-deck shoes were the most widely available games in Las Vegas by that time, this original approach was brilliant. The casinos looked for card counters by watching for their betting spreads. It had never occurred to the casinos that a counter might be watching a table from the aisles, waiting for an advantageous count before jumping in to bet.

The counting system Wong published was the Hi-Lo Count, and like Revere’s count, used the easy divide-by-remaining-deck(s) approach to running count adjustments. So, at last, some twelve years after Harvey Dubner had proposed the Hi-Lo count values, his system was available in a format both fully optimized with strategy indices, and presented with a simple methodology of play. Wong’s table-hopping approach to shoe games was in many ways similar to Al Francesco’s Big Player (BP) team approach, but allowed a solo card counter to attack shoe games invisibly, and without a team of spotters. This playing style has since become widely known as wonging.

During the early 70th, Dr. Keith Taft began developing the first concealed blackjack computer, and by 1972, Keith had started using a computer in the Nevada casinos to play “perfect” blackjack. Nevada had no laws at that time prohibiting the use of devices at their tables. Keith’s first computer weighed fifteen pounds. He went on to develop dozens of concealable computers and other electronic devices over the next two decades, ever smaller and more powerful. By the mid-’70s, Keith and his son, Marty, had met Al Francesco, and they would be putting together teams of players using computers to beat the blackjack tables.

Here’s how it worked (more…)

Contrary to what many gamblers may think, blackjack is not just a guessing game. Most casino games are guessing games. But with any blackjack hand there is a correct strategy and an incorrect strategy. Basic strategy is the correct strategy. The correct strategy is the mathematically optimal strategy—that is, it will maximize your wins and minimize your losses on each hand over time. (more…)