BETTING SYSTEMS AND THE HOUSE EDGE

By Dr. Eliot Jacobson

**"Eliot Jacobson has a Ph.D. in Mathematics from the University of Arizona. He was Professor of Mathematics from 1983 to 1998 at Ohio University, and currently holds a teaching position in the Department of Computer Science at the University of California, Santa Barbara. Jacobson recently published his first book on blackjack ("The Blackjack Zone," Blue Point Books, 2005) and it is available in the BJI store. To read a review of Jacobson’s book that appeared in issue #61 of BJI, click here.**There is no mystery to the success of casinos. People place wagers on games that have a built in house edge. The players win or lose the individual bets, but that’s of no concern to the management. The only concern is that players continue pumping wagers through the system. In this case, the large variance of individual bets evens out and the house earns according to the following basic equation:

Earnings = (Total Wagers) x (House Edge)

A progression betting system is based on the belief that this equation is wrong. It is an attempt to defy the laws of economics and mathematics by placing wagers according to a fixed pattern in an attempt to change the house edge.

A progression betting pattern is one that bases the current wager on the previous amount wagered and the result of the previous hand. Many authors write books about these systems, claiming they will win if combined with stop-loss and money management methods. Because of their simplicity, many people try them at the tables. Most lose. Some win.

Those who see individuals win using betting systems may come to regard these systems as an advantage method. Moreover, the arguments in favor of betting systems appear logical. But it is important to understand that it is the large variance of the games that lures most customers. Of course players will win. There are always winners. There have to be winners. But others players will lose. In the end, the losses will more than compensate for the wins so that the final result represents the house edge.

On the other hand, the "authors" and "experts" who extol betting systems usually blame the losers for their losses. They claim the losers are not disciplined or don’t fully understand the system (which essentially means that the loser is not able to foretell the future perfectly). They point to the myriad of winners (there are always winners, that’s a given). They claim that the computer simulations that show their systems are fraudulent don’t model the "real world." They invent fancy theories involving chaos and fractals and never fully explain them. They post defensive messages on Internet bulletin boards, using terms like "math boyz" and "flaw." They hire publicists who send out press releases. They gain media exposure. And worst of all, they gain credibility among the gaming public.

But betting systems do not give the player an advantage over the casino. Fallacious arguments, anecdotal accounts, and slick book covers cannot overcome the physical laws of the universe.Wagering Law. A betting system can not change the house edge; players using these systems as a whole lose at exactly the predicted rate.

However, progression betting systems do change the way in which losses occur. To understand the appeal of these systems, we will look at two of them in detail.

The first progression we will consider is called the "Martingale system." This is the most common progression used by blackjack players. In it, a player starts with a basic unit bet (say $10). If he loses a wager, he then doubles his wager for the next bet. He continues doubling each wager until he wins. After a win, his wager returns to its original value of $10. On a push, the wager stays the same. By always leaving on a win, the player ensures himself a winning session.

This seems to be a sure thing. For example, if the sequence is lose, lose, win (LLW) then the player will bet $10, $20, $40. He lost the $10 and $20 bets for a net loss of $30, but he won $40 for an overall gain of $10. For a longer sequence, consider

LLWLWLLWWLLLLLLLLLLWIt is easy to figure out the profit for the player: it is his minimum bet times the total number of wins in the sequence, in this case $10 ´ 5 wins = $50.

How can there be anything wrong with this logic? Just leave on a win and the player walks away with profit in his pocket every time.

However, for many reasons, the player can’t always leave on a win. For example, in the previous sequence, the player was actually down $10,190 on the wager before the final win. Very few people can sustain this type of loss and keep on playing. The player placed a wager of $10,240 on the last bet in an effort to win $10. The situation of losing 10 hands in a row is not rare. It occurs about once every 1,540 hands (or 15 hours of play). A series of 10 consecutive losses is almost a certainty on any prolonged trip to Las Vegas. What if the sequence of losses was 15 hands? Then the player will need to wager $327,680. At blackjack, a sequence of 15 losses in a row occurs on average about once in every 100 hours of play. What if he needed to split and double down? What if he lost that hand?"By Dr. Eliot Jacobson

"The house edge is not just another number; it’s The Law."By the way, Dr. Eliot Jacobson is also one of the regular posters on the wizardofvegasSo why don't you post your question there???