Probability and Dead European Mathematicians

Craps wouldn’t be a game of chance if you knew the outcome of the roll in advance. Why? By definition, the outcome of any game of chance must be uncertain. The branch of mathematics that deals with this uncertainty is called Probability.

The science of Probability was born in the seventeenth century when the Chevalier de Mere, a French nobleman who enjoyed a good gamble as much as the rest of us, began posing questions about the probable outcome of certain dice wagers to prominent mathematicians. The Chevalier had made a considerable amount of money on even money bets – wagering that the number six would be rolled at least once in four rolls of a single die. He did so well with this wager that he sought to expand upon it by wagering that if two dice were rolled the double-six would show up at least once every twenty-four rolls. Needless to say, his math failed him and he lost his money just as quickly as he won it with the single die wager.

Baffled by his misfortune, the Chevalier took his problem to the mathematician Blaise Pascal. Pascal, in turn, consulted with another mathematician, Pierre de Fermat, and the two of them solved the double-six problem and laid the foundations of the Probability branch of mathematics.

By the way, the rule of mathematics used to solve this problem was the Multiplication Rule of Independent Events. It states simply that “For independent events, the probability of all of them occurring equals the product of their individual probabilities.

Another name well known in gaming circles is that of Jean le Rond d’Alembert, a French mathematician and philosopher who lived from 1717 – 1783. In addition to coming up with the betting strategy that bears his name he developed the Wave Equation in mathematics and was something of an expert on fluid mechanics. While he made great strides in mathematics and physics, d’Alembert is also known for incorrectly arguing in Croix ou Pile that the probability of a coin landing heads increased for every time that it came up tails – hence giving birth to what we know today as “due number theory.”  For what it’s worth, the probability of the coion landing on heads remains the same on every toss – 50/50.

The D’Alembert system is a type of martingale, which calls for increasing ones bets when losing and decreasing them on a win. The concept behind this system is simple enough – that two events of roughly equal probability will happen roughly the same number of times over the long run. Unfortunately, the strategy depends on this happening in the short run. If you have enough time and money then perhaps you can make it work for you. Of course, the longer you play the more you risk losing.

The goal of the D’Alembert system is to win on even-money bets such as the Pass Line or Don’t Pass in craps. It really does not matter which way you play. Simply make a decision and stick with it. The second decision is how much money to you will initially risk.

Let’s say your initial bankroll is $500 and you are playing on a $5 table. We will start out with five unit bets. Your first wager will be $25 on either the Pass or Don’t Pass. If the bet wins your next wager is four units, or $20. If it loses your next bet is six units, or $30. Simple, right? Decrease your bets by one unit on a win and increase your bets by one unit on a loss. Should the worst happen and you lose five consecutive decisions your loss will total $375.

The D’Alembert is a negative progression strategy, but with its built-in money management it is not as dangerous to play as the Martingale or Grand Martingale. Your bets increase slowly, and the fact that you reduce your bets on every win means you reduce the risk of losing your entire bankroll while attempting to overcome a bad trend.

The Contra-D’Alembert is exactly the opposite of the classic D’Alembert system. With this strategy you increase your bets by one unit on each win while reducing them by one unit on a loss. It is designed to gain as much as possible during the positive series. As this system offers reasonable protection of the downside, it is probably safer for the average player to attempt than the D’Alembert. Why? Because when the inevitable losses come your bets will regress to the base one-unit level and remain at that level until the streak ends and the winning begins again. The trade-off is there are few large winnings with this system, as one loss can effectively wipe out a small streak of wins.

There are many other systems on the market based on the principles of these ancient mathematicians – and others.  Instead of paying your hard earned money for one of those systems, take one of these, modify it however you wish and make it your own. Use the money you saved to take in a show or enjoy a nice dinner with someone special in your life. Just remember that regardless of how you modify the D’Alembert it is a mathematical system and as such cannot overcome the house advantage. If you enjoy experimenting with gambling systems feel free to do so. Just remember that it IS gambling – not advantage play.