Section: Advice > Money Management

Money Honey - The First and Last Word on Money Management
by Peter Ruchman

Part Two - Too Many Fish in the Sea

Named after Jean le Rond D'Alembert, this system postulates that in any trial or series of events, even though one outcome may occur more often than another, it would be inevitable in the long haul, for the other side to catch up, forming the law of equilibrium.The D'Alembert system is based on the concept that any two choices must, sooner or later, equal each other in outcomes. If heads comes up repeatedly, then tails is "due" to make up the difference and soon.

In this system, following every losing bet, you add an additional unit to your bet at the next opportunity. After every winning bet, one unit is removed. The inherent problem is that the adherents are taking a short term view of the laws of probability. Those laws are taking a long term view. The small sample under consideration by the short-sighted player looking to recoup quickly doesn't contain enough data to make a difference. There are variations on this concept, like the Flexible-D'Alembert, and the Contra-D'Alembert systems, with many of the same problems.

A few words concerning "due." It is a very popular notion that is difficult to dispel. There's morning dew, dog doo, honeydew, and money due. No team is ever due. Repeat these two words after me: Anthony Young. As an exciting rookie prospect for the NY Mets, Young drew a lot of attention. He lost his first few games, and the words were circulating: He's due. Solid citizens were betting hard-earned cash on this thought. He lost a few more games. Hard luck pitcher. When the losing streak reached 12, there were folks who counted the days until Young's next start. "He's due!" Bottom line here was at 23 losses, the Mets traded this now-suffering head case to, who else? The Chicago Cubs. He proceeded to lose his first five starts as a Cub. 28 straight loses, and if you had bet him, you'd be a good candidate for life beneath the freeway.

Next, there's Oscar's Grind, first noted by casino expert Allan Wilson. Betting one unit, if it is lost, make the same size bet. If the second bet wins, the next bet is increased by one unit unless you win a bet that produces a profit in excess of one unit. If this happens, reduce the bet so if you win, you are ahead exactly one unit. Each time this cycle occurs, you begin a new one. In effect, the outcome is a slow-death version of the Martingale. House-edge being what it is, sooner or later, you will encounter a streak of bad luck, find yourself at the table limit, unable to make the bet to recoup. No wonder Oscar's grouchy.

Then there's the Reverse-Martingale. This system dictates that you leave your winnings in play each time you win until you hit a predetermined number of wins. Anytime you lose before you hit that number, you have lost only one unit. This system is based on minimal losses with the potential of large wins. Of course, the downside is that if there is choppy going and you don't establish a stop-win point, you'll never see daylight.

The Contra-d'Alembert starts with a one-unit bet. If this wins, the bet is increased by one unit. Any loss is followed by decreasing the bet size one unit or repeated bets at the table minimum. This system is like the previous: small losses, occasional big wins, but the same inherent dangers as above.

Arthur Reber, writing in his book, The New Gambler's Bible cites an analysis of these systems run on a computer against a simple pass line bet for craps. The computer was programmed to shoot craps by Ken Elliott, who has produced the finest craps analyzer we know, entitled Craps Sim II. Using a $5 bet, each system was given 100 rolls of the dice, which corresponds to the typical crap shooter's session.

"No surprises here, " Reber writes. "All systems cost the player significant amounts over the straight pass line bet." The simple pass line bet lost $1.52. Oscar's grind lost $2.60. The d'Alembert lost $3.57. The Contra-d'Alembert lost $3.91. The Reverse-Martingale lost $4.86. The Martingale lost $5.26.

This is money management?

John Beasley, in his book, The Mathematics of Games, writes that, "Mathematicians know that there is no such thing as the popular 'law of averages'. Events determined by chance do not remember previous results so as to even themselves out." Cards, dice, roulette balls and wheels have no collective memory. Remember Anthony Young and his dues. For anyone looking to take an chance using any of these systems betting against the previous outcome (red/black; pass/don't pass, banker/player, win/loss, etc.) you might want to rethink that position.

There are theorists and gamblers who espouse the view that any form of money management is akin to restraint of trade barriers, a personal embargo, or worse, a loss of personal freedom that challenges the Bill of Rights. They range from the starry-eyed player with wild dreams of the big score to even-tempered professionals who routinely plow through fields of money in huge swings.

The latter group may possess the character and skill to withstand the gnarly twists and turns of this life (in fact many pass on with little profit to show). Their style precludes any attention to money management. They will gamble until they win OR have nothing left. Patience and discipline are not the operative concepts, and these words will have no meaning in their lives.

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