What Money Management Can and Can't Do

21 January 1997

By Alan Krigman

Everyone who knows the way to a casino wants badly to believe in the magic of money management. Why the elevation to an element of faith? It's common knowledge that the house has an edge at every machine or table. Folks who willfully wager with negative expectation need an escape hatch. To balance the scales. Just as in Judeo-Christian tradition, sin is unavoidable so Catholics have confession, Jews Yom Kippur, and Protestants grace.

Most garrulous gambling gurus espouse money management, although each has a unique perspective on what it means and how to go about it. Similarly, seasoned solid citizens all suppose they practice this fine art, although each does it differently.

Often, the recipe of success boils down to the lard of loss limits and win goals. Occasionally, other elements are added. Dividing a gambling budget into sessions. Pocketing an initial stake when winnings reach a target, then playing off the profit. Raising or lowering bets at the start of hot or cold streaks.

Alternate approaches to managing money affect the characteristics of gambling sessions. They skew results. But they don't void the laws of probability as the sycophants suggest and adherents hope.

I'll explain in terms of eight-deck blackjack, no resplitting or surrender but doubling on any two cards including split hands. You play perfect basic strategy with no card counting, shuffle tracking, or other such fancy dancing. Say your money management method is to make big bets of fixed size - for instance, $100 - and quit when you get ahead by any amount. This usually means $100 profit; however, due to splits, doubles, and blackjacks, you could win from $50 to $200. You're willing to play as long as necessary to achieve your goal or bust your entire bankroll.

What determines your chances of a losing session? That is, what affects the likelihood you'll lose your first bet and eventually go broke, never getting ahead? Only one factor. Bankroll size. Here are approximate probabilities that'll happen:

The figures show that if your money management system is to quit as soon as you get ahead, you can reduce the odds of a losing session by increasing your bankroll. The catch is obvious. Larger bankrolls mean more frequent small wins. But you can't completely eliminate the prospect of a loss. And, when it occurs, it'll hurt. One $50,000 wipe-out can cancel lots of $100 and $200 wins. The chances of that loss are low; you could play weekly for years before it happens. Still, you could be in big trouble if you sustained a hit of this magnitude early in your money management career, before you accumulated enough of a cushion to cover it.

Other money management schemes work analogously. Some, like this, improve your chances of modest wins, but leave you vulnerable to occasional large losses. Others give you a small chance for substantial victory, but normally subject you to moderate failure. A few offer you a 50-50 chance of winning, but you'll find yourself picking up slightly less than you put down in the long run.

In all such cases, your expectation remains negative to an extent determined by the house's inherent edge. Money management can't change that. The theoretical loss times the probability of losing will exceed the theoretical win times the probability of winning.

I want to believe otherwise. I also want to believe that when Thunder, my money-finding dog, leads me to coins in the street on a day I go to a casino, my first game is virtually in the bag. I even want to believe in the fantasy fashioned by the immortal minstrel of money management, Sumner A Ingmark:

Some day I'll board a space ship fast,
And cross to a world parallel,
Wherein the future is the past,
Which, knowing, 'sures my doing well.