How Money Management Helps You Achieve Balance

16 March 1998

By Alan Krigman

Money management is like alchemy. Neither will turn lead to gold. And both can burn buffs who rebuff reality. Nice to have the law of unintended consequences! Alchemy served society by yielding useful metal alloys; money management benefits bettors by shaping gambling sessions to individual preferences.

Money management takes many forms. So don't be fooled by the frills. They're all variations of what to risk in a session, how much to bet in a round, which wagers to make, and when to quit.

Money management can't overcome the critical barrier solid citizens face in a casino - the house edge. Still, within the bounds of this constraint, it's a lever for players to balance potentials of win and loss versus prospects of ecstasy and agony.

You don't have to be a Nikolai Ivanovitch Lobachevski to deduce that the higher you aspire, the less likely you'll succeed. But few bettors understand how they can apply this insight.

I'll illustrate the idea with three elementary money management systems for single-zero roulette. The same principles extend to other games and systems.

All three cases involve starting with $100, betting $10 on each of 10 spins, then quitting. They differ in the wagers: a) $10 on red, b) $1 on each of 10 numbers, c) $10 on a single number.

These three strategies are equivalent as far as the casino is concerned. The edge in single-zero roulette is 2.7 percent so the house has theoretical earnings of $2.70 after $100 is bet in 10 spins, one way or another. And the approaches are similar in that the player's maximum exposure is $100 in each instance.

The distinctions arise in the specific nets which can be won or lost and the associated chances. These are shown for each system in the accompanying tables for zero to 10 wins in 10 spins.

Here's how to interpret the tables.

What's the probability of losing the entire $100 in each case? Betting $10 on red, the likelihood is low at one out of 784. This rises to 1 out of 23 with $1 on each of 10 numbers, and to 1 out of 1.3 - that's 10 out of 13 - dropping $10 on a single number.

On the other hand a practical goal such as winning $260 has a fighting chance, one out of 4.7, with $10 on a single number. This falls to a remote one out of 480,859 with $1 on each of 10 numbers, and is wholly beyond reach with $10 on red. Further, high wins are possible betting on longshots, but don't risk your lunch money on the one out of 5 quadrillion probability you'll hit 10 single numbers in a row at $10 each and earn $3,500.

In general, money management practices can help position sessions in the range between frequent/modest and rare/spectacular wins. Good players know where their preferences lay along the spectrum, then act accordingly. And, they don't err by naively thinking they've discovered some secret of "almost always winning" or "hitting it big" the casino bosses don't want them to know.

Sumner A Ingmark, bard of balance in betting as in all behavior, said it simply:

Those who to modest goals adapt,
Oft know that they're to win more apt.
While others, setting targets tall,
Should grasp that they've shrunk prospects small.

 

$10 on red
wins	net ($)	chance
0	-100	1/784
1	-80	1/83
2	-60	1/19
3	-40	1/7.7
4	-20	1/4.6
5	0	1/4.0
6	20	1/5.2
7	40	1/10
8	60	1/27
9	80	1/128
10	100	1/1,347

 

$1 each on 10 numbers
wins	net ($)	chance
0	-100	1/23
1	-64	1/6.3
2	-28	1/3.8
3	8	1/3.8
4	44	1/5.9
5	80	1/13
6	116	1/43
7	152	1/204
8	188	1/1,466
9	224	1/17,810
10	260	1/480,859

 

$10 on a single number
wins	net ($)	chance
0	-100	1/1.3
1	260	1/4.7
2	620	1/38
3	980	1/511
4	1,340	1/10,519
5	1,700	1/315,576
6	2,060	1/13 million
7	2,420	1/858 million
8	2,780	1/82 billion
9	3,140	1/13 trillion
10	3,500	1/5 quadrillion