Good Gambling Involves more than Going for Broke

12 April 2006

By Alan Krigman

Many people think of casino gambling as taking money into their friendly neighborhood punting palace and playing their favorite game until they hit a jackpot, go belly-up, or run out of time. The latter, hopefully, at a profit. Even more hopefully, a profit near the peak they reached during the drill so they won't have to blubber later about not quitting before giving some of it back.

More sophisticated players know that the amount they're willing to risk, the earnings that will make them happy, and the chance of reaching this level are related. It's not necessary to put precise numbers on these elements to understand the compromises involved and enter the fray with some general trade-offs in mind.

The concept applies to sessions or casino visits regardless of what's being played. Using a parameter known as "risk of ruin," math mavens can estimate the likelihood of hitting a specified target before busting out on a certain bankroll, with bets of a given size, knowing only the edge and volatility of a game.

At roulette, and to a lesser extent craps, the basic ideas apply all the way down to individual bets. The phenomenon is not only useful in devising a wagering strategy for this specific game, it also helps solid citizens picture how the give-and-take works for other gambles.

Say you have a $100 bankroll and elect to risk it on one spin of double-zero roulette. You have lots of choices as to how to bet.

One possibility would be to drop the $100 on one number and hope your $9.95/minute 1-900-PSY-CHIC advisor was right. The prospects are one out of 38 (2.63 percent) you'll win $3,500 versus 37 out of 38 (97.37 percent) you'll bust out. An alternative would be to put $10 on each of 10 numbers. This yields 10 out of 38 chances (26.3 percent) to win $260 and 28 out of 38 (73.7 percent) to go broke. What about $5 on each of 20 numbers? The probability is 20 out of 38 (52.6 percent) better than 50-50 to net $80 as opposed to 18 out of 38 (47.4 percent) to lose your $100. Another choice might be to bet $50 on one column and $5 on each of 10 numbers in the other two columns. This yields 22 out of 38 chances (57.9 percent) to win either $50 or $80 rather than 16 out of 38 chances (42.1 percent) to be beaten out of your C-note, with wins apportioned as 12 chances out of 38 (31.6 percent) on the $50 and 10 out of 38 (26.3 percent) the $80.

These examples aren't cited as recommendations, although if any fits your fancy - go it. They're intended mainly to show how you can tailor your play to meet different criteria, down to the single round in the case of roulette.

In most other games, including slots, the principles apply to sessions rather than particular bets. Overall, the lower the profit at which you'll cut and run, the greater your chance of success. Further, a larger bankroll relative to the bets you make whether achieved by a bigger stake or lower wagers improves your chance of successfully attaining a more moderate target.

This isn't to say that going for the gold is a fool's quest. It's legitimate to gamble for a shot at the limo ride to Easy Street you're pretty sure you won't otherwise get. But you should understand why, so far, you've been heading home with heavy heart and an empty fanny pack.

It's also not to imply that settling for a modest profit, perhaps only a fraction of your bankroll, is a secret the casino bosses are trying to keep under wraps. It may be true that, by starting with $100 and quitting as soon as you're up $20, you'll succeed most of the time. Almost five out of six tries, on the average. Closer as the house's edge goes down, more remote as your bets shrink relative to your bankroll. But when that slightly over one out of six times hits the fan, it can easily chew up those nearly five gains. Still, as the beloved bard, Sumner A Ingmark, wrote:

A fact about an average that optimists all love:
Though some will go below it, yet others rise above.