How to balance chance vs. payoff

June 25, 2001 1:02 AM


Most boys and girls in India know the fable about the blind men and the elephant. In Western cultures, the story is familiar due largely to the poem by John Godfrey Saxe. Adults who love Dagwood Bumstead and Three Stooges slots, but snivel at the childishness of the elephant parable, may forget that one blind man stumbled into the side of the animal and thought it was like a wall, another grabbed a tusk and imagined the creature as similar to a spear, a third grasped the trunk and was sure the beast resembled a snake, and so on - leg-tree, ear-fan, tail-rope.

Casinos are to players much like the elephant was to the blind men. Each person perceives gambling differently. And, one of the principal planes on which the distinctions are evident involves the seesawing chance of winning a bet and the associated payoff.

Of course, you can’t have it both ways - a high probability of winning and a rich return. But you can select games and bets to get good chances of small paybacks, remote prospects of monster scores, or something intermediate.

In taking their picks, perceptive punters know that trade-offs among the various electives not only influence what can be expected to happen from round to round, but also shape the parameters of the sessions they’re liable to experience. Games are quirky enough to defy side-by-side comparisons. Still, it’s possible to generalize about the implications of the diverse options by contrasting a series of alternate bets at roulette - which all have the identical house advantage and involve placing the same amount of money at risk over a given period of time.

For this purpose, make believe you start with a bankroll of $250 and bet a total of $10 per spin. You’d like to double your money or, if not, at least enjoy two hours of action - roughly 80 spins - without emptying your fanny-pack. The first three columns of the accompanying table show seven ways to bet the $10, the probability of winning, and the corresponding payoff. The fourth column gives the chance that you’ll double your money before losing your stake, irrespective of how many spins are required to hit one extreme or the other. And the fifth column indicates how apt you are to survive 80 spins on your $250.

The figures in the chart are specific to the indicated $10 bets, $250 bankroll, and $250 win goal at double-zero roulette. They don’t map directly onto other games. However, the insight to be gleaned isn’t the precise chance of some result or other in this specific situation. Rather, it’s the way that the likelihoods of these outcomes offset one another and change with the balance between the probability of winning a bet and the payoff.

It’s OK if your main motivation in visiting a casino is to strike it rich - provided you realize that the higher your aspirations, the more your risk of bottoming-out in the attempt. A strategy based on longshots with big payoffs may then be suitable. It’s also fine to aim for a modest profit, hoping to maximize your time in action and minimize your risk of going belly-up. Wagers having close to or better than 50-50 chance of winning, with low or fractional payoff multiples, may then fit the bill nicely.

What’s best? It’s a matter of personal perspective. Although, you wouldn’t know it from the polemics among players, many of whom consider solid citizens with alternate objectives to be idiots. In this context, the humble Helicon of the wagering world, Sumner A Ingmark, bows to John Godfrey Saxe who said of the blind men:

And so these men of Indostan
Disputed loud and long,
Each in his own opinion
Exceeding stiff and strong,
Though each was partly in the right,
And all were in the wrong!