Confusion, Illusion, and the Art of Slot Machine Design

How do politicians, journalists, and others who know what's best for everybody else depict situations in which anything can happen and one guess is as good as another? They frequently invoke game of chance metaphors. "It's a crapshoot" is a perennial favorite. "Russian roulette," a second-order reference, is also common.

True enough, games of chance are random and not causal. This may disappoint folks who credit or blame patterns, trends, the unseen hands of casino bosses, telekinesis, or scapegoats. But past or present conditions don't anticipate future states. Modern slot machines go so far as to use electronic random number generators to determine the results of each round. And gaming gurus often study rules and strategies for table games with simulations -- computer programs incorporating random number generators.

Randomness in gambling, however, doesn't mean that all results are equally likely. That one bet or strategy is the same as any other. That solid citizens have nothing to gain by exploiting how odds are distributed in various games and approaches to betting.

At craps, for instance, each die lands randomly with from one to six spots showing on top. All numbers have the same probability -- one out of six. But, when the numbers on two dice are summed, a seven has six times the chance of appearing as a twelve. If your fate hinged on calling the roll, and nothing else mattered, the seven would obviously be the choice. Similarly at roulette, the ball lands randomly in one of 38 grooves on the wheel. But 18 grooves are red while only one is numbered nine. So red is 18 times more apt to show than a nine. If your goal was to win the next spin, regardless of amount, red would surely be the bet.

The converse would apply if you began with a moderate bankroll and had one try at winning enough to pay off your credit cards. Maybe a $300 stake and a $9,000 wolf at the door. Now, the seven can't work. A one-roll bet on seven for $300 can only win $1,200. Betting the whole shebang on red on one spin at roulette is no good either. You can only win $300. The twelve at craps and the nine at roulette, though, could do the trick with profits of $9,000 and $10,500, respectively. Even given repeated chances as opposed to a single try, starting with $300, the longshots offer a far better chance to reach $9,000 before going belly-up.

Another way randomness in casino games is nonuniformly profiled involves the dual sets of odds associated with every wager. The odds you'll win. The odds you're paid when you do.

To see what this means, assume you bet $5 on the five at craps. The odds against winning are 6-to-4 and the bet pays 7-to-5; putting these on equal footing, they reduce to 1.5-to-1 and 1.4-to-1. Instead, bet $5 on the four. Now the odds against winning are 6-to-3 and the bet pays 9-to-5; the equivalents are 2-to-1 and 1.8-to-1. Effort and reward diverge in either case.

Similar deviations are inherent in all casino bets. They're the source of the house advantage, and offer a means of comparing the quality of alternate bets. With a little arithmetic that I'll spare you this time, the discrepancies can be standardized to a percentage indicating house edge. It happens to be 4 percent for bets on the five and 6.67 percent for bets on the four at craps.

Table games in which players can vary bet size from round to round offer added flexibility for sophisticated gamblers to shape the cumulative effects of random events over playing sessions. For the same propositions, for instance red at roulette, raising bets when winning yields a small chance at big bucks. Increasing wagers when losing affords a good chance at modest profits.

The bottom line is that you can't predict what will happen in a game of chance. But you can work with the known probabilities associated with results and betting strategies to tailor your casino experience according to your personal criteria. The poet, Sumner A Ingmark, wasn't rhyming randomly when he wrote: