Can You Spin Your Way to a Giant Slot Jackpot?

The newest craze at your friendly neighborhood casino is the spin-a-winner giant jackpot slot machine. First you "qualify" by hitting a jackpot combination on the regular reels. Then you go into adrenaline mode where the electronic equivalent of a whirling wheel determines how much you're paid.

Several types of these machines are available, all recognizable by the spinning wheel. Players like 'em. The new slots yield more jackpots than did last year's favorites, and the top payoffs look better, too. Casinos also like 'em. The machines keep the patrons pumping in the coins, and you can be sure that none of the joints is losing money at every station but making it up in volume.

Here's how both of these conditions can be true at the same time.

Imagine two machines, identical in every respect but one. That is, the chances and amounts of all intermediate payoffs, and the overall theoretical payback percentages, are the same. The slots only differ in that the old DeSoto design has a conventional jackpot and the new LeBaron version uses a Ring of Riches to determine a winner's destiny.

Say that the chance of going to the moon in the DeSoto is one out of 25,000, and the jackpot is 5,000-to-1. The jackpot accordingly contributes 5,000/25,000 or 20 percent to the machine's payback.

The LeBaron isn't much more complicated to figure. Suppose the chance of qualifying for the jackpot is one out of 5,000. Winning combinations occur five times as often as on the DeSoto because 1/5,000 is five times greater than 1/25,000. For the bottom lines to balance, average jackpots paid by the rotating Ring of Riches must therefore be 1000-to-1, one-fifth of the DeSoto's 5,000-to-1. This is easily done if, for instance, the Ring has five sectors with the chances and payoffs in the following list.

To verify the math, multiply each chance by the corresponding payoff. The product equals 200. Add up the 200s from all five sectors and the sum is the 1,000-to-1 average jackpot.

You don't have to be Nikolai Ivanovitch Lobachevski to see where this has led. The LeBaron pays five times as many jackpots as the DeSoto, topping out at a whopping 20,000-to-1 rather than a mere 5,000-to-1, with consolation prizes of 400-to-1, 800-to-1, 1,000-to-1, and 5,000-to-1. The lesser loot still earns bragging rights for bettors who think they had a good shot or two at the biggie. Compare these alternatives in a different way. Picture a sophisticated slot salon with 100 of each, DeSotos and LeBarons. During a busy 10-hour stretch, individual machines might average 10,000 plays -- a million bets -- on each type of model.

DeSoto players can expect to hit 1,000,000/25,000 or 40 jackpots -- that's four per hour -- at 5,000 units each. The machines will pay 5,000 x 40 or 200,000 units in jackpots during the 10 hours.

LeBaron bettors can expect to hit 1,000,000/5,000 or 200 jackpots -- 20 per hour. Statistically, numbers of payouts at the various levels should be as shown below. Multiply the numbers times the amounts and add up the products. You'll find that the jackpots still total 200,000 units in the 10 hypothetical hours.

DeSotos made 40 players feel like millionaires at 5,000 units each. In the same period, LeBarons gave 200 solid citizens the Rockefeller rush -- 100 players to the tune of 400 units, two at 20,000 units, and 98 in between. You now know the casino paid out 200,000 units either way. A win-win situation... or smoke and mirrors? Sumner A Ingmark, muse of the machines, answered thus: