Choosing Slot Machines
by Alan Krigman



Many folks who try their luck at casinos during vacations, conventions, or even junkets head directly for the slot machines. They're much less intimidating than table games for beginners, offer lots of playing time and plenty of excitement for relatively modest bankrolls, are available in many configurations, and promise jackpots that can change a person's lifestyle. But, how do you decide which machine to play?

Experienced slot buffs often make their first level of decision in terms of the game. Maybe they like the simplicity of a classic three- or four-reeler. Or the challenge of video poker. Or the opportunity to hone their blackjack skills before bellying up to a live table. Or the dazzle of some of the new multi-row multi-column machines. Significant differences can be found even within these categories. The most important have to do with the chances and amounts you can win.

In theory, you can find the slot machines that offer the "best bets." How? Multiply each listed payout by its corresponding probability. Add the products to get "expectations." Compare results and choose the machine with the greatest expectation. So much for theory. On reel-type slots, you can't do this because the probabilities are state secrets. At video poker, where you can determine the chances of each hand, you'd have to be numerate enough to program the computers on a space probe. And you'd have to know the optimum strategy for each game, since the probabilities presuppose perfect play. So. What if you like three-, four- or five-reelers? Or prefer poker but are no Nikolai Ivanovich Lobachevski? Or don't know whether to hold a three-card inside straight flush or two nines?

You could do what solid citizens do the world over. Run in and grab the first available seat. Ask a slot attendant which machines are hot or due to pay. Find the game you think your cousin said was lucky. Return to the little devil that ran you dry earlier in the day because you have an investment in it. That sort of thing. Or, you could be as scientific as possible under uncertain circumstances. You could turn to the branch of decision theory governing situations in which the chances associated with alternate outcomes are unknown. There, you'll find standard methods to help you select the best machine to play. I'll present four of these in terms of hypothetical machines A, B and C, with the simplified payout lists shown in the following table.

Payoff Lists for Hypothetical Slot Machines

machine A B C 1 2 1 >6 4 5 10 15 20 50 40 40

1) Laplace criterion: You know payouts become less likely as they get richer. But you're also convinced that anything could happen on the next fateful push of the button. So assume all results are equally probable, add up the payouts for each machine, and play the one with the highest total. For the games in the table, the sums are A=69, B=64, and C=70. The highest is 70; play machine C.

2) Maximum-minimum criterion: You're conservative -- figuring you'll score, but not big. So check the lowest (minimum) payout for each machine and play the one with the highest (maximum) of these values. For the games in the table, the minimum payouts are A=1, B=2, C=1. The highest of these is 2; play machine B.

3) Maximum-maximum criterion: You're adventurous -- always going for the gold. So check the biggest (maximum) payout for each machine and play the one with the highest (maximum) of these values. For the games in the table, the maximum payouts are A=50, B=40, C=40. The highest of these is 50; play machine A.

4) Optimism index: Rate your optimism, x, from 0 to 10 -- 0 being gloomy, 10 being cocksure. For each machine, multiply the highest payout by x and the lowest payout by (10-x). Subtract, and play the one with the greatest result. Say you're mildly optimistic and rate yourself at x=6. The arithmetic yields A=294, B=228, C=234. The highest is 294; play machine A.

Granted, these methods are less than rigorous. But they're the same techniques corporate honchos, even powerful government leaders, use to support decisions in the face of uncertainty. Or, do you think aspiring dictators play the game of coup d'etat by running in and usurping the first available presidential palace?Sumner A Ingmark, whose poetic dictates are definitely diffused with indeterminacy, derided difficulties posed by doubt this way: Indecision's an affliction, When results defy prediction, But precaution's not restriction.

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