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Best of Alan Krigman

Gaming Guru

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Choosing Slot Machines When You Don't Know Your Chances

8 December 1997

The slots are versatile. Every machine seems to offer its own twists. I'll cite a few, just for video poker. Wild cards: none, one or two jokers, deuces. Bonus hands: none, four-of-a-kind of one or more selected ranks, flushes of a certain suit. And payout lists for different winning hands: no two look quite alike.

How do you decide which machine is best for you to play?

In theory... Multiply each listed payout by its corresponding probability. Add the products to get "expectations." Compare results and choose the machine with the greatest expectation.

In reality... On reel-type slots, you can't do it 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 last time 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 accompanying table.

I) 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.

II) 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.

III) 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.

IV) 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'état 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.

 

Payoff Lists
for Hypothetical
Slot Machines
machine
a
b
c
1
2
1
2
3
4
6
4
5
10
15
20
50
40
40

 

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.