Issue 206
August 23 - 29, 2004
Volume 4
page 3
 

Would You Play the Slots if You Could See How They Worked?
By Alan Krigman

Would slot machines be as popular as they are if the details of their operation were transparent to players? Sure, anyone who's at all interested knows or can find out about independent trials and random events, odds and probabilities, and expected values and return percentages. But the way the devices are designed, players don't see what causes the reels to stop precisely where they do or what determines which images appear on the video screens. It's therefore easy to believe myths and superstitions like machines that become due for or build toward a big hit, the person who scored after taking over someone else's machine got the jackpot that would have gone to the preceding player, and the devices learn about and adapt to solid citizens' personalities.

Say, instead, that the workings of the slots were so obvious everyone could understand them on sight. For example, the machines might resemble the contraptions used by the state lottery agencies to determine winning numbers. One possible configuration would be based on a large clear-walled container filled with lightweight spheres, each bearing a payout number. Some method of keeping the spheres constantly agitated would be needed, like air jets or mechanical mixing paddles. A simple implementation of a one-line game might then involve a means by which a bettor could cause a small door to open, letting a sphere enter a result chamber, where the associated payout number could be seen by the player and read by an automated sensor.

The chance of any result would be easy to determine if you knew how many spheres were in the container, labeled with each number. Say that a machine had 10,000 spheres marked as follows ("coins back" are the figures in parentheses): 7,000 (0), 1,500 (1), 750 (2), 500 (3), 200 (5), 40 (50), 9 (100) and 1 (1,000).

The probability of losing on a round would be the 7,000 spheres marked "0" divided by the 10,000 total or 70 percent. Hit rate would be the complimentary 3,000 out of 10,000 or 30 percent. The shot at the 1,000-unit jackpot would be the one sphere marked "1,000" divided by 10,000; this is 0.0001, or 0.01 percent. The likelihood of intermediate payoffs would be found analogously.

The overall return percentage on the machine is the probability at each level, times the number of coins back, all added together. This is shown for the hypothetical set of spheres in the accompanying table. Varying the number of spheres at each return level, or the amounts to be paid, would alter the dynamics of the game. You can see how it could be loosened or tightened, with greater or lesser return percentage, respectively. Likewise, it's evident how performance can be skewed toward a high probability of a modest win or a small chance at a big payday.

Probabilities and Expectations of the Hypothetical Game

probability
coins back
expected return
(probability x coins back)
7,000/10,000 = 0.7000
0
0.00
1,500/10,000 = 0.1500
1
0.15
750/10,000 = 0.0750
2
0.15
500/10,000 = 0.0500
3
0.15
200/10,000 = 0.0200
5
0.10
40/10,000 = 0.0040
50
0.20
9/10,000 = 0.0009
100
0.09
1/10,000 = 0.0001
1,000
0.10
Total
0.94

Were slots to be based on this hypothetical design, it would be obvious from the chaotic movement of the spheres that each round is an independent random event, decided at the instant the system (here, the door latch) is activated, and not an element in some predetermined chain of events. Many of the common misconceptions about the machines wouldn't arise. For instance, watching the motion of the spheres would indicate that patterns perceived in results are mere coincidences. Likewise, that a machine doesn't somehow become due for a big hit after a string of misses or small returns. Also, since the spheres don't queue up in front of the door, that a person who gets "your" machine and scores right after you leave hasn't grabbed "your" jackpot.

Not that there aren't myths and superstitions surrounding the lotteries, despite the transparency of the workings. Or that knowing exactly how something works is necessarily desirable. Illustrating the observation by the odester, Sumner A Ingmark:

While truth will out, it's sometimes tragic,
To bust the bubble of the magic.

About the Author

Alan Krigman is a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns are focused on those who are interested in gambling probability and statistics.

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