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Best of Alan Krigman

Gaming Guru

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If the Slots are Random, What Makes the Paybacks Work Out?

27 May 2000

Bettors have lots of befuddled beliefs about how casinos assure themselves of an edge. And, no befuddlements are bigger than those about the setting of slot payback percentages.

Here's the quintessence of the confusion.

1) Reputable gaming gurus assert that the result of every spin is determined by a random number generator. Apparent patterns and trends are therefore meaningless. Likewise, there's no way to predict whether a machine will be hot or cold in the future, let alone when a jackpot will hit. And, the casino bosses can't pick, choose, or foretell who's gonna do what, when, or where.

2) Solid citizens savvy enough to earn points for their action by putting club cards in the readers also know that slots are "set" for certain paybacks. Say, 96 percent. Meaning that the casinos keep four cents out of every dollar and distribute the rest to players. Unevenly, of course, so a few lucky ducks get big bucks and everyone else pockets a modest profit or goes home broke.

3) But, if the machines are really random, what's the guarantee they'll return the specified percent? Does randomness mean that slots run in cycles, but because the cycles are secret, nobody knows the sequence or where he or she is in the series? Or, do machines monitor the tides of fortune and make mid-course corrections to align the percentages, for instance tightening when folks are winning too much and loosening when they're being drained too dry. Or, does some master bestower of beneficence check reports coming from the floor, and push a button that sends someone a jackpot to balance the books? Or, what?

The "or, what" turns out to be the laws of probability and how they work when huge numbers of trials are involved. I'll show you the idea for a realistic machine with a 96.28 percent payback.

For each spin, assume the random number generator picks a value from 1 to 10,000,000. The machine is programmed with 11 winning combinations of symbols, each of which is assigned to a range of the 10 million possible numbers. Ranges, along with payouts for three coins bet per spin, are shown in the accompanying list.

result  payout range
A 5000 1-19
B 1000 20-3, 014
C 100 3,015-3,414
D 75 3,415-4,674
E 55 4,675-253,174
F 50 253,175-351,369
G 30 351,370-353,620
H 25 353,630-415,019
I 20 415,020-441,489
J 10 441,490-585,019
k 5 585,020-1,288,079
Lose 0 1,288,080-10,000,000

When a random number is chosen, the corresponding symbols appear on the machine and the indicated money is paid. The chance of each result is the size of the range divided by the 10 million possible numbers. As an example, the 55-coin return range (4,675-253,174) includes 248,500 of the 10 million possibilities, so the chance of this hitting is 2.485 percent. Do the math or trust me, but multiplying the chance of each result by the payout and adding the products gives the 96.28 percent theoretical average.

Setting a machine entails specifying the ranges and payouts. The payback is then the theoretical average. The laws of probability take care of the rest -- without finagling, manual or automated.

During a brief period, payback is usually far from the average. This is why someone might make a mint or go belly-up in short order. After an hour, at 8 spins per minute, statistical analysis shows the chance of being within 1 percent of nominal payback is only 2 percent. After a million spins, the chance of being this close to the set return is 83 percent. And when 10 million spins are history, confidence in being this near is 99.998 percent.

So, once the programmers have entered the ranges and payouts into the microchip, the forces of the universe deliver the payback percentages. As the immortal poet, Sumner A Ingmark, wrote:

Laws of nature, oft inscrutable,
Though we wish they were refutable,
Work in ways that are immutable.

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.