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Best of Alan Krigman

Gaming Guru

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Not All Gambling is One Spin at Russian Roulette

21 April 2000

Nobody plays a fancy new slot machine because it's intellectually stimulating. Or because the action, in and of itself, is inherently fascinating, let alone fun. Video versions of games you found boring when you were 10 years old? C'mon now! Solid citizens pump in the pennies hoping to win money. Or, at least, to earn points for free meals at the all-you-can-eat buffet.

This being the case, why have casinos installed such a wide variety of machines already? And why do they add more innovative configurations by the day? Answers are legion. Some are profound and plumb the psyche of middle America at the millennium. One, simultaneously simple yet important, is that more complex games create an impression of being easier to win.

Beneath the sound, animation, and spinning doo-dads, slots are essentially all alike. They're mechanized games of chance with sets of probabilities to lose or to win various amounts. In theory, values of prospects and returns are arbitrary. In practice, they're constrained so the house has an edge, gamblers "hit" reinforcingly often, and normal bankroll swings give bettors a shot at fulfilling their fantasies when fortune is smiling and reasonable playing time when ... well, you know when.

System parameters can be varied within these constraints to tailor the characteristics of particular slots to meet players' individual preferences. And the more complex the games get, the more flexibility is available for this purpose.

Consider a hypothetical machine with the five levels of returns and probabilities indicated in the first two columns of the accompanying list. A real machine would be just like this, except that the 10 percent chance of a four-coin return might be divided into multiple levels, having returns averaging four coins and probabilities adding up to 10 percent. Snazzy new models sport dozens, perhaps hundreds, of return-probability combinations.

return
(coins)
probability payback
10,000 0.001% 10%
4 10.000% 40%
2 10.000% 20%
1 20.000% 20%
0 59.999%

Add up the probabilities of the non-zero returns to get the hit rate. For this machine, it's 40.001 percent. Multiply the returns by the corresponding probabilities to get the contributions to payback at each level. Add these results to get the overall payback. For the values shown, it's 90 percent. The house edge is what's left after the payback, or 10 percent in this instance.

To change the characteristics of the machine, just vary the probabilities and amounts, honoring whatever constraints apply. I'll give you a few examples with this five-level set-up. You can noodle out other variations yourself.

Say a casino wants to increase hit rate but not change edge. If the chance of a one-coin return is raised to 25 percent, hit rate goes up to 45.001 percent. But one or more returns must be cut to keep overall payback the same. A 5,000-coin jackpot will do it. Keeping the jackpot at 10,000 but splitting the second level into three- and four-coin returns at 5 percent each would also work.

Alternately, pretend a marketing muckety-muck decides that more folks will flock to the casino if jackpots are raised to 100,000 coins. But the bean counters want the edge to stay at 10 percent. Here again, choices abound. One would be to cut the chance of hitting the jackpot from 0.001 percent to 0.0001 percent -- that is, from one out of 100,000 to one out of a million. The overall payback would still be 90 percent. The hit rate would drop from 40.001 to 40.0001 percent, hardly enough for players to notice.

A complex machine with dozens of probability-return levels offers much greater flexibility than this example. And, think about it. Isn't that exactly what slots with umpteen different paylines or results that qualify you to try for bonuses are all about? The muse of the machines, Sumner A Ingmark, thought of it like this:

Adding complexity fosters illusion,
Showing the value of widespread confusion.

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.