PLAYING IT SMART by ALAN KRIGMAN

How slot machines "work" and how the casino bosses set them

A rocket scientist at a party was complaining to everyone who'd listen that people were using high-tech products with no idea how they work. "Automobiles are good examples," he said. Someone in the group responded, "I know how cars work. Turn the key and they start. Then pull the handle to D or R, step on the gas, and they go. To change direction, turn the steering wheel." The two were talking about different levels of "how they work," of course.

The slots are like this, too. They work on three levels. Computer chips and other electronics implement the functionality of the games. Math and logic underlie this functionality. And a user interface lets solid citizens place bets, make gambling choices and trigger the action, monitor results, and collect payoffs.

Players think in terms of the interface, casinos the math and logic, and machine manufacturers the electronics. Bettors needn't know about the electronics. And they can enjoy casino visits, even win money, without understanding the math and logic. However, their gambling judgement and strategy will be better with at least an intuitive grasp of how the chance of each result is established, the way this is related to the assigned payoffs, and the impact of these factors on expectations for a session.

For this purpose, picture a bin like those you see in lottery drawings. Say it contains a million ping-pong balls, 500,000 each marked +1 and -1. Bet $1 per round. Your chance is 500,000 out of 1,000,000, one out of two, you'll win $1. After a million rounds, you can figure on being at or close to break even.

This wouldn't be much of a game, though. Players would stay away because prospects of a big haul are dim. The casinos wouldn't like it because, on the average, they make no profit.

To address the first issue, the bosses scribe big values on some of the balls. Maybe they write +100,000 on one. And put +1000, +500, +250, +50, +25, +10, +5, +1, and 0 (you get back $1 and the machine announces a "win" but you really just push) on others.

To solve the second problem, the casinos must pick how many they load of each value. They typically start with a desired edge and what they consider a "hit rate" players won't find discouraging, and calculate the numbers that will provide both. Pretend they decide on 10 percent edge (in a million "statistically correct" rounds, they'll keep $600,000 and pay $500,000, earning $100,000). And they pick a 40 percent -- four out of 10 -- hit rate (players get a return on 400,000 rounds).

Getting the hit rate to be four out of 10 is easy. The bin needs 600,000 -1's. Imagine they mark just one ball +100,000 (chance is then one out of a million). They could determine numbers for the other values by hand, using a trial-and-error method, but this would be a Herculean task. A computer technique called "linear programming" will yield answers in seconds. And there are multiple solutions so they can generate a few and choose from among them. The following table shows one possibility.

Numbers of ping-pong balls assigned various values and results of a statistically correct game with the desired payoff levels, 10% house edge, and 40% hit rate

amount no of total won or lost ping-pong won or lost per round balls 100,000 1 100,000 1000 1 1,000 500 17 8,500 250 19 4,750 50 21 1,050 25 23 575 10 25 250 5 48,104 240,520 1 143,355 143,355 0 208,434 0 -1 600,000 -600,000

A computer chip can be programmed to select a number at random from 1 through 1,000,000. It can also be programmed to assign one of these numbers to refer to a value of 100,000, one to a value of 1,000, 17 to a value of 500, 19 to a value of 250, and so forth. When done, the electronic and ping-pong ball versions of the game would be effectively indistinguishable, despite one being shrouded in myth and mystery and the other intuitively obvious. It's as the minstrel, Sumner A Ingmark, mused:

If two things are equivalent in every key dimension,
Then arguing their differences is frivolous contention.

(c) 2008, ICON/Information Concepts Inc

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