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The Slot Mathemagician Presents: A Vicious Cycle

Article Author
John Wilson
Publish Date
March 31, 2009
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John Wilson

It would be a great understatement to say that slot machines have changed over the past 10 years. The addition of rich multimedia sound, sharp, colorful graphics on crystal-clear LCD monitors, and eye-catching top-boxes featuring exciting bonus games makes the player’s experience more exciting. Add in the chance of a large, life-changing jackpot, and the player is not only entertained, but also has a chance to win something significant. But, not all changes have been for the better. Some have made it difficult for the operator to offer compelling games that will attract players while allowing a reasonable hold percentage in return.

One of the greatest thrills for many of today’s players is the ubiquitous bonus round. While generally associated with video slots, many stepper models also offer exciting bonus rounds. Barcrest and AC Coin have taken classic stepper games and added exciting top-boxes matching the mechanical feel of the base game.

In recent years, bonus rounds have started offering incredible awards. When nine- and 15-line games were introduced, players could expect a bonus game to give several hundred credits. The jackpot equivalent of the bonus round would see a few thousand credits paid out. Today, however, many players demand higher wins. They now think of a 400-credit bonus round as a “zonk,” expecting a good bonus round to yield 10,000 credits or more. Many players get excited when they finally get a rare bonus round, expecting to receive a hand-pay amount.

Along with the growing bonus round awards, these games frequently offer higher symbol awards in the base game. The attraction of a $1 million progressive jackpot on a penny game is obviously enticing. Nobody knows this more than Boulder, Colo., city resident Jo Ann Argyris. In 2004, she won the million-dollar jackpot on Aristrocrat’s Millioni$er penny slot. Less than a year later, she won again. When she won the second time, she had wagered roughly $35 and played for 10 minutes. This is, of course, the exception. But news stories like these show players that it is possible to catch lightning in a bottle.

Is this a good thing? How do these large jackpots occur? Using simple mathematics, we know that the game must take in more money than it gives out in order to allow the operator to make a profit. If we think of the basic game, forgetting about participation games and super jackpots like this, we can study how these mega-awards came about. Perhaps more importantly, we can determine the pitfalls for the operator.

How Much Can We Give Away?
There is an old (and not particularly funny) joke that applies to this question. The joke is about a slot mathemagician who wants to make some quick cash. He buys 100 watermelons from a local farmer for one dollar each. Setting up a roadside stand, he offers watermelons for sale for $1. After selling his entire inventory, he has a friend help him count his income. “How much did the watermelons cost?” asks his friend. “$100 for the lot,” he answers. “Well, you have $100 income,” states his friend. “I broke even,” the mathemagician realizes. “Guess you better buy more watermelons next time,” says his friend.

The point of the joke is that volume equates to profit. Generally this is true, except that each unit must be sold for a profit. The same principle applies to the games on your floor. If one game has an average wager of 45 credits and pays 97 percent, then the average profit per game is 3 percent or 1.35 credits. The more games that are played, the more profit you make. The higher the handle, the happier the operator becomes. Or does he or she? One significant problem, which we will study in the next installment, is the cycle. The cycle, the result of the technological changes made to allow higher payouts and more entertainment, can be an extremely dangerous entity for the operator.

This principle of volume equating to higher profits has one significant fallacy. This assumes that the average hold is 3 percent. In order to reach an average, some results must fall below the average and some must fall above the average. When the player makes a wager and wins nothing, the operator is temporarily ahead of the average. The amount by which the operator can be ahead is easy to determine. If the game allows a maximum of 200 credits to be wagered, the operator cannot make more than 200 credits during any particular game. For the player, the same principle applies. If they wager 200 credits, the most they can lose is 200 credits. They know their absolute risk at any given time. Of course this compounds when more games are played, but for any one particular game they cannot lose more than they wager. For the player, risk is manageable. The operator does not necessarily have this luxury.

The operator can tell their maximum risk for any game by looking at the PAR sheet or paytable. The top award is the maximum risk for any one game. It will be significantly more than the wager amount, however, and can skew the payout results for a long time. The worst-case scenario involves a new machine being placed on the floor and the top award being won on the first game played. A wager of 200 pennies paying out $100,000 dollars results in a payout of 10,000,000 pennies / 200 pennies = 50,000 x the wager.

How did we get to the position where the operator faces such risk? How were we able to offer awards of millions of dollars on a penny denomination game? What happened to make large awards possible? Let’s step back in time and see.

The Tallest Building Begins with the Foundation

The first slot game, Charles Fey’s Liberty Bell, was a three-reel mechanical with 10 stops per reel. This game had a cycle of 1,000 games, which is calculated by multiplying the number of stops on each reel. Assuming a single coin wager, the game will take in 1,000 coins for each cycle. It must, therefore, pay out less than 1,000 coins in order to have a positive hold. The maximum jackpot that this game could offer and still be profitable was 999 coins. However, this would mean there was only one winning combination in the 1,000 games. Realistically, the largest jackpot that could be offered and still keep the game appealing to the players would be quite small, perhaps in the order of 50 coins. The player was not given an opportunity to “strike it rich,” even if they won the jackpot. The operator, however, had a minimal risk involved. It was a safe game for the operator and a safe game for the player. This safety meant that nobody would lose too much. Nobody could win too much either, but overall both the operator and any individual player had a reasonable chance of coming out ahead of the game.

As time and technology progressed, operators could add excitement for the player by increasing the amount of any individual payout. This was accomplished by increasing the risk. A player may not win as much on average, but there was the opportunity to win more during any one game. This risk attracted people who wanted to gamble more for the chance of winning larger amounts. Today we know this as volatility. Volatility is not unique to the gaming industry. If your mutual fund investment is in risky stocks, you are giving up the security of keeping your initial investment for the chance of making a higher return on your investment. Some investors come out ahead, making a significant return. Others lose most of their investment. The higher the risk, or volatility, the closer the player comes to an “all-or-nothing” situation.

IGT’s “Hundred or Nothing” is an excellent example of this. This three-reel stepper has one symbol—a red seven. The player invests a single credit in a high-denomination machine. The outcome is either three red sevens and a 100-credit pay, or nothing. There is no bonus game, no small awards. You win big or you lose it all. Even the most cautious player doesn’t mind risking $1 for the chance to win $100. For many, this game is a novelty play and the investment by the player is limited. However, it shows that volatility can be a good thing, and people are willing to give up the security of their wager for a chance of a big win, especially if it is controlled. How many times they are willing to do this determines the comfort level the player has for this volatility level.

Would a senior citizen, visiting the casino as part of a bus tour, play this game? Suppose she brought $50 with her and a three-hour period before her bus leaves. This $1 all-or-nothing game would give her 50 chances at $100. During this time, she may win the $100 once or twice. However, there is a chance that she will win nothing. At three games per minute, and no wins, she’s out of money in just over 15 minutes, giving her two hours and 45 minutes to regret her decision. If she were to win once during that period, she would have $100 after playing 50 games. Would she be satisfied with doubling her money and then waiting for the bus? For a strictly monetary result, this would be a good visit to the casino. For entertainment, however, the visit is going to come up short. What is required is a bit of both—profit and entertainment. And the amount of each depends greatly upon the particular customer, the amount of profit and the amount of entertainment. Jo Ann Argyris would be quite happy playing for 35 minutes then waiting around for hours. A million dollar profit in itself provides an incredible entertainment value. But for the average player, how do we balance both sides? And does the proper mix for the player match the operator’s risk level as well?

The Liberty Bell is an excellent foundation for this study. We can move from this basic platform and study changes that will provide player profitability and player entertainment value. By expanding this game, we can see how today’s slot machines have evolved.

Stay Tuned—Same Time, Same Channel

This article has mentioned many concepts of today’s slot machines in an attempt to pique your curiosity and to get you thinking about the attributes of many games on your floor. Profit alone will not cause player satisfaction, unless it offers life-changing results. Entertainment alone isn’t the basis for player satisfaction. If players are only looking for a multimedia experience, they will see a movie or attend a live performance or concert. It is the mixture, with safeguards for the operator’s hold, that makes for a satisfied player.

The game velocity, handle level and minimum wager are all thought to contribute to a positive hold. However, higher volatility and unmitigated risk can pose serious problems for the operator. We may have gone beyond the limits of good risk management in order to make the games appealing to the players. In the end, each of these factors has manifested itself in the cycle. It is this cycle—a vicious cycle—that can pose serious risks to the operator. These risks are in the form of a negative hold and intense player dissatisfaction.

In an economy where attracting new players and retaining current ones is paramount, the long-term affect to your operations must be considered. Proponents of current high-cycle video slots say that the risk is minimal and that mathematically, a large cycle is not as serious as it seems. However, others feel that these large cycles pose considerable risk to the operator and have taken today’s slots too far. What is the truth?

Next month we’ll study how we got here, and more importantly, what it means to you.

John Wilson is the Technology Editor for Casino Enterprise Management and Owner of ICS Gaming, providing slot consulting services and game design. He has designed several slot games in both Class II and Class III markets.  He can be reached at jwilson@icsgaming.com.

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