Casino Enterprise Management

Friday. 9:32 p.m.

It was a dark and stormy night. Somewhere in the distance a dog barked. My day read like a cheesy detective novel. And my night was no better. It had been a long day, and I should have been at home. But where is home anyway? My office is my home. I'm a gumshoe. A hawkshaw. A private eye. I had just finished a rather difficult case and was taking a break. It was a case of 12-year-old Scotch, but that's beside the point. So there I was: leaning back in my chair, my feet crossed on the desk, blowing smoke rings in the air. I was blowing the smoke rings, not my feet. I looked over to the door, and there she was. She would tell me her name was Jane. She was standing in the doorway, the light from the hall forming a perfect silhouette. She was tall and as thin as I wasn't. She looked to be in her early twenties. And she was in the bad part of town. I didn't know if she was there for me or if she was looking for help. I figured she was looking for help.

"I'm looking for help," she said.

Well, that answered my question. I offered her a chair and she sat across from me, crossing her legs and placing her hands on her knee. She sat perfectly straight and brushed her hair back. I sat up, put my feet on the floor, leaned across the desk and offered her a cigarette. "Eww, gross. No, thanks," she said, waving her hand in front of her face.

This certainly wasn't the good ol' days anymore. "You came to the right place, doll," I told her. "I'm your man."

"I hope so," she said, the softness in her voice captivating me. "I need your help solving a mystery. You're the only one who can help."

Smart girl! I thought to myself. They always come to me when they need help. And I do love a good mystery.

She explained her problem. And she was right. She needed my help. It seemed this mystery was bigger than it sounded. It would take some serious sleuthing to get to the bottom of it. One thing was certain: She had come to the right place. It was late into the night when she finished her story. She was worried, and I did my best to reassure her. "I'll solve your mystery, doll. I'm on the case," I said.

Story was this dame worked at the local casino. Seemed they had just put in a bunch of new slot machine games. These games were different, though. Mystery games. Some offered a mystery progressive jackpot. Some just gave a mystery payout from time to time. She needed to know how they worked, how the math figured out.

I told her I'd call as soon as I had some information and asked how I could get ahold of her. "You can't," she replied. "I'll get in touch with you."

She didn't want me knowing her number. Smart girl. I was on the case: The Case of the Mystery Progressives. I knew that before I solved it, I'd likely have to make a few calls. A few calls to some old acquaintances, like Frank and Joe Hardy, and Michael Mastropietro at WMS.

It was late and I needed some rest. That case I'd just finished was making me tired. I grabbed my overcoat and fedora and headed out of my office. I locked the door and walked down the stairs to the parking lot. I got in my car and shook the water off me — it was a dark and stormy night, after all. I sat there for a few moments thinking about this girl and the mystery she needed solved. I decided that I could rest later. She came to me for help, and I was on the case. I left my office and headed to where it all started.

Saturday. 1:03 a.m.

I could see the glow of neon several blocks before I arrived. The local casino was open 24/7, and early in the morning was an excellent time to visit. Walking into the foyer, I could hear the familiar hum of the slot machines. I stepped onto the casino floor and surveyed the vast expanse before me. Lights were flashing and people were scurrying around like ants. I slowly walked around the perimeter, trying to decide where I would start my investigation. Then, out of the blue, it hit me like a ton of bricks. I saw a sign. And I knew that I was in the right place. It was, curiously enough, a large neon sign. With a plasma display and flashing LEDs. "Mystery Progressive," it read. And that's just what the lady had said.

It seemed that the mystery was widespread and had recently found its way to this local casino. They had taken a bank of slot machines and somehow added a strange payout. A mystery payout. It wasnÕt a hidden thing, either. Hey, they had this large neon sign advertising it. But they were giving money to the slot players, and nobody seemed to know why. I knew at once that I could get to the bottom of this.

I sat down at a machine and fed it a couple of bucks. An old broad was playing the game beside me. I asked her if she knew about these mystery payouts. "They're pretty nice," she said. "But there is a secret to them."

My interest piqued, I stopped playing and turned to her. Maybe I could wrap up this case on the spot. "What's the secret?" I asked.

She leaned closer, whispering, obviously not wanting others to hear her secret. "You have to rub the screen while the reels are spinning," she confided. "This helps the jackpot symbol show up."

"Rub the screen?" I asked.

"Yes. It really works."

"I see," I replied, not knowing what else to say. Afraid of the answer I might hear, I asked, "Anything else?"

"Oh, yes," she said, leaning even closer. "If you cover one of the reels with a $10 bill, the reels will soak up the luck from your money."

"Osmosis?" I asked.

"No, just a bit of dry skin," she replied. "And when you have your players' card, make sure you pull it out when the reels are spinning. Otherwise, they know, and if you've won too much already, they won't let you win any more. It confuses them."

"Them?" I asked. She pointed to a small black dome in the ceiling above.

"In the security room. They watch everything. They can control your machine, you know."

This time I was speechless.

"But what about the mystery?" I finally asked.

"Keep rubbing the screen." she said. "Keep rubbing the screen!"

In case your space ship comes back for you, I guess I'd better keep watching the skies, too, I thought.

One thing was clear: My work was done for the evening. I looked up at the black dome and waved, nodded my head in the direction of the old broad, and shrugged my shoulders. Maybe her story would make more sense in the morning. For now, it was time to get some rest.

Saturday. 9:18 a.m.

I woke up and saw the sun shining through my window. The day was fresh and I had a mystery to solve. After a hearty breakfast I sat down and thought about the old broad I had met the night before. I knew I'd better take a different direction in my research. The games certainly advertised a mystery payout, but didn't say how it happened. I noticed that one had a mystery jackpot that kept increasing. The sign said it would pay between $20 and $50. I thought that curious, got up and looked in my little black book. Seems there is a company called WMS that makes some of these mystery jackpot machines. I called a friend who works there. His name was Mike, a senior game strategist. I got him on the phone and explained the situation.

"Oh, yes, the mystery pays," he said. "There are two types of mystery progressives."

I knew at once I'd find my answers. "What are the two types?" I asked.

"First, when the award is pre-determined to occur at a specific value in a range of values, such as $20 to $50. Second, when the award is not pre-determined but the jackpot, or a game that awards a jackpot, has a fixed probability of triggering a bonus event on each spin — this probability depending on wager."

Hmm, I thought. This guy seems to know his stuff!

Mike explained how this works and how it affected the base math. It seemed complicated when I first looked at it, but it really wasn't. It was all how you looked at the payouts and related them to the base math. He provided a complete explanation of this type of mystery payout, and I was anxious to get the complete picture. "What about the second type? How do they work?" I asked.

"For the second type, where the trigger is random, but the prize is unbounded, the calculation is slightly different. The probability depends upon the bet, so the expected value is independent of how much you are betting. Again, it is the case that a player betting twice as much has twice the odds of winning," he explained. "There are also games with mystery triggered bonus events often called 'Bonus Banks,' like WMS titles Goldfish™ and the new Instant Winner Bonus Bank™. These games are not linked, but each game has a fixed probability of triggering the bonus event on each spin, though this probability does not depend on wager."

Mike went through several examples and described the formula used for each type of mystery pay. It was time to work through the formulas and make some graphs for that Jane dame. It was going to be a long day, but I knew that in the end Jane would have her answers.

Before he hung up, I had to ask Mike the all-important question. "Mike, I have one more question," I said.

"Sure. What is it?"

"Is it true that rubbing the screen helps you win?"

We must have had a bad connection because the line went dead. I wondered what the probability of that happening was.

Saturday. 7:32 p.m.

Jane sat in the chair across from my desk. I opened my desk drawer and pulled out a large manila envelope. "It's all in here," I said. "The solution to your mystery. The math. Everything."

I opened it, pulled out several papers, a couple of graphs and some charts. "Alright, here it is," I told her. "See, there are a couple of ways that these mystery pays can be done. First, let's look at the mystery progressives. They pay out between a certain range, guaranteed. They have a base amount, which is the minimum amount they can pay. They start out at this amount. Some of the machines in your casino are set to pay between $20 and $50. When the pay is awarded, it resets to $20. From there, it works like a regular progressive jackpot. A certain percentage of all the coin-in is added to the mystery jackpot. And every machine that's being played contributes to this jackpot. Each game that's played has a random chance of winning."

"How is that done?" she asked.

"Quite simply," I replied. "The winning award is selected at random. There is an equal probability of any value within the range being selected. Now, let's assume that we contribute 1 percent of the coin-in to this progressive amount. For each dollar wagered, 1 cent is added to the current level. When that level reaches the pre-determined award, the player wins the award."

"Let me see if I understand this," Jane said. I could see her wheels turning. "A winning award is selected, somewhere within the range. Let's say it's $42.26. The contribution starts out at $20. I make a $1 wager and it increases by 1 percent, or a penny. It's now $20.01. The person beside me bets $1. We're now at $20.02. Whoever makes the bet with the contribution that meets $42.26 is awarded that amount."

"You got it," I told her. "Then another award amount is selected at random and the process starts over. Now, if you were to make a $2 wager, you would increase the amount by two cents. The more you wager, the greater the chance you have of winning the progressive."

"That seems pretty straightforward," Jane replied. "Each time a number is chosen, then, it's a mystery. It could be $20; it could be $50, or anything in between. That's how you can guarantee the payout range. But how do we calculate the payout to the game? I was thinking that you would have an entry in the PAR sheet with a $20 payout, and then a 1 percent progressive contribution. But how do you determine how frequently the $20 is paid?"

"That way will work, but my source tells me an important consideration is that the award is 'fundamentally independent of the game cycle,'" I explained. "It's a side award that isn't based on symbols landing on the payline or scatter awards. In fact, we can't have the award pay on a combination of symbols. What happens if the symbols don't show up before the upper amount is reached? Let's look at the math: If we guarantee the payout is between $20 and $50, then the average award will be $35. We add up the high and the low award and divide by two."

"Right," she said. "And if the award were between $20 and $100, then the average would be $60."

"Exactly, doll," I told her. "Now, the average increase in the progressive payout is $15. We pay, on average, $35. The base amount is $20. That leaves a $15 difference. In order to have the progressive jackpot increase by $15, we have to know the contribution. At a 1 percent contribution rate, we need $1,500 coin-in. One percent of $1,500 is $15. In order to determine the expected value of this award, we divide the average award by the coin-in contribution. That's $35 divided by $1,500, which gives us 2.33 percent. This tells us how much it really takes to pay this award. In simple terms, you could consider this award the same as a 2.33 percent progressive jackpot. That takes into account the $20 starting amount. Take a look at Figure 1 in the envelope."

"I think I'm following you," she replied. "Let's try the other example, paying between $20 and $100. The average payout is $60. The increase would be $40, which is how much we have to go from the base amount to reach the average payout. At 1 percent, we would need $4,000 coin-in to reach this value. Now, we take the average amount — the $60 — and divide by the coin-in contribution, $4,000. $60 divided by $4,000 is 1.5 percent ... That doesn't seem right. We've increased the maximum award but decreased the expected value."

"Oh, that's right," I reassured her. "In the first case we didn't pay too much above the base amount. Here we are. More of the award comes from the progressive contribution and less from the base amount. As a result, the $20 is paid less frequently, on average. Therefore, the expected value will be closer to the progressive contribution. If we made the top award $10,000, the expected value would be 1.004 percent because most of the award is comprised of the progressive contribution and less from the initial progressive base."

"That's great!" she replied. "That solves that part of the mystery. But we have the other one as well."

"Yes, where the amount is just paid at random — without any guaranteed amount," I said. "This is called an unbounded award. And in this way, we can break the mystery pays into several categories. It may increase, like a progressive, or just remain at a fixed amount. You may have a better chance of winning the mystery award by betting more. Or you may have the same probability of winning the award no matter what you wager, but the more you wager the larger the mystery award you receive."

"Let me take this and read it over. I'll be back tomorrow for the rest," she told me.

With that she stood up and walked out of my office. But she would be back. We'd just scratched the surface of these exciting mystery pays. Just wait 'til she sees the rest!

John Wilson is the 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[at]icsgaming.com.