The gaming industry is big business in the U.S., contributing an estimated US$240 billion to the economy each year, while generating $38 billion in tax revenues and supporting 17 million jobs.
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What people may not realize is that slot machines, video poker machines and other electronic gaming devices make up the bulk of all that economic activity. At casinos in Iowa and South Dakota, for example, such devices have contributed up to 89 percent of annual gaming revenue.
Spinning-reel slots in particular are profit juggernauts for most casinos, outperforming table games like blackjack, video poker machines and other forms of gambling.
What about slot machines makes them such reliable money makers? In part, it has something to do with casinos’ ability to hide their true price from even the savviest of gamblers.
The price of a slot
An important economic theory holds that when the price of something goes up, demand for it tends to fall.
But that depends on price transparency, which exists for most of the day-to-day purchases we make. That is, other than visits to the doctor’s office and possibly the auto mechanic, we know the price of most products and services before we decide to pay for them.
Slots may be even worse than the doctor’s office, in that most of us will never know the true price of our wagers. Which means the law of supply and demand breaks down.
Casino operators usually think of price in terms of what is known as the average or expected house advantage on each bet placed by players. Basically, it’s the long-term edge that is built into the game. For an individual player, his or her limited interaction with the game will result in a “price” that looks a lot different.
For example, consider a game with a 10 percent house advantage – which is fairly typical. This means that over the long run, the game will return 10 percent of all wagers it accepts to the casino that owns it. So if it accepts $1 million in wagers over 2 million spins, it would be expected to pay out $900,000, resulting in a casino gain of $100,000. Thus from the management’s perspective, the “price” it charges is the 10 percent it expects to collect from gamblers over time.
Individual players, however, will likely define price as the cost of the spin. For example, if a player bets $1, spins the reels and receives no payout, that’ll be the price – not 10 cents.
So who is correct? Both, in a way. While the game has certainly collected $1 from the player, management knows that eventually 90 cents of that will be dispensed to other players.
A player could never know this, however, given he will only be playing for an hour or two, during which he may hope a large payout will make up for his many losses and then some. And at this rate of play it could take years of playing a single slot machine for the casino’s long-term advantage to become evident.
Short-term vs. long-term
This difference in price perspective is rooted in the gap between the short-term view of the players and the long-term view of management. This is one of the lessons I’ve learned in my more than three decades in the gambling industry analyzing the performance of casino games and as a researcher studying them.
Let’s consider George, who just got his paycheck and heads to the casino with $80 to spend over an hour on a Tuesday night. There are basically three outcomes: He loses everything, hits a considerable jackpot and wins big, or makes or loses a little but manages to walk away before the odds turn decidedly against him.
Of course, the first outcome is far more common than the other two – it has to be for the casino to maintain its house advantage. The funds to pay big jackpots come from frequent losers (who get wiped out). Without all these losers, there can be no big winners – which is why so many people play in the first place.
Specifically, the sum of all the individual losses is used to fund the big jackpots. Therefore, to provide enticing jackpots, many players must lose all of their Tuesday night bankroll.
What is less obvious to many is that the long-term experience rarely occurs at the player level. That is, players rarely lose their $80 in a uniform manner (that is, a rate of 10 percent per spin). If this were the typical slot experience, it would be predictably disappointing. But it would make it very easy for a player to identify the price he’s paying.
Raising the price
Ultimately, the casino is selling excitement, which is comprised of hope and variance. Even though a slot may have a modest house advantage from management’s perspective, such as 4 percent, it can and often does win all of George’s Tuesday night bankroll in short order.
This is primarily due to the variance in the slot machine’s pay table – which lists all the winning symbol combinations and the number of credits awarded for each one. While the pay table is visible to the player, the probability of producing each winning symbol combination remains hidden. Of course, these probabilities are a critical determinant of the house advantage – that is, the long-term price of the wager.
This rare ability to hide the price of a good or service offers an opportunity for casino management to raise the price without notifying the players – if they can get away with it.
Casino managers are under tremendous pressure to maximize their all-important slot revenue, but they do not want to kill the golden goose by raising the “price” too much. If players are able to detect these concealed price increases simply by playing the games, then they may choose to play at another casino.
This terrifies casino operators, as it is difficult and expensive to recover from perceptions of a high-priced slot product.
Getting away with it
Consequently, many operators resist increasing the house advantages of their slot machines, believing that players can detect these price shocks.
Our new research, however, has found that increases in the casino advantage have produced significant gains in revenue with no signs of detection even by savvy players. In multiple comparisons of two otherwise identical reel games, the high-priced games produced significantly greater revenue for the casino. These findings were confirmed in a second study.
Further analysis revealed no evidence of play migration from the high-priced games, despite the fact their low-priced counterparts were located a mere 3 feet away.
Importantly, these results occurred in spite of the egregious economic disincentive to play the high-priced games. That is, the visible pay tables were identical on both the high- and low-priced games, within each of the two-game pairings. The only difference was the concealed probabilities of each payout.
Armed with this knowledge, management may be more willing to increase prices. And for price-sensitive gamblers, reel slot machines may become something to avoid.
Spinning Slot Machine Effect Pedals
I was bored and that can be a dangerous thing. Like doodling on the phone book while you are talking on the phone, I doodle code while answering questions on DIC. Yeah, it means I have no life and yes it means I was born a coder. During this little doodle I decided to make a slot machine. But not your standard slot machine per say, but one designed a little bit more like the real thing. Sure it could have been done a little more simpler and not even using a Wheel class at all, but what fun is that? In this entry I show the creation of a slot machine from a bit more of a mechanical aspect than a purely computerized one. It should provide a small sampling of classes and how they can represent real life machines. We cover it all right here on the Programming Underground!
So as I have already said, this little project was just something to play around with. It turned out kinda nice, so I thought I would share it. But what did I mean about it being mechanical in nature? Well, if you have ever played a real slot machine, not the digital ones they have in casinos now, you would see a metal case with a series of wheels. Typically it would be three wheels with pictures on them. When you put your money in and pull the handle the wheels would be set into motion. They would spin and then the first wheel would stop, followed by the second and then the third. After they have all stopped, the winnings are determined and you are paid out in coinage or credits.
I thought, why not be a bit mechanical in this slot machine design and create the wheels as a class called “Wheel” and give it the ability to spin independently of the other wheels? Have the wheel keep track of which picture (or in our case number) is flying by and report the results to the actual slot machine class. I could have done this mechanism without the need of a wheel at all and instead load up an array and have it randomly pick a number from the wheel. Little slimmer, little more efficient but wouldn’t show much programming theory.
What do we gain by recreating these Wheel classes and spinning them independently? Well, you gain a slight bit of flexibility. Independently we are able to control the speed of the spinning if we wanted to, we are able to grasp the idea of the wheel as a concept in our mind and manipulate it. We could easily built in features like if the wheel lands on a certain number it will adjust itself. Like some slots in Vegas, if you land on lets say a rocket in the center line, the machine would see the rocket and correct the wheel to spin backwards 1 spot (in the direction of the rocket as if the rocket was controlling the wheel). We could spin one wheel one way and another wheel another. We could inherit from that wheel and create a specialized wheel that does a slew of new different behaviors. All encapsulated into one solid object making the actual Machine class oblivious to the trickery of the wheel itself… encapsulation at its finest!
The machine class we create will contain 3 pointers. Each to one of the wheels. The machine itself will be in charge of a few different tasks. Taking money, issuing and removing credits, determining when to spin, telling each of the wheels to spin and checking our winnings based on some chart we create. It has enough on its plate than worrying about the wheels and reading their values.
So lets start with our Wheel class and its declaration/implementation…
wheel.h
As you can see the wheel itself is not a difficult concept to envision. The bulk of the work is in the read() method. Here we simply read the values from our internal array of integers (the values on the wheel) and return those values as an array of the three integers… representing the visible column. This column will then be loaded into our 2-Dimensional Array back in the Machine class. The 2D array represents the view or screen by which the user sees the results. Remember that the user never gets to see the entire wheel. Only the 3 consecutive values on the face of the wheel.
Here is how it may look in the real world. We have our machine with the three wheels and our 2D array called “Screen” which acts as our viewing window. Each wheel will report its values and those values will be put into the screen…
Below is our machine class…
machine.h
This looks like a lot of code but really it is not if you look at each function. Most of them are very very simple to understand. We have a spin method which essentially spins each of the wheels, reads their values back from the Wheel class into a pointer (representing each column), then they are loaded into the 2D array one column at a time (our view screen), printed for the user to see the results and lastly the winnings are checked. The checkwinnings() method determines which rows to check based on the amount of the bet. If they chose 1 line, it checks for winning combinations on the middle row only. If they choose 2 lines, it checks the middle and top lines, 3 line bet checks all three horizontal rows, 4 line bet checks the first diagonal as well and 5 line bet checks both diagonals in addition to the lines.
How does it check the lines? Well each line is given to the checkline() helper function which compares the 3 values of the line against an enumerated type of various symbols. Here we are just assigning a symbol against each numbered value to help the programmer determine which numbers correspond to which winning combos. For instance, luckyseven represents the number 3 in the enumeration. So if it runs across a line with 3 number 3s, then it knows it hit the grand jackpot and credits the player 1000. This method makes things easy because if we ever wanted to change the win patterns later, we could change the enum and checkline method to do so. We could also build in multiple types of symbols and even let the user choose what slot machine game they want to go by. It becomes very flexible and is a testament to great design!
Lastly we can put some tests together just to show some the various aspects of how this thing works and how the programmer can use the classes…
Spinning Slot Machine Effect Pedal
slotmachine.cpp
Spinning Slot Machine Effect Game
This simply inserts a 5 dollar bill and a coin for good luck. Then bets 5 lines and spins. Despite the outcome we go and bet five lines again and spin once more. Hopefully we win something this time around! But either way, those are the classes for you and I hope you like them. As always, all code here on the Programming Underground is in the public domain and free for the taking (just don’t cause a mess in isle 3, I am tired of running out there for cleanup). Thanks for stopping by and reading my blog. 🙂