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Today, the mathematics of slot machines. The University of Houston mathematics department presents this program about the machines that make our civilization run, and the people whose ingenuity created them.
Mathematicians first got interested in randomness by studying games of chance. Ever since, the histories of mathematics and gambling have been intertwined. Clever gamblers use mathematics to look for the smallest advantages, and casinos use sophisticated mathematical tools to devise new ways of drawing in players.
Indeed, a patent granted to the Norwegian mathematician Inge Telnaes in 1984 transformed the gambling industry. Prior to Telnaes’ invention, slot machines were essentially mechanical devices. Besides being difficult to tune and maintain, mechanical slot machines suffered from an essential problem: Let’s look at a machine with three reels, each with 12 symbols, with one of those 12 symbols a cherry. The likelihood of getting three cherries, and winning the jackpot, is 1 in 1,728. If the casino wants to make money, the jackpot payout should be, say $1,700 on a $1 bet. That does not seem attractive by today’s standards. However, the only way to increase the payout is to decrease the chances of hitting a jackpot.
Adding another reel is a possibility. For instance adding a fourth reel in the previous example would get us to a jackpot of about $20,000. But people do not like machines with more reels — they intuitively, and rightfully, feel that extra reels diminish their chance of winning. Another possibility is to put more symbols on each reel. But the astronomical jackpots you see in casinos today would then require truly enormous machines.
Inge Telnaes proposed a simple solution: Let a random number generator — a computer chip — determine the combination of symbols that appear when the reels stop. In other words, use a chip to control where the reels stop on a spin, but create the illusion that the wheels stopped on their own. The number of possible outcomes on the slot machine does not change. However, by reprogramming the chip, the operator has full control over the likelihood of each of the different outcomes. For instance, the operator could make the three cherries appear only once in a million spins.
This was a brilliant insight: Suppose I pick a number between one and a million. Would you be willing to bet that you can guess that number? The answer is probably not. But let a computer chip pick such a number, put the chip in a machine with blinking lights and spinning reels, and many people will be more than willing to make the bet. It is simply because what people assume is happening in a slot machine is very different from what is actually happening.
The Magician oil painting by Hieronymus Boschfrom between 1475 and 1480
The history of gambling is also intertwined with that of a less reputable group — tricksters and swindlers. In the long run, the only sure way to make money by gambling is to create the illusion that your opponent can win, while keeping the odds firmly on your side. And that gives those who know math a very solid advantage.
Slot Machine Images Jackpot
I'm Krešimir Josić, at the University of Houston, where we're interested in the way inventive minds work.
NOTE: In the example with three cherries, I assumed that one only wins in the case the spin results in three cherries, and there is no other winning combination. In actuality, there are typically many winning combination, and as a result, the jackpot would have to be even smaller.
The following story in Wired Magazine shows the drawbacks of the new generation of slot machines — they are easier to hack and to counterfit than their mechanical counterpart http://www.wired.com/magazine/2011/07/ff_scammingslots/.
Here is a more exhaustive discussion of the history of slot machines, and the random number generators within them http://catlin.casinocitytimes.com/article/non-random-randomness-part-1-1243. You may want to scroll towards the end of the article to read about how flaws in the design of gambling machine resulted in somebody picking 19 out of 20 winning numbers in a game of KENO — and doing so 3 times in a row. That person walked away with $620,000, but only after some controversy.
Both images are from Wikipedia. The slot machine image was taken by Jeff Kubina.
For more mathematics in everyday life, visitkjosic.wordpress.com.
This episode was first aired on September 7th, 2011
This is a slot machine that resembles the real slot machines in the casinos. To create the project, you need to insert three image boxes into the form and program them so that they will display a set of three different pictures randomly when the user presses on the spin button. It involves a randomization process. Next, a timer needs to be incorporated into the procedures so that the program can produce animated effects. In addition, you can also insert the Microsoft Multimedia Control so that it can play sounds in synchronization with the spinning of the slot machine as well as when the player hits the jackpot. You can design any interface you like. We have created an interface as shown below:
The Interface
The Video Demo
The Code for Spin Sub Procedure
The three random variables a, b and c will be randomly assigned the values 1, 2 and 3 using the RND function. Based on these three random numbers, three different pictures will be loaded into the three image boxes randomly using the LoadPicture method. Animated effects are created by putting the above procedure under the control of Timer1, which will call the spin procedure after every interval until it fulfills a certain condition. Sounds are also added using the Microsoft Multimedia Control to make the game more realistic and interesting. The amount won is controlled by the If...Then...End If statements
It is important that you define the correct path for the LoadPicture method, otherwise the program will not be able to run. For example, our path is C:VB programImagesgrape.gif, you need to create the necessary folders and have the necessary image file if you wish to copy the program directly. If you place the image file in a differently folder, you need to modify the path accordingly. For example, if your image file is in D:VB programImagesgrape.gif, then you need to modify the LoadPicture method to LoadPicture('D:VB programImagesgrape.gif').
If you wish to use our image files, you can download from the links below:
sound and the other for the jackpot sound. Below is the video demo of the slot machine simulator.Winning Slot Machine Images
Slot Machine Games
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