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.
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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.
Free 3 Reel Slot Machines
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. Winning at the slots free book.
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.
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Choosing the right slot machine requires you to decide which type of game you would like to play, how much you are willing to bet, which theme you would prefer and what types of bonuses you would like. Introduction to Choosing Slot Machines. Once a specific casino has been determined to currently be the best of any available, choosing slot machines becomes the next step towards making a profit at slots. The best you can do is just pick a slot that’s fun to play. Even though all slots work in the same basic manner, they come in all different types and styles. You have traditional reel slots, video slots complete with storylines and even 3D slots like those found at Bovada. It’s best to forget about getting an advantage when playing slots. In general, it’s believed that casinos usually put their tight slot machines, yet the ones that. For example, you can play amusing Alaskan Fishing slot with 243 Ways to Win and Free Spins during which all your prizes are doubled. The top jackpots offered are not so impressive if compare with other slot machines. How to pick the right slot machine to play.
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This episode was first aired on September 7th, 2011
The problem
A slot machine is a gambling device that the user inserts money into and then pulls a lever (or presses a button). The slot machine then displays a set of random images. If two or more of the images match, the user wins an amount of money that the slot machine dispenses back to the user.
Create a program that simulates a slot machine. When the program runs, it should do the following:
- Ask the user to enter the amount of money he or she wants to enter into the slot machine.
- Instead of displaying images, the program will randomly select a word from the following list: Cherries, Oranges, Plums, Bells, Melons, Bars
- To select a word, the program can generate a random number in the range of 0 through 5. If the number is 0, the selected word is Cherries; if the number is 1, the selected word is Oranges; and so forth. The program should randomly select a word from the list three times and display all three of the words.
- If none of the randomly selected words match, the program will inform the user that he or she has won $0.
- If two of the words match, the program will inform the user that he or she was won two times the amount entered.
- If three of the words match, the program will inform the user that he or she has won three times the amount entered.
- The program will ask whether the user wants to play again. If so, these steps are repeated. If not, the program displays the total amount of money entered into the slot machine and the total amount won.
Breaking it down
Initialize constants
Declare variables
Create supporting methods
Play slot machine, record results
Display totals
Output
Slot Machine Code Java
Unit tests
Level Up
- Randomly allocate the number a pool of $.
- Enhance output to look like a real slot machine.
- Enhance getReal to be more efficient.
- Create an ENUM to represent reel type and change parameter type to method getReel.
- What changes would need to be made to play a slot machine with 4 reels?
- Determine the algorithim flaw with the output.