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.

Originally, casinos installed slot machines as a diversion for casual gamers. Unlike traditional table games (such as blackjack or craps), slot machines don't require any gambling knowledge, and anyone can get in the game with a very small bet. This idea proved to be a monstrous success - slot machines eventually moved off the sidelines to become the most popular and the most profitable game.
Slot machine video from casino expert Steve Bourie that teaches you the insider secrets to winning at slot machines and how a slot machine really works.

My job for the past many years has involved writing the software that runs casino slot machines and their back end systems (player's club software and most recently server based gaming systems). I have experience not just with the software, but also with the on-site operations of multiple casinos - as I've had to go on-site to fix issues at times.

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.

I'm Krešimir Josić, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)
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

How To Write A Slot Machine Game Apps

Introduction to How to Play Slot Machines

Do you remember the first time you entered a casino as a beginner slots player? I know I do. What I remember most is being extremely confused. It was so dark, yet with so many lights. And the smoke was everywhere! Perhaps you remember something similar.

My intent is to be genuinely helpful to slots players. While I think I still have a long way yet to go, I also believe I have been somewhat of service so far.

But, perhaps you are only just beginning your slots journey. What have I done for you to ease your way into becoming a healthy, happy slots enthusiast? So, this blog is for you, the beginner slots player, to, well, help.

Always a good time! Always something different and big bonuses! These games are great, but it gets real annoying when your trying to play and it keeps asking you to give them a rating. Other than that, no complaints. https://runyellow.amebaownd.com/posts/19060991.

Throughout this blog article, I’ll be referencing other articles I’ve written on various aspects of slot machine casino gambling. These articles are freely available to all.

This article has the following sections:

Introduction to Learn How to Play Slot Machines
Entering a Casino for the First Time
My Initial Gambling Rules
The Changing State of Gambling, in Brief
Beginning Your Slots Journey
The Golden Rule
Journey into the Unknown
Summary of Learn How to Play Slot Machines

Keep Reading … or Listen Instead!

Entering a Casino for the First Time

My first experience at slot machine gambling was in 2003 at a small tribal casino (Kewadin Casino) in the upper peninsula of Michigan. I was taking a long drive back to graduate school in Iowa after visiting family in the lower peninsula and had found a hotel at which to spend the night.

A casino was located just down the highway from that hotel. I wasn’t aware of the casino being there until the hotel provided $20 worth of tokens to play at it.

I remember feeling a little nervous about entering a casino for the first time in my life. I mean, what would my family of non-gamblers think? But, I gathered up my courage and went on in.

I found it to be a highly distracting place: loud, lots of flashing lights, and smoke. This was a time when smoking was more fashionable than it is today, so there was a great deal of cigarette and cigar smoke in the air. This is still true today in some states, such as Nevada, although ventilation has gotten a whole lot better.

I distinctly remember rapidly spending the $20 worth of tokens on slots. Plus, another $50 besides which I could ill afford to lose. At the time I was a poor graduate student on a research stipend working a side job as a temporary instructor of college physics. I’d just spent my food mo