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? https://omgsiam.netlify.app/free-slots-play-as-guest-free-tokens.html. 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

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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.

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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/.

Slot Machine Cherries Clipart Svg

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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This episode was first aired on September 7th, 2011

Have you ever played a slot machine and wondered how they came up with the symbols they use? And why cherries in particular? Well, pull up a chair because you’re going to hear about the history of anti-gambling laws – and chewing gum.

Lucky Charms

The earliest slot machines officially on record date back to 1891 in Brooklyn, where a poker-based machine with five drums and 10 cards per drum became popular at the local drinking holes. But the traditional slot machine as we know it today was invented in 1895 (don’t quote me because some say it was in 1887) by Charles Fey, a mechanic from San Francisco. Fey’s simpler version had just three drums with five symbols: diamonds, spades, hearts, horseshoes, and the Liberty Bell. You can even swing in the Nevada State Museum for a look at the original Liberty Bell machine if you’re ever in Carson City.

These Bell machines became widespread in saloons and barbershops across the United States in the very early 1900s. But anti-gambling legislation also became popular around the same time. It was bad enough that by 1910 (when slots were first banned in Nevada), the Mills Novelty Company of Chicago put out a machine that was billed as a trade stimulator. It was a game of chance where people could win cigarettes or candy. In this case, the “prize” was gum.

Chew on This

Except people usually didn’t take the gum. The real prize was cash; the gum was just there to throw off the authorities. The charade was made complete by taking the playing card-style symbols off the drums and replacing them with the flavors of gum you could “win.” That’s how we ended up with cherries – and oranges, plums and lemons, among other variants. That’s also why slot machines are sometimes referred to as fruit machines, especially in England.

Slot Machine Cherries Clipart Png

That’s only four symbols, though. The fifth symbol, which used to be the Liberty Bell, was replaced by the familiar “BAR” symbol that we know today. This symbol represented the label on the gum wrapper, which featured the logo of the Bell-Fruit Gum Company. Trivia time: the band “1910 Fruitgum Company” claimed its name from the same wrapper. The Mills Company, in collaboration with Fey, produced 30,000 of these machines.

Rise of the Machines

By nominally offering prizes of gum or other foodstuffs, these slot machine variants were able to continue spreading throughout the United States, but they couldn’t stay ahead of the law forever. Legal cases were brought against many operators of slot machines, and the passing of Prohibition laws in 1920 reduced their footprint even further because the saloons were shut down.

Slot Machine Clipart Free

As anti-gambling laws relaxed, the charade with the gum was lifted, but the cherries and the other symbols remain to this day. So do many of the Bell machines. You can even buy one from antique dealers or private collectors if you’re willing to shell out a few thousand bucks. Just don’t expect the gum to be fresh.