The Peoples Slot Machine
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.
- It’s actually unlikely to find a simple three scroll slot 30 win line machine like the old days anymore. Now online slots offer three scroll games, five scroll games, and variations that take some games up to 100 win lines. One of the most common variations you’ll encounter is free slot machines with Wild symbols.
- Gambling authorities are there to ensure that the gaming industry is operating correctly.
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.
Video Slot Machines. Video slots are basically computer software that represents the reels spinning and the symbols lining up. The main difference between reel and video slots is that the latter can offer more than 5 paylines, depending on the casino's needs. Some video slots have 9, 15, 25, 30, or even 100 different paylines. Class 2 slot machines are generally found in smaller gambling locations. The players are all playing against each other and competing for the jackpot. The more people that lose money to the game, the higher the jackpot is. Class 3 slot machines are more common in large gambling cities such as Las Vegas.
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.
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
While every slot player will have their favourite game name, what you might not know is that people call them all sorts of things. From regional dialect to local slang, here are ten things people call slot machines that you might not have heard of…
10 – Fruit Machine (British English)
This term comes from the traditional fruit images on the spinning reels, such as lemons and cherries. But often there was also bars (But mostly fruit).
9 – Puggy (Scottish English Slang)
Also called Puggies, it is a term for something playful and is meant as a term for endearment and fondness!
8 – Slots (Canadian and American English)
Games Slot Machine Free
The classic name. The slot refers to the currency detector hole that you ‘slot’ you money into. Any gambling machine without one of these isn’t truly a slot machine.
7 – Pokies (Australian English and New Zealand English)
Pokies is short for poker machines and it pretty much an exclusive to Australian word. But these days it is catching on in many other parts of the world.
6 – Liberty Bells (American English)
This was the brand of the very first slot machine and once upon a time that was all people knew to call them.
5 – One-Armed Bandits (American English)
This was the classic name for the classic types of slot machines. With one big handle on the side, you would pull it to spin the reels. But it got its name bandit because it would take all your money (most the time anyway).
4 – Betting Units (British English)
This is a more official name than one used by the players. Betting Units or the Fixed Odds Betting Terminals (FOBTs) often seen in bookies.
3 – Video Slots (American English)
Some people like the video slots, some don’t But these are the ones that have digital reels rather than real ones like our next name.
What People Play The Slot Machines
2 – Reel Spinners (American English)
This name was only really used since the invention of the video slots. Some people just like to play games with real reels rather than digital ones.
The Peoples Slot Machines
1 – The Stand Up’s (American English)
These are often older slot machines that used to be played stood up obviously. Think of the older classic penny arcades and you will know what I am talking about.