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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.
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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.
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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.
/new-bee-slot-machine.html. In order to activate the bonus round, you must get the Male Bee, the Bees Logo, and the Female Bee on the 2nd, 3rd, and 4th reels, respectively. Once in the bonus round screen, collect Flower Pendants for credits, or 5 raindrops for a special Swap icon which can be used in the game to swap out icons on winning combinations to get even more. Bee Land Slot Machine. Masterpieces come in all shapes and sizes, especially within the realm of online slots play. Released amongst a myriad of dud titles comes Bee Land, a game that takes place in a garden, but carries certain characteristics that put it a hair ahead of the competition. The Honey Honey Honey slot machine boasts flexible betting options to ensure you won’t have a bee in your bonnet about the stakes available. With sweet and sticky wins created over 20 fixed paylines and coin values starting at just 0.01, this means you can start extracting honey from as little as 0.20 credits. The following looks at why New Honey Bees is sure to grab the attention of slots fans in the weeks to come! New Honey Bees comes to us from the Cozy Games team, the up and coming online casino software developer. The graphics of the slot machine are as cartoony as you’d expect and the symbols are set on 5 reels and 20 paylines.
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
There are more varieties of slot machines than you may have ever imagined. Slots were created as a simple game in the 1800s, working as three spinning mechanical reels. The first gambling slot machine had only five symbols: horseshoes, diamonds, spades, hearts, and a Liberty Bell.
Video Slot Machines and Reel Slot Machines
Since that first slot machine, many things have changed, but the concept remains the same. The slot machine will choose a random number for each reel and will slot a symbol into a position on the reel when it stops spinning. The player wins if the reels line up symbols incorrectly on a payline.
There are now video slot machines with multiple pay lines, traditional reel slot machines, and progressive slot machines that can have huge jackpots. You can now play slot machines online and on a mobile phone. While slot machine technology has changed a lot aesthetically, the game still essentially works the same.
Random Number Generator
A Random Number Generator chip operates Today’s slot machines. These RNG chips choose outcomes of the video or reels at random for every spin. There are no patterns or hot/cold streaks, and your odds are the same for each spin with today’s slot machine. The only specific number that an RNG must adhere to is the payout scheduled by the game operator. Slot machines are set to return a specific amount of money played. The minimum amount of money returned to the player is designated by the gaming control board.
The format of a slot machine still plays a role in selecting a machine. Reel slot machines continue the tradition of the original slot machines. Many players continue to enjoy the sound of the reels whizzing around before landing on a payline. Newer reel slot machines still feature that traditional gameplay while competing with video slot machines that have as many as nine different pay lines.
Technology allows video slot machines to have as many pay lines as can fit on the screen. Today you’ll see video slot machines and online slot machine games with up to 100 pay lines. These games can be so elaborate to incorporate video clips of movies, television shows, and music videos. There are even communal video slot machines in some casinos where bonus rounds and progressive jackpots are generated and played by multiple players at different machines.
Higher Limits = Higher Payouts
One of the reasons that players still gravitate to reel slot machines is because many have fewer pay lines so they may take fewer credits to play. Slots with low credit needs come in handy when playing higher limits slot machines. Typically higher limits slot machines will return a higher percentage of money than lower limits slot machines. A slot machine where one credit is equal to $5 will return a higher percentage of the money played, than a $1 slot machine, a 25 cent slot machine, and so forth.
Some slot machine players feel more comfortable playing three credits for $15 in a $5 slot machine because of the higher return percentage than they do by playing 50 lines in a 25 cent slot machine. It’s easier for a player to understand the math behind a slot machine with fewer lines and symbol combinations.
A reel slot machine can only hold up to about 20 symbols per reel, so possible combinations are limited. A video slot machine may have up to 100 reels and symbols. Without reading the actual odds on each video slot machine, it’s almost impossible to predict the probability of winning video slot machines. It can be confusing for players who are looking for a mellow activity.
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Progressive Jackpots
This math comes into play when looking at progressive jackpots on both video slot machines and reel slot machines. Players look at the progressive jackpots and wonder if it will be easier to win with fewer reels than it would be with more. The RNG will dictate when the progressive jackpots will pay out, but the psychology of the game may impact players preference for playing a certain progressive jackpot game.
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Progressive slot machine jackpots build by players contributing a portion of their play to a prize pot to be won by one person. Progressive jackpots can be individual slot machines, groups of slot machines in a casino and now even in multiple states. Some progressive jackpots can be so massive that they will change someone’s life, so it’s worth it to know what you’re doing.
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Be sure to check out the Ultimate Online Slots Guide for even more in-depth information into how to play slots, slot strategy, as well as, slot payouts and symbols!