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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.
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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.
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. Hard rock casino online nj reviews. 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. Slot machines probability winning. 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
The modern slot machine uses an algorithm known as a random number generator, RNG, which does not use any form of memory to determine when a number should be generated.
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Although it is known as a random number generator, the modern, Online slot machine actually randomly generates the different tiles used on the different spaces of a slot machine. All the different combinations of numbers, whether generated across three, five, or even greater numbers of reels, are random and must generate numbers independent of each other.
The history of slot machines began with metal reels filled with numbers that would spin and stop with a magnetic braking system. This system would randomly generate a stopping point for each drum after the reels were spun by the player. Some players would believe they had seen a moment when a slot machine became hot or would stop paying out.
RNG is used in video slots in casinos around the world. The modern slot machine does not have any built-in memory and generates hundreds of numbers per minute.
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The lack of memory means the algorithm used to generate each number is completely independent of each reel on the slot machine. It is possible for a player to hit a jackpot on a number of occasions in specific plays, but this is a purely random part of the gameplay developed through the use of algorithms.
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Every slot machine at a casino uses something called a par sheet which provides information about the odds for each tile on a reel. Each reel is weighted to reach a certain number of spins for every time a certain tile is generated by the algorithm. The lower the number of tiles appearing on each reel lowers the odds of a jackpot. Spin palace online casino promotions.
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Each slot machine algorithm also includes the payback percentage which gives an insight into the winnings a player can expect as they play. The percentage is usually given as a number of around 97 percent which means a player can expect to win from $3 gambled in every $100. This number is not a figure of how much money a player will win but is part of the algorithm deciding how often the slot machine will offer a winning spin.
Want to know where slot machines came from? Check out the history here!
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