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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.
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
Slot Machine For Sale
The wild symbols in slot machine games can also act as a multiplier, depending upon the type of the slots game. When one of the wild symbols in slots games online is used in order to complete the winning combination, it acts as a multiplier and multiplies the payout for that combination. Let us take an example of a free slots game known as the T-Rex slots game. As mentioned above, in this game, the symbols in digital free slot play double the payouts. In this particular game, there are five stegosaurus symbols used to enable payline and it pays out 5,000 coins. However in case there are 4 symbols of stegosaurus and 1 T-Rex symbol then the payout equals 10,000 coins. The majority of slots games are having the fixed quantum multiplier. This indicates that in this case, the wild symbols in free online slot machine games will multiply the payouts by a fixed amount irrespective of how many wild symbols have been put into use to complete the winning combination. In other games the multiplier is dependent on the number of wild symbols which are featured in the winning combination.
The use of wild symbols in online slotmachines has resulted in making the modern day online slots games more exciting and fun to play. The most popular wild symbols for slots games is the stacked. When this wild symbol appears then all other symbols in each reel are wild symbols. The slots games named as the Summer Holiday have this property. When the stacked wild symbols get featured in the reels one or two, it results in a huge payout since a large number of different winning combinations get hit simultaneously on slot machines.
The other form of wild symbols for free games slot machine is called as the expanding wild symbol. In this form too, the whole of the reel is covered with a wild symbol. However, the symbol does not get featured as a separate symbol in each row as was the case in the stacked wild symbols in slots games. in this case , the wild symbol expands so as to cover the entire reel as one symbol. The example in this case are the slots games named as the dancing girl where symbols expand to fill all four rows of a reel and the second game falling under this category is named as the Samba Nights.
The wild symbols in free casino slot machine games can also be used to activate another game on the separate screen. This game is actually a bonus game and is based on a theme. It is used to provide players with extra credits.