Slot Machine Probability Mathematics

 

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The Probability of Slot Machines



Everyone has either heard of, or seen a slot machine, but where did they originate? The first Slot Machine ever to be made was the Liberty Bell, built by Charles Fe in 1895. It had three reels and four symbols. The symbols were a heart, a spade, a diamond, and the Liberty Bell. If you spun, and landed all three Liberty Bells at once, you would get the maximum payout of fifty cents. Charles Fe's slot machines were becoming famous and were in high demand. Many gambling companies offered to buy the rights of the machine off of him but he refused. In 1907, a man named Herbert Mills began a knockoff version of the Liberty Bell and added the fruit symbols we commonly see today. Slot Machine production continued, as people integrated more and more computers into the slot machines. One day, in 1984, a man named Inge Telnaes revolutionized the slot machine industry. He added a computer chip into the slot machine. This chip was a random number generator. The effect of this chip is that it made the odds of winning a jackpot much much less, even making it possible for someone to watch you play and change the odds of you winning. The probability of you getting the jackpot is exactly the same, however, whoever is watching that machine could easily make it so that you only got it one in every one-hundred-thousand times. This computer chip method is used in modern slot machines today.


In order to find the probability of a slot machine, you need to know how many symbols there are per wheel as well as how many wheels. Let's find the probability of winning the jackpot on the Liberty Bell.
Reels=3 1.) Count the reels
4*4*4=56 3.) Raise the number symbols to the power of the number of reels

The probability of winning a jackpot on the Liberty Bell is 1/56.

Pricing and Winning:
The payout you see on a slot machine is not determined by how many people have played; it is purely determined by chance. In a modern day casino, if the probability was 1/56, the jackpot would be about 56 dollars. This seems strange, if the probability says you will win one in 56 times, and the jackpot is 56 dollars, how do they make any money? The answer to this question is all in the hidden computer chip. The computer chip could easily turn the odds of 1/56 to 1/1000. You may ask, 'who in their right minds would play a game that many times?' Well one solution casinos have developed is to give you small payouts. If someone is on the verge of quitting and they win five dollars, odds are they will probably get right back at it.







“Slot Machine Math.” Gamblers Bookcase. Gamblers Bookcase, n.d. Web. 9 May 2014. <http://www.gamblersbookcase.com/Slots-Math.htm>.

“No. 2740 Slot Machines.” Engines of Ingenuity. Engines of Ingenuity, n.d. Web. 9 May 2014. <http://www.uh.edu/engines/epi2740.htm>.

Liberty Bell Slot Machine. Uniquely Nevada. Uniquely Nevada, n.d. Web. 14 May 2014. <http://uniquelynv.com/wp-content/uploads/2013/09/slot-machine.jpg>.


Bellis, Mary. “The History of Slot Machines - Liberty Bell.” About.Com: Inventors. About.Com, n.d. Web. 14 May 2014.

<http://inventors.about.com/od/sstartinventions/a/Slot_Machines.htm>.


3-Reel Slots. Winners Island. Winners Island, n.d. Web. 14 May 2014. <http://blog.winnersisland.com/wp-content/uploads/2012/08/chili_printScreen1.jpg>.



  • The probability of you getting the jackpot is exactly the same, however, whoever is watching that machine could easily make it so that you only got it one in every one-hundred-thousand times. This computer chip method is used in modern slot machines today.
  • The backbone of casino game mathematics is “probability.” Informally, we understand probability as a number that describes the chance that something will occur. It is usually given as a fraction or decimal with a value between 0 and 1, or as a percent with value between 0% and 100%.

Slot machines use maths to operate, so why can’t you use mathematics too beat them? Let’s fight fire with fire. Find below a math based approach to playing online slots at sites such as Thorslots.com.

One of the great things about video poker is that even though it looks like a slot machine, it’s NOT a slot machine. Here’s why that’s great: Slot machines are the only game in the casino that have opaque math behind them. In other words, you have no way of knowing what the odds and/or payouts are on a slots game. Yes, slots have pay tables.

Understanding the mathematics behind online slot games is invaluable in helping players choose the best machine. So let’s start by explaining how mathematics is used to operate slot machines.

Slots mathematics

The outcome of each spin on a slot machine is determined by a Random Number Generator (RNG). These Random Number Generators use mathematical formulas to generate random numbers, which correspond to the symbols on any given slot. If the random numbers generated correspond to a winning symbol combination, you win.

Probability Of Winning Slot Machines

Calculating probabilities playing slots games

Probability refers to the likelihood of players winning at a slot machine. In order to calculate the probability of a specific slot, you need to know what a specific winning combination pays, as well as the probability of landing that combination.

How much any given combination pays out is usually listed in the paytable, but how do you calculate the probability of landing that combination? Easy. Just calculate the amount of stops in that slot. Let’s use a simple example. Let’s say that a slot contains 3 reels, with 5 symbols on each reel. To calculate the number of possible combinations on this machine, just multiply the number of symbols on each reel, by the number of stops on each reel. So this would be 5 x 5 x 5 = 125 possible winning combinations. If the jackpot in this slot pays out only for three cherries across the reels, and only one cherry occurs per reel, the calculation would be as follows: 1/5 x 1/5 x1/5 which equals a 0.008% chance at hitting the jackpot.

It is thus possible to calculate the probability of landing any combination as long as you know the number of times that each symbol appears on every reel, which is not information usually shared by online slots. Modern machines also come with many different numbers of reels and winning combinations, which could make it difficult to calculate its probability.

Slot Machine Probability Mathematics Problems

Probability mathematics pdf

It is quite possible to calculate the probabilities of a simple and traditional slot machine. However, with modern slots it would be pretty much impossible, as slots can have as many as ten reels and 200 stops.

RTP percentages for online slot games

Return to Player percentages (RTP) refers to the overall percentage of total wagers that a video slot game will pay out back to players over a period of time. Each online slot has a Return to Player percentage. For example, if a slot has an RTP of 98%, that means that for every dollar you bet, you will get back 98 cents. So to increase you odds of winning, you would want to choose the slot machines with the highest RTP rates, preferably 90+.
These are just a few of the ways in which you can use maths to choose the right online slot and improve your chances at winning.