Slot Machine Mathematics

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In one of our lectures we looked at the fundamental concept of chance and probability. Applications of probability can be seen in many different areas, not just in mathematics. One example that came up during the input was the link of probability to gambling. Gambling is a widespread, popular and recreational activity (Fabiansson, 2010, p.1). This was something that I found particularly interesting and therefore, decided to find out more about the applications of mathematics in gambling by analysing slot machines.

While there are various different slot machines, I have decided to focus on the three slot machine with six different symbols in each piece. The symbols I have chosen (see below) are banana, orange, cherry, mellon, grapes and seven.

Screen Shot 2015-11-29 at 17.24.10

Before we look at the chances of specific combinations using these symbols, it is important to find the total number of different combinations. As there are three slots with six symbols in each, there must be a total of 216 combinations. This is because 6 x 6 x 6 = 216.

The payouts of this particular three slot machine is as follows:

Screen Shot 2015-11-29 at 17.02.43

 

Three sevens pays 30 coins.

 

Any three of the same fruit pays 10 coins.

 

Two sevens pays 4 coins.

 

One seven pays 1 coin (break even).

 

While there are 216 different combinations, not all of them are winning combinations. To calculate the number of winning combinations, Shore (2014) states that we must consider the following:

  • Three sevens is a winning combination and there is only one possible figuration for this.
  • Any three of the same fruit are winning combinations and as there are five different fruit. This means that there are five different winning combinations.
  • Two sevens is also a winning combination. This means that one slot will have fruit. Therefore the winning combination for this configuration is calculated by (1 x 1 x 5) + (1 x 5 x 1) + (5 x 1 x 1) = 15
  • One seven is also a winning combination. This means that the two other slots will have fruit. Therefore the winning combination for this configuration is calculated by (1 x 5 x 5) + (5 x 1 x 5) + (5 x 5 x 1) = 75

To find out the total number of winning combinations we must add 1 + 5 + 15 + 75 = 96

This shows that in this three slot machine there are 96 possible combinations which are winning ones.

Using this information it is possible to calculate the payoff percentage. This can be defined as the amount of money a slot machine should return to player over a period of time (Casinomanuel, 2015).  To calculate the payoff percentage of this particular three slot machine we must multiply the each winning combination with the corresponding about of coins it gives. Adding all these winning amounts together and dividing this by the total number of combinations will give the payoff percentage (Shore, 2014). This is shown by the following calculation:

((1 x 30) + (5 x 10) + (15 x 4) + (75 x 1)) / (6 x 6 x 6) = 0.995 (3 significant figures)

0.995 x 100 = 99.5 %

This shows that the payout percentage is 99.5% which is very high.

Future Practice

Finding out about probability and its uses in society will be useful for my future practice as a primary school teacher. Slot machines offer visual representation of probability. The use of this particular example needs to be carefully considered as gambling may be a rather controversial concept to use in the primary school setting. I really enjoyed finding out about the mathematics behind slot machines and think that visual representation are a great way to bring concepts such as probability closer to the students.

References

Casinomanual (2015) Percentage Payout. Available at:http://www.casinomanual.co.uk/online-casino-games/guide-to-slots/payout-percentage/ (Accessed: 29 November 2015)

Fabiansson, A. (2010) Pathways to Excessive Gambling : A Societal Perspective on Youth and Adult Gambling Pursuits. Surrey: Ashgate Publishing Limided.

Image 1. Photograph. Available at: http://www.modern-canvas-art.com/ekmps/shops/robboweb1/images/slot-machine-symbols-pop-art-canvas-print-4252-p.jpg (Accessed: 29 November 2015)

Image 2. Photograph. Available at: http://www.appcelerator.com.s3.amazonaws.com/blog/dev/platinoslot/mask.png (Accessed: 29 November 2015)

Shore, E. (2014) ‘Probability: Odds of Winning at Slot Machines’, Eddie’s Math and Calculator Blog, 7 January. Available at: http://edspi31415.blogspot.co.uk/2014/01/probability-odds-of-winning-at-slot.html (Accessed: 29 November 2015)

40 thoughts on “Slot Machine Mathematics”

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  14. I love slots because they’re so easy to play! They don’t require a lot of skill, but they can still be fun and addictive.

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  27. Awesome article! This is certainly one of the best, most convenient, and informative articles I’ve ever read. I’m excited to do some research and put the resources you’ve provided to good use. Kudos!

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