Thursday, February 9

Math-Based Approach to Win Slot Games

The mathematics of slots is an oddly fascinating thing to learn about, which is a lot more nuanced than you would probably think. United Kingdom casino expert Joe Booth from covers free onlines slots and notes that digital slots make calculating your chance of winning a lot more complicated.

The Intersection Between Math and Slots

Britain has an extensive history of great mathematicians. Isaac Newton is revered as a hero of academia and created most of the fundamental theories that modern mathematics is based on.

Alan Turing is highly relevant to the development of math-based slot theory. Turing is notable for developing computer technologies and for creating fundamental texts on computerisation and computer mechanics. However, he is most known for his work with probability theory.

Probability theory is a branch of mathematics that tries to calculate random phenomena. For example, slots and other casino games operate using relative frequency. Probability theorists try to make complex calculations about unexpected events occurring based on many recordings of a given thing happening.

The Beginning of Math-Based Theory

Slots operate on a random number generator (RNG) system. Different numbers correspond to different symbols on a slot reel. When you believe you are spinning the reels, a calculation determines the spin’s output. Generally, each reel calculates its random number independently. Given the number of symbols a reel has and how they interact, the total number of paylines can seem boundless. 

The idea that digital slots make the math-based calculation more difficult holds especially more true if you consider that digital slots use computer code to add bonus features separate from traditional slots. Wilds scatters and progressive game mechanics completely change your odds of winning.

Most popular in-person slot games operate using a three-reel, five-symbol fruit machine. Each fruit symbol corresponds to a different value, and no symbols stick or change value after each turn.

There are a total of 125 different outcomes (5x5x5=125). However, not every outcome will result in you winning. For example, a combination of three of the same symbol has a 0.008 percent chance of occurring. Therefore, to determine your chance of winning, you have to add all of the positive outcomes. Similarly, if you want to calculate your average win per spin, you have to multiply each chance of winning by the payment and subtract that with the possibility of losing. 

Paytable and RTP

Almost all digital slot games provide a help menu that describes the functions of each of its symbols and also provides a paytable with the return to player (RTP) of the game.

Paytables directly show you your possibility of winning. In addition, paytables showcase the statistics behind each potential spin, showing how likely it is that you will land specific paylines.

For example, if a three-reel slot game has four symbols, each symbol has a one-fourth probability of landing. So, to calculate the chance that you will land on three of a kind, multiply one-fourth or 0.25 by itself three times.

Paytables organise all of the paylines into rounded aggregates over many spins. After all, your volatility goes down as you spin more times.

RTP calculates the average return you will get from a spin. Slot games are always on the dealer’s side, so expect the RTP to be below 100%. Better slot games have returns above 96%.

You should also consider the variance of the slot game. Slot games with high variance, or high volatility, have bigger wins that are less likely to be hit. Conversely, low variance games often allow for smaller and safer bets.


If you can understand the relative frequency and translate that into a slots game, you will improve your possibility of winning drastically. Math can be fun for everyone, especially if there is the incentive of winning big while playing slots.

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