Casino Game Mathematics Guide | Fruity King

by James Smith |
Date of Publishing: 18/08/2021

5/5 - (1 vote)

Casino titles rely on randomness and lady luck, and in some cases, skill. Game mathematics refers to the numbers behind them. For instance, you might notice the RTP or house-edge mentioned in the small print of your favourite casino game – but not fully understand what it means?

If this sounds like you, fear not. In this guide, we at Fruity King will divulge what game mathematics is from top to bottom. This will include some of the main terminologies used, and how you might use that to your advantage when deciding what titles to play.

What is Meant by Game Mathematics?

Whilst most of us play online for a bit of light entertainment and escapism, it’s good to know what chance you have of winning and how much risk you are taking. This might be the deciding factor in how much you decide to stake.

To calculate risk when playing casino titles – you need to have a basic understanding of the mathematics behind the games you play.

You will often see promotions that mention RTPs, RNGs, house edges, and odds. These are all terms that represent the mathematics behind the casino games we play. We explain these terms throughout this guide.

Game Mathematics: House Edge

The house edge is a percentage that represents the mathematical advantage that the casino has over you. In other words, this is the portion of your initial bet the platform will keep as profit – it is a business, after all.

See an example to clear the mist:

  • The game you want to play has a house edge of 5%
  • This indicates that over time, for every £1 you play – the casino will keep £0.05

You will also see below some of the most popular casino games – along with a rough indication of what the house edge is likely to be on certain bets:

    • Craps – Pass Line Bet: 1.41%
    • Traditional Multi Variant Blackjack: Under 0.50%
    • Three Card Poker – Play Bet (1-4-5 bonus pay): 3.37%
    • Three Card Poker – Pair Plus Bet (1-3-6-30-40 bonus pay): 7.28%
    • Slots: Anywhere from 2 to 20% depending on the type of slot game
    • Jacks or Better: 2.70%
    • Roulette: 2.70%, apart from Double 0 roulette ‘first 5’ bet, which is 7.89%
    • Baccarat – Player bet: 1.24%

Any slot titles with a house edge of more than 8% are considered ‘tight’, anything under 4% is loose. Note that the house edge will differ depending on the game, variant, number of card decks and the platform you play on.

With that said, you can check out the pay table for the specific title easily at most online casinos.

Game Mathematics: Return to Player Percentage

The return to player percentage will usually be displayed as the ‘RTP’, and each casino title will show this figure in the small print of the respective game. This refers to the amount of your stake that you should expect to be returned to you – throughout many, many plays.

See a simple example below:

  • Let’s say the slot game you like shows an RTP of 95%
  • If you play £100 – theoretically, £95 will be returned to you
  • Importantly, this is based on at least one million plays or spins

This is where game mathematics comes into play and things get a little more complicated. The RTP of any title is calculated by testing companies that use sophisticated mathematical software.

The purpose is to evaluate pay amalgamations and characteristics such as volatility, jackpots, feature games contribution, and the base game itself. Put simply, testing houses simulate a huge quantity of plays for the game in question and analyse every possible outcome.

This is to give you an idea of how much of the amount you wagered you are likely to win back – over at least one million spins.

See another example below to explain further:

  • Let’s say there are 100 people playing the same title
  • The game has an RTP of 98%
  • Each person wagers £1
  • As such, the 100 players have invested a total of £100
  • On paper, you would expect that £98 would be shared between the 100 people at the end of the game
  • However, because the RTP is based on algorithms over millions of plays – one player could win the jackpot whilst the rest get nothing

Software developers tasked with creating our favourite games send every finished title to a third-party testing house to establish its house edge and RTP – amongst other things, which we talk about next.


Game Mathematics: Random Number Generator

A random number generator, or ‘RNG’, is software tasked with deciding the outcome of each spin on slots and other casino favourites.

This software is nothing new, as land-based gaming houses and pubs of yesteryear had this mechanism installed in every single-armed bandit – and they still do.

As well as the aforementioned pre-set values, this mathematical algorithm ensures every game is as random as the last. So, what is the purpose of the RNG?

Without this software, we would have no way of knowing whether or not a game is set up to never payout by a dishonest developer. As such, all regulated developers go through the testing house process.

Game Mathematics: Hit Frequency

When you are searching for a casino title to play, you may want to take a look at the ‘hit frequency’. This is quite simply informing you of how often the game is likely to land on a winning combination.

You will often spot this when looking at the finer details of titles that payout 1 for 1 – such as slots, keno, video poker, and lotteries.

See an example of a low-frequency game with a high payout below:

  • Let’s say you are playing the lottery, and the hit frequency is 0.0009%
  • Each ticket will cost you £1 and there are one million of them in existence for this particular game
  • The prize is £100,000
  • This means that 9 of the lottery tickets will payout £100,000
  • The remaining 999,991 tickets lose

Next, let’s take a look at a high-frequency slot game with a low payout:

  • Imagine you are now playing slots and the hit frequency is 90%
  • Each ticket costs £1 and you play a million spins – over a long time
  • The prize is 1 for 1 – meaning if you win, you will get your £1 back
  • This hit frequency means that 900,000 spins would result in a £1 win
  • The other 100,000 spins will not payout.

High-frequency games are often more attractive to beginners or casual players. This is because the game is entertaining to play over a longer period and is less likely to break the bank by chasing a big jackpot that may or may not happen.

Game Mathematics: Volatility

The volatility index will tell you how frequently or infrequently and how much or little you might win. This matters because it offers you insight into how risky it is to play and might alter how much you want to wager.

See a simple explanation below using slots as an example:

  • Low Volatility: This category usually offers a lower jackpot but pays out smaller amounts, more frequently. You may find that less volatile slots offer fewer bonuses too.
  • High Volatility: This type of slot game will have a wide differentiation between the bottom and top prizes. Furthermore, the jackpot will usually be much bigger and wins will come less frequently. Many titles in this category require a higher minimum bet.

As such, if you aren’t interested in big prizes and would like to play for a while, you may want to opt for low volatility. By playing high-risk games there is a higher chance of your cash dwindling – with hardly anything to show for it at the end of the day.

Game Mathematics: To Conclude

Game mathematics is the backbone of the data behind the titles we play. Without this information, we wouldn’t be able to manage risk effectively – let alone know what the probability of winning would be.

Another bonus about having a grasp on the mathematics behind online games is having realistic expectations when playing. This keeps gameplay fun and entertaining and saves you from falling into that trap of chasing the prize pot and wiping out your casino budget – or worse.


How are game mathematics used?

Game mathematics are used so that players have a greater idea of what their chances of winning might be – as well as the volatility, risk and reward of the title in question.

What is an RNG in online casino games?

An RNG is a random number generator. In layman’s terms, this is software that creates a massive sequence of digits that cannot be preempted – as a result – each game or spin will be as random as the last. In other words – this mathematical algorithm determines whether you win an avalanche multiplier on Gonzo’s Quest, or where the dice land in online craps.

Can any game be beaten with mathematics?

There are no guarantees; however, many players believe that mathematics can beat some games of skill. This includes blackjack and is largely down to the changing probabilities of specific outcomes – which some people believe they can calculate.

What does RTP mean in game mathematics?

RTP stands for ‘return to player’. This will be shown as a percentage or ratio and refers to the total amount you might expect a game to return to the player. So, if the RTP is 94%, this means that if £10,000 is wagered, the payout should theoretically be £9,400, with £6,000 going to the casino. Crucially, this is calculated over a huge number of spins or plays – usually a minimum of a million.

What type of mathematics is used in casino games?

A large part of probability software in games of chance relies on combinatorial calculus in the form of an algorithm. In a nutshell, this entails counting and considering a wide range of combinations and probabilities..

About the Author

Author: James Smith.

James Smith has been writing about casino games and strategies for over a decade. He is an expert in the industry and loves to help people get started with online gambling. In his free time, James enjoys reading books by other successful authors, cycling around town, or playing poker.