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A structured course in casino maths

Learn how casino games work, one lesson at a time.

Numbered lessons that build in order, from odds and the house edge to RTP, volatility and random number generators. Each one assumes the last, so nothing is explained twice and nothing is skipped.

Start with Lesson 1 →See the syllabus
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  • In ordereach lesson builds on the last
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How every lesson works

Five steps, the same every time.

Every lesson follows one teaching pattern, so you always know where you are and what comes next.

  1. Learning outcome

    What you will be able to do by the end, stated up front.

  2. Teaching

    One new idea at a time, built on the lessons before it.

  3. Worked example

    Real games and real numbers, worked through step by step.

  4. Quick check

    A question to test yourself before you reveal the answer.

  5. Recap

    The lesson in a few lines, and what the next one covers.

The syllabus

Take the lessons in order.

Lessons are grouped into modules. Mark each one complete as you go and the course remembers where you stopped.

  1. ​

    Lesson 5: Paylines, Line Bets and the Wild Multiplier, Worked Through on Fruit Shop

    What you will be able to do by the end By the end of this lesson you will be able to look at a slot's grid, find out how many paylines it uses, work out what each line is costing you, and follow how a single winning line turns into money on your balance. The game used throughout is Fruit Shop by NetEnt, a 5x3 slot with 15 fixed paylines, a 96.71% RTP and Low volatility. Three new terms appear in this lesson: payline , line bet and Wild multiplier . Nothing else is new. Teaching: how a slot decides what counts as a win Paylines A payline is a fixed path across a 5x3 grid that picks one position on each reel, from left to right. Fruit Shop has 15 of these paths. A win needs three or more matching symbols on the same payline, starting from the leftmost reel and running right without a gap. Three cherries spread across the screen but on different paylines pay nothing. Three cherries on reels 1,…

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  2. ​

    Lesson 4: Random Number Generators, Independent Spins and the Gambler's Fallacy

    By the end of this lesson you will be able to explain what a random number generator does when you press spin, why one result never changes the odds of the next, and how to spot the gambler's fallacy when it shows up in your own thinking. Three new terms, one worked example on a roulette wheel, and a short recap. What you will be able to do Describe in one sentence what a random number generator (RNG) is. Explain why a casino game result is an independent event . Recognise the gambler's fallacy and say exactly where its logic breaks. That is the whole list. Three terms is the limit for one lesson, so everything else here is explanation and practice. Term 1: the random number generator Every licensed online slot, and every digital version of roulette, blackjack or baccarat, uses software called a random number generator. Its job is narrow. It produces a long stream of numbers with no pat…

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    Lesson 3: Volatility, or Why Two Games With the Same RTP Behave Nothing Alike

    By the end of this lesson, you'll be able to explain what volatility means, read a game's volatility rating alongside its RTP, and say why two slots with exactly the same RTP can behave nothing alike across a single evening. Learning Outcome You'll be able to define volatility, use a game's max win figure as a clue to its volatility, and explain why volatility tells you about the shape of a session while RTP tells you about the long run. This lesson adds two new terms: volatility and max win . Everything else builds on Lessons 1 and 2. Teaching: The Question RTP Can't Answer In Lesson 2 you learned that RTP and house edge are the same fact seen from two sides. A 96.52% RTP means the game pays back 96.52% of everything wagered on it, on average, over a very large number of spins. Notice the words "on average". Averages hide the route. Two games can both return 96.5…

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  4. ​

    Lesson 1: Odds, Probability, and the House Edge

    By the end of this lesson, you'll be able to explain why a casino makes money on every game it offers, using two ideas that everything else in this course builds on: probability and house edge. Learning Outcome You'll be able to define probability, explain what house edge actually means in plain terms, and calculate a simple house edge figure yourself using one worked example. Teaching: Probability, in Plain Terms Probability is a way of writing down how likely something is, as a number between 0 and 1, or as a percentage between 0% and 100%. Flip a fair coin, and the probability of heads is 0.5, or 50%. Roll a standard six-sided die, and the probability of rolling a 4 is 1 in 6, or about 16.7%. Every casino game, underneath its theme and its features, is built on probabilities like these. A roulette wheel has a fixed number of pockets. A deck of cards has a fixed number of each card…

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  5. ​

    Lesson 2: RTP and House Edge Are the Same Coin, Seen From Two Sides

    By the end of this lesson, you'll be able to explain what RTP means, show why it's the same fact as house edge told from the other direction, and convert between the two figures without a calculator. Learning Outcome You'll be able to define RTP, explain why RTP plus house edge always adds up to 100%, and work out either figure yourself when you're only given the other one. Teaching: RTP, Defined RTP stands for Return to Player, and it describes the average percentage of every dollar wagered that a game pays back to players over a very large number of bets. If a slot has an RTP of 96%, that means that across a huge number of spins, the game returns 96% of everything wagered on it, back to players as winnings, on average. As you learned in Lesson 1, that's an average over a large number of bets, not a promise about any single spin. You'll see RTP printed on almost ever…

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New lessons are added in sequence. Each one assumes the lesson before it.

Glossary

Every term the course teaches.

Pick a term to see the lessons that cover it.