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Game Design Maths

Design a fair dice game

Use dice outcomes to investigate chance, fairness and why some games feel luckier than others.

Quick answer

You can design a fair dice game by making sure each outcome has an equal chance of happening, using dice with equal sides, and checking that the game rules treat all players the same way.

Learning outcome

By the end of this page, you will be able to design a fair dice game where all players have the same chance of winning and all outcomes are equally likely. Success signs:
  • You can explain why a dice game is fair
  • You can create a game with equal chances for all players
  • You can predict what might happen if you play the game many times
  • You can check if a dice game is fair or not

Why this matters

When you design a fair dice game, you're using maths to make sure everyone has a fair chance to win. This helps you understand how chance works, why some games feel more exciting than others, and how to make games that are fun for everyone. This maths is used in real life when you play board games, go to the casino, or even when you're trying to decide who gets to choose the next game to play.

How it works

To design a fair dice game, you need to think about:
  1. What kind of dice you will use
  2. How the dice will be rolled
  3. How players will win or lose
  4. Whether each player has the same chance of winning

Examples you can see

Let's imagine you're designing a game where you roll a dice and move forward that many spaces on a board game. If you roll a 1, you move 1 space. If you roll a 2, you move 2 spaces, and so on. Example 1: Simple Dice Game
  • Players roll a dice
  • Move forward the number of spaces shown
  • First to reach the end wins
This game is fair because each number (1 through 6) has an equal chance of appearing on a normal dice. Example 2: Dice Game with Points
  • Roll two dice
  • Add the numbers together
  • Player with the highest total wins
This game is also fair because all numbers from 2 to 12 can happen, and each number has a chance of appearing.

Try it as a mini adventure

Adventure: The Dice Game Designer Challenge You are a game designer who needs to create a new dice game for your school's maths fair. You have a bag of dice and some game boards. Your task is to make a game that is fair and exciting. Here's your challenge:
  1. First, you must choose what kind of dice to use
  2. Then, decide how players will win
  3. Next, test your game with a friend
  4. Finally, explain why your game is fair
Let's say you choose to use a normal six-sided dice. You decide that:
  • Players roll the dice
  • They move forward the number of spaces shown
  • The first to reach the end of the board wins
4th time: You roll a 3 and move 3 spaces forward. 5th time: You roll a 5 and move 5 spaces forward. 6th time: You roll a 1 and move 1 space forward. 7th time: You roll a 6 and move 6 spaces forward. What happens if you play this game 10 times? How many times do you think you might roll a 6? A 1?

Common mistakes

  • Mistake: Thinking that rolling a 6 is more likely than rolling a 1. Why it happens: Some children think that because 6 is the highest number, it must happen more often. Fix: Remember that with a fair dice, each number has exactly the same chance of coming up.
  • Mistake: Not checking if all players have the same chance to win. Why it happens: Children might make rules that favour one player over another. Fix: Make sure the same rules apply to everyone, and that the dice outcomes are treated equally.
  • Mistake: Believing that if you roll a dice 10 times, you'll get each number exactly once. Why it happens: Children think that because there are 6 numbers, each must appear 1/6 of the time. Fix: Explain that with chance, it's not about exact numbers but about probability over many rolls.

Parent and carer guide

  1. Explain the concept: Help your child understand that fair means equal chance for everyone.
  2. Play together: Try designing a simple dice game together. Use dice and a simple board.
  3. Ask questions: Ask "Why do you think this game is fair?" or "What happens if we change the rules?"
  4. Encourage testing: Let your child test their game with a friend or family member.
  5. Focus on probability: Explain that while we can't predict what one roll will be, we can predict what happens over many rolls.

Practice questions

  1. Is it fair to say that if you roll a dice, you will definitely get a 3? Why or why not?
  2. If you have two dice and add the numbers, which total is most likely to appear? Why?
  3. Design a simple dice game where all players have an equal chance of winning.
  4. Can you think of a dice game where it's not fair? Explain why.
  5. Why is it important that dice games are fair?
Answers:
  1. No, because each number on a fair dice has an equal chance of appearing, so getting a 3 is just as likely as getting any other number.
  2. The total of 7 is most likely because there are more ways to make 7 than any other number (1+6, 2+5, 3+4).
  3. Example: Roll a dice, move forward that many spaces. First to reach the end wins. All players have equal chance.
  4. Example: A game where one player gets extra points for rolling a 6. This isn't fair because it gives one player an advantage.
  5. Because fairness makes games fun for everyone, and helps us understand how chance works.

FAQ

What makes a dice game fair?

A dice game is fair when each player has the same chance of winning and each possible outcome of the dice roll has an equal chance of happening.

How can I test if my dice game is fair?

You can test your game by playing it many times and recording the results. If each outcome happens about the same number of times, your game is likely fair.

Can I make a dice game that's not fair?

Yes, you can make a game that's not fair by giving some players special advantages or by using unfair dice.

Why do some dice games feel luckier than others?

Some games feel luckier because they have more exciting outcomes, or because the rules make it feel like you have more control over the results.

How does probability relate to dice games?

Probability tells us how likely each outcome is. With a fair dice, each number from 1 to 6 has a probability of 1 in 6 of appearing.