X Tables
probability

Fair and unfair games

Explore whether every player has the same chance of winning.

Quick answer

A fair game is one where everyone has the same chance of winning, and an unfair game is one where some players have better or worse chances than others.

Learning outcome

By the end of this page, you will be able to tell if a game is fair or unfair by looking at the chances of winning for each player. Success signs:
  • You can explain what makes a game fair or unfair
  • You can compare chances using words like "more likely", "less likely", and "same chance"
  • You can play a game and decide if it is fair or unfair
  • You can give examples of fair and unfair games from everyday life

Why this matters

Understanding fair and unfair games helps you make good choices when playing with friends. It also helps you understand how things work in real life, like sharing toys, winning prizes, or even voting in class. When you know about fair games, you can spot when someone is being unfair and make sure everyone gets a good chance to win.

How it works

To figure out if a game is fair or unfair, you need to:
  1. Look at what each player can do
  2. Check if everyone has the same number of ways to win
  3. Count how many chances each player has
  4. Compare the chances to see if they are equal
Think of it like sharing cookies. If everyone gets the same number of cookies, it's fair. If some people get more and others get less, it's unfair.

Examples you can see

Let's look at some examples of fair and unfair games. Example 1: Coin flip You and your friend are flipping a coin to decide who gets the last cookie.
  • There are two sides: heads and tails
  • Each side has one chance out of two
  • So you both have the same chance of winning
  • This is a fair game
Example 2: Dice game You roll a dice to see who wins. If you roll a 6, you win. If your friend rolls a 6, they win.
  • There are 6 numbers on a dice
  • Each number has one chance out of six
  • Both players have the same chance of rolling a 6
  • This is a fair game
Example 3: Spin the wheel A wheel has 6 sections: 3 red, 2 blue, 1 green.
  • You win if the wheel lands on red
  • Your friend wins if it lands on blue
  • Red sections: 3 chances out of 6
  • Blue sections: 2 chances out of 6
  • Red has more chances to win
  • This is an unfair game

Try it as a mini adventure

The Great Toy Swap Adventure You are planning a toy swap with your friends. You have 3 toy cars, 4 toy dinosaurs, and 2 toy planes. You want to make sure everyone gets a fair share of toys.
  1. First, you count all the toys: 3 + 4 + 2 = 9 toys
  2. Then you decide to share them equally among 3 friends
  3. Each friend gets 9 รท 3 = 3 toys
  4. Next, you check if everyone got the same kinds of toys
  5. You make a list:
    • Friend 1: 1 car, 1 dinosaur, 1 plane
    • Friend 2: 1 car, 1 dinosaur, 1 plane
    • Friend 3: 1 car, 1 dinosaur, 1 plane
  6. Everyone gets the same number and type of toys
  7. This is a fair swap!
Now try this challenge: What if you had 5 toy cars, 3 toy dinosaurs, and 4 toy planes, and you wanted to share them among 4 friends? How many toys would each friend get? Is this fair?

Common mistakes

  • Mistake: Thinking that if you have more toys, it's fair. Why it happens: Children often think more things means more chance. Fix: Remember, fairness means equal chances, not equal numbers of things.
  • Mistake: Believing that if you have the same number of things, it's fair. Why it happens: Children focus on numbers instead of chances. Fix: Check if each person has the same chance to win, not just the same number of items.
  • Mistake: Not counting all the possible outcomes. Why it happens: Rushing through the game. Fix: List all the possible results to make sure you count correctly.
  • Mistake: Saying that a game is unfair just because one person lost. Why it happens: Confusing losing with unfairness. Fix: A game can be fair even if one person loses. Fair means equal chances.

Parent and carer guide

Parents and carers can help by:
  • Asking questions like: "Do you think this game is fair? Why or why not?"
  • Playing games together and discussing chances
  • Using everyday situations to talk about fairness
  • Encouraging children to explain their thinking
  • Noticing when children are confused about equal chances
When helping at home:
  • Use simple language like "chance" and "equal"
  • Use real objects like coins, dice, or counters
  • Ask your child to explain their thinking
  • Don't worry if they get it wrong at first
  • Practice with fun games and everyday examples

Practice questions

  1. Is it fair if one player gets 5 chances to win and another gets 3 chances? Why or why not?
  2. Two friends are playing a dice game. Each rolls a dice. If the number is even, they win. If it's odd, they lose. Is this fair?
  3. There are 8 marbles in a bag: 4 red, 3 blue, 1 green. Is it fair for each player to pick one marble? Why?
  4. If you flip a coin 10 times, how many times would you expect it to land on heads?
  5. Two friends are playing rock, paper, scissors. Is this fair? Why?
Answers:
  1. No, it's unfair because one player has more chances to win.
  2. Yes, it's fair because each number (1,2,3,4,5,6) has one chance out of six, so both players have the same chance of rolling an even or odd number.
  3. No, it's unfair because red has 4 chances out of 8, blue has 3 chances out of 8, and green has 1 chance out of 8.
  4. You would expect it to land on heads 5 times out of 10.
  5. Yes, it's fair because each player has the same chance of winning, losing, or drawing.

FAQ

What does it mean for a game to be fair?

A fair game is one where everyone has the same chance of winning. This means no one has better or worse odds than anyone else.

Can a game be fair even if someone loses?

Yes! A game is fair if the chances are equal for everyone, even if one person loses. The game can be fair but still have a winner.

How can I tell if a game is unfair?

Look for situations where one player has more or fewer chances to win than others. If the chances are not equal, the game is unfair.

Are all games fair?

No, not all games are fair. Some games are designed to give one player an advantage, or they might have rules that make some players more likely to win.

Why is it important to know about fair and unfair games?

Knowing about fair games helps you make good choices, understand sharing, and recognize when someone is being unfair. It also helps you enjoy games more and feel confident in your chances.