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Recognize fair and unfair games

A fair game gives each player the same chance of winning, whereas an unfair game gives some players a greater chance, even if short-term results appear balanced. In simple games involving equally likely outcomes, such as coins, number cubes, or spinners, the chances can be compared by listing or counting the outcomes that favor each player; formal probability calculations, expected value, and conditional or dependent events are not included.

Detailed Explanation: Recognize fair and unfair games

A game is fair when every player has the same number of equally likely chances to win. It is unfair when one player has more chances to win.

To check a game:

  1. List or count all the possible outcomes.
  2. Count which outcomes help each player.
  3. Compare the counts.
  4. If the counts are equal, the game is fair. If they are not equal, the game is unfair.

Example: A spinner has 6 equal sections:

  • 4 sections are red.
  • 2 sections are blue.
  • Maya wins when the spinner lands on red.
  • Leo wins when the spinner lands on blue.

There are 66 possible sections altogether.

  • Maya can win in 44 ways.
  • Leo can win in 22 ways.

Because Maya has more winning sections, she has a greater chance of winning. Therefore, this game is unfair to Leo.

A game can still have a close score for a short time, but it is fair only when the players have the same number of chances to win.

Learn by doing: Recognize fair and unfair games

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Probability - Coins (1), All Specific, To Fraction


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