Evaluating Game Fairness

Overview

In this lesson, students use probability and experimental data to decide whether carnival games are fair. They justify conclusions with numbers, compare theoretical and experimental chances, and propose practical improvements.

Learning intentions

• Students will be able to define what “fair” means in probability terms for a game with clear outcomes.
• Students will calculate and compare theoretical and experimental probabilities from game data.
• Students will evaluate fairness using evidence and explain whether the game favours a player or operator.
• Students will suggest an improvement to make a game fairer (or more transparent).

Success criteria

• I can describe fairness using probability language (equally likely outcomes or equal chance of winning).
• I can calculate theoretical probability for each key event in the game.
• I can compute experimental probability from collected results.
• I can make a justified recommendation for improving fairness.

Curriculum links

• Students use chance and probability to predict, compare and interpret likelihoods for events.
• Students conduct chance experiments, organise data and calculate experimental probability.
• Students compare experimental and theoretical probability and explain differences using evidence.
• Students use fractions, decimals and percentages to represent probability and communicate reasoning.

Lesson structure (45 minutes)

1. 0–5 min: Launch and focus

• Recap from the unit: “probability helps us judge chance events fairly.”
• Show the key question: “Is this carnival game fair for a player?”

2. 5–12 min: Model fairness with one game

• Teacher models using a simple carnival-style game with two outcomes (for example, winning or not winning based on an event like landing on a marked section).
• Students help compute theoretical probability (e.g., if 1 winning section out of 4 equal sections, probability of winning is 1/4).
• Teacher explains: a fair game means the player’s chance of winning matches the stated/expected chance (or is equally likely where relevant).

3. 12–18 min: Data to probability mini-worked example

• Provide a short dataset (pre-prepared) from a class trial: number of wins and total plays.
• Students convert experimental probability to a fraction, decimal and percentage.
• Quick class check: “If experimental probability is much lower than theoretical, what might that suggest?”

4. 18–30 min: Group evaluation task (stations)

• In small groups, students evaluate 2 different games using the same fairness method:
• Game A: “target probability” game (clearly stated chance from design)
• Game B: “mystery probability” game (results provided, fairness questioned)
• For each game, students complete:
• Theoretical probability of winning (from game description)
• Experimental probability of winning (from given results or rapid role-play trial if needed)
• A fairness statement supported by numeric comparison
• One improvement suggestion (e.g., adjust number of winning spaces, change scoring rules, clarify instructions, randomise spinner/selection)

5. 30–40 min: Gallery share and critique

• Groups rotate or share their findings with another group.
• Class discussion prompts:
• “What evidence supports your fairness claim?”
• “Is the difference between theoretical and experimental plausible? Why might it happen?”
• “What fairness change would have the biggest impact?”

6. 40–45 min: Exit ticket (individual assessment)

• Students answer one scenario:
• “The theoretical chance of winning is 25%. In 40 plays, a player wins 6 times. Is the game fair? Give a justified probability comparison.”
• Collect exit tickets for next lesson planning.

Resources

• Pre-prepared game cards (Game A and Game B) including rules, diagram/description, and either theoretical details or trial results.
• Data tables for wins/total plays for each group (dyslexia-friendly formatting: short lines, lots of spacing).
• Calculators (optional, depending on school policy) and scrap paper.
• Worksheets: “Fairness evidence sheet” with sentence starters:
• “The theoretical probability of winning is …”
• “The experimental probability of winning is …”
• “The game is (fair/unfair) because …”
• “To improve fairness, we would …”
• Coloured markers or highlighters for identifying winning outcomes.
• Timer for station rotations.
• Example improvement ideas list (generic, not answers): adjust winning region size, scoring, or clarify rules.

Assessment

• Formative: teacher circulates during group station work, checking theoretical probability setup, correct experimental probability, and fairness reasoning.
• Summative within the lesson: exit ticket comparing theoretical vs experimental probability and making a justified fairness claim.
• Teacher uses a quick rubric checklist: correct probability representation (fraction/decimal/percent), evidence-based conclusion, and feasible improvement suggestion.

Differentiation

• Support:
• Provide a partially completed “fairness evidence sheet” for students who need structure (e.g., theoretical probability line pre-filled from the game card).
• Offer a simplified second dataset with smaller totals (e.g., out of 20 plays) to reduce calculation load.
• Use sentence starters and a worked example before stations.
• Extension (advanced learners):
• Challenge students to estimate how many plays are needed for experimental probability to stabilise (discuss “more trials reduce random variation”).
• Require a “proposed fairness plan” that includes the exact probability change needed (e.g., adjust winning section from 1/4 to 2/8) and show the updated theoretical probability.
• EAL support:
• Use consistent icons for win/lose, probability bars, and bilingual-friendly number frames where possible.
• Provide audio support by reading game cards aloud and repeating instructions at stations.
• Dyslexia-friendly reading options:
• Game cards on single sheets with large font, high contrast, and minimal text.
• Read aloud game rules and key questions before group work.
• Offer a “trace and rewrite” option: students highlight key numbers (total outcomes, number of wins) and then complete the calculations.

Extension (optional)

• Advanced or interested students research a real carnival game (at a local fair, arcade, or online info) and present a brief fairness analysis:
• Identify the claimed rules and stated odds (if any)
• Collect or estimate outcomes (survey, observation counts, or sample trial)
• Compare theoretical/claimed probability to observed experimental probability
• Conclude whether it appears fair and suggest one improvement to increase fairness or transparency.