Designing a fair board game: a maths EPQ idea
A title to start from
Can a board game be designed so that every player has an equal chance of winning?
Why it works as an EPQ
Probability and simulation decide the rules; the artefact is the finished, tested game.
Scope and difficulty
Accessible. Accessible. A simple race game, analysed and then simulated.
The maths
Builds on these A Level topics: Probability · Statistical distributions.
You would learn:
- Expected values and Markov chains
- Simulation
- Balancing first-player advantage
One possible plan
- Analyse an existing simple game for fairness.
- Design your own rules and analyse them.
- Simulate thousands of games and adjust.
- Playtest and evaluate.
Pitfalls
- Too complex to analyse.
- Playtesting too little.
Where to start reading
- Search for: snakes and ladders Markov chain expected length
- Search for: first player advantage board games
Making something? Read the artefact guide first: an artefact still needs a research-based written report.
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Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.