Can you beat people at rock–paper–scissors?

AI SLAI HLAA SLAA HL Accessible Also in: Probability, Statistics

Research question

Do people choose rock, paper and scissors equally often and independently of their previous move, and can a strategy based on observed patterns win significantly more than a third of games?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Game theory says play randomly; real people do not. Recording hundreds of games and testing for patterns gives a clear chi-squared question and a strategy you can test.

The mathematics you'll need

Mixed strategies and expected value
Chi-squared goodness-of-fit (are choices uniform?)
Chi-squared test of independence (previous result × next move)
Binomial test of a strategy's win rate

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Record 300+ games with volunteers (move sequences and results).

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain the equilibrium strategy.
Collect move data.
Test for uniform choices and for dependence on previous outcomes.
Design a counter-strategy.
Test it on new games and reflect.

Pitfalls that cost marks

Testing the strategy on the data used to build it.
Too few games.
Ignoring different players' styles.

Showing personal engagement

Play the games yourself.
Compare players who know game theory with those who do not.
Build a simple predictor and let friends try to beat it.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Build a Markov-chain predictor of the next move and measure its accuracy.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).