Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

Can you beat people at rock–paper–scissors?

AI SLAI HLAA SLAA HL Accessible Also in: Probability, Statistics, Voting & game theory

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?

Make it yours, then agree it with your teacher.

Next step: plan this IA free — the planner opens with this question filled in. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.

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

The statistics, step by step

Worked with every number shown, with what examiners look for and the common mistakes: Chi-squared test for independence · Chi-squared goodness of fit. Then run the same steps on your own data in Analyse my data, or start from the statistics workflow.

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.

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.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Mixed strategies and expected value; Chi-squared goodness-of-fit (are choices uniform?)
AA HL	Fits, but add an HL technique	Mixed strategies and expected value; Chi-squared goodness-of-fit (are choices uniform?)
AI SL	Good fit	Mixed strategies and expected value; Chi-squared goodness-of-fit (are choices uniform?)
AI HL	Fits, but add an HL technique	Mixed strategies and expected value; Chi-squared goodness-of-fit (are choices uniform?)

Level: Accessible. A good first extended piece of maths, with room to go deeper. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: testing the strategy on the data used to build it; and too few games. Say how each one affects your answer.

Use of mathematics (E)

SL: 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, each explained in your own words and carried out correctly.

How games & puzzles explorations reach the top bands in general: Games & puzzles IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

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

Extending it for HL

Add an HL technique the question genuinely needs: what an HL games & puzzles exploration adds.

See a complete IA, marked

How long does a game of Snakes and Ladders last on my grandmother's board? (AI HL) is a complete games & puzzles exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AI SL, AI HL, AA SL and AA HL. We rate it Accessible: a good first extended piece of maths, with room to go deeper.

What mathematics does this IA use?

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

Where can I get data for this IA?

Record 300+ games with volunteers (move sequences and results). Checked sources and tools: Desmos graphing calculator.

Turn this idea into your IA

The planner opens with “Can you beat people at rock–paper–scissors?” filled in: the question, the maths and the data sources.

Plan this IA free

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Writing it up: how to write a Maths IA, step by step · structure and format · mistakes that cost marks · annotated exemplars, marked on every criterion