Where should you build your first settlement in Catan?

AA SLAI SLAA HLAI HL Accessible Also in: Probability, Statistics

Research question

Using the probability distribution of the sum of two dice, which settlement spots give the highest expected number of resources per turn, and does expected value alone make a good strategy?

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

Why it makes a good exploration

Catan players learn that 6 and 8 are good, but how good? Expected resources per turn, plus variance and diversity of resources, turns a board-game habit into a quantitative decision.

The mathematics you'll need

Probability distribution of the sum of two dice
Expected value and variance
Comparing spots by expected production
Simulation of games

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 a board setup; play and record production over several games.

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

Derive the two-dice distribution.
Compute expected production for each spot.
Consider variance and resource diversity.
Compare predictions with game records.
Reflect on trading and the robber.

Pitfalls that cost marks

Only expected value, no variance.
Too few recorded games.
Ignoring the robber rule.

Showing personal engagement

Use your family's board.
Test your strategy in games.
Design a fairer board and justify it.

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

Taking it further

Simulate 10,000 games' first 20 turns to compare placement strategies.

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).