IA idea · Games & puzzles
Which Monopoly squares are landed on most often?
Research question
Using a Markov chain that includes the Jail rules and the Go-to-Jail square, what is the long-run probability of landing on each square, and which property group gives the best return on investment?
Adapt it: change the place, the data or the comparison until the question is yours.
Why it makes a good exploration
Players argue about which sets are best. A Markov chain gives long-run landing frequencies — Jail and the squares after it stand out — and combining them with rents gives an evidence-based strategy.
The mathematics you'll need
- Transition matrices with sums of two dice
- Steady-state vectors (eigenvectors or high powers)
- Expected rent per turn and payback period
- Simplifying assumptions and their effect
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
Use the board's published rules and rent values for the edition you own.
- 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
- State the rules modelled and simplifications (cards, doubles).
- Build the transition matrix.
- Find the steady state.
- Combine with rents and costs.
- Reflect on the simplifications and test with simulated games.
Pitfalls that cost marks
- Ignoring Jail (the main effect).
- Including every card without a plan — start simple.
- Steady state without interpretation.
Showing personal engagement
- Use your own edition of the board.
- Test your strategy against family members.
- Add the chance and community-chest cards and see what changes.
See Criterion C: personal engagement for what examiners look for.
Taking it further
Model the three-doubles rule and the choice to stay in Jail late in the game.