Probability · Maths EE idea · Solid
Long-run behaviour of a board game
A research question to start from
How can a Markov chain model of a simplified board game predict the long-run proportion of time spent on each square?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
A real application where linear algebra gives exact answers you can test.
Mathematics you would need
- Transition matrices
- Stationary distributions
- Eigenvectors
- Convergence of matrix powers
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Build the transition matrix for a game you simplify.
- Find the stationary distribution.
- Check by simulation and discuss what the simplifications cost.
Scope and difficulty
Solid. Solid; choose a game small enough to analyse by hand.
Pitfalls
- Huge matrices handled only by software.
- No discussion of assumptions.
Where to start reading
Search a library catalogue or a university's open lecture notes for: Markov chain stationary distribution board game; transition matrix eigenvector. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).