Markov Chains in Spreadsheets: Transition Matrices, Steady States & Board Games

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Turn a year of day-to-day weather counts into a transition matrix, check that every row sums to 1, multiply along a two-day path and estimate how long a rainy spell lasts.
• Square the weather matrix three times to get 2-, 4- and 8-day probabilities, watch the rows become equal and push today's uncertain forecast four days ahead.
• Push a sunny day 12 days forward until the probabilities stop changing, then solve the long-run distribution exactly with one MINVERSE and read the mean time between rainy days.
• Split a student-progression chain into Q and R, build the fundamental matrix N = (I − Q)⁻¹, read the expected years until a student graduates or leaves and the probability of graduating from each year.
• Calculate, for every starting bankroll from 0 to 10, the chance to reach the target before ruin, the expected number of rounds and the expected net result in a slightly unfair game.
• Build the transition matrix of a small snakes-and-ladders board from the six die rolls, then compute the expected number of rolls to finish and the chance to finish within eight rolls.
• Project four brands' market shares month by month from a switching matrix, solve the long-run shares, value the long-run gain for one brand and chart the shares converging.
• Simulate 80 days of weather from given random numbers with the inverse-transform trick, count the simulated shares and compare them with the exact steady state in a table and a chart.