Albion College

Mathematics and Computer Science

Mathematics and Computer Science

COLLOQUIUM

Chutes and Ladders for the Impatient

Michael A. Jones

I will review the rules and game board for Chutes and Ladders, define a Markov chain to model the game, and describe how properties of Markov chains can be used to determine the expected length of the game. Because the resulting Markov chain has 101 states, the analysis is first done for a 10-state variation in which the board has a single chute and a single ladder. The approach is used to determine the optimal spinner range to minimize the expected number of turns for a player to complete the game. This allows one to modify the game so it takes less time to play—perfect for the impatient player!