Chutes and Ladders for the Impatient
Leslie A. Cheteyan, Stewart Hengeveld, Michael A. Jones · College Mathematics Journal · 2011
SummaryIn this paper, we review the rules and game board for Chutes and Ladders, define a Markov chain to model the game regardless of the spinner range, and describe how properties of Markov chains are used to determine that an optimal spinner range of 15 minimizes the expected number of turns for a player to complete the game. Because the Markov chain consists of 101 states, we demonstrate the analysis with a 10-state variation with a single chute and single ladder. The resulting 10 ⨉ 10 transition matrix is easier to display and the manipulations are comparable. We conclude with an unsolved problem about expected lengths for generalized Chutes and Ladders games.