How long is a game of snakes and ladders?

Abstract

“There is really only one Game, the Game in which each of us is a player acting out his role. The Game is Leela, the universal play of cosmic energy.” Thus begins Harish Johari in Leela: the game of selfknowledge, a serious commentary and religious interpretation of the Hindu board game Leela. Leela is essentially the game Snakes and Ladders, which in the U.S. is the popular children’s game of snakes and ladders, England’s famous indoor sport,” for 50ø in 1943 by the Milton Bradley Company of Springfield, Massachusetts. This game is really a 101 state absorbing Markov chain, which is amenable to mathematical as well as moral analysis. In what follows we investigate only the mathematical side of this diversion, specifically the expected playing time.