Limit Cases And Strategy In Chutes and Ladders

TL;DR

This paper investigates how the average game duration of Chutes and Ladders changes as dice roll probabilities approach certainty, incorporating strategies that influence game length through probabilistic decisions.

Contribution

It introduces a novel strategic element allowing players to decide on flipping a coin after each roll, significantly affecting game duration, analyzed through Markov models and simulations.

Findings

Game duration increases as dice probability approaches 100%

Player strategies significantly impact average game length

Six different strategies show varied effects on game duration

Abstract

We analyze what happens to the average duration of a game of Chutes and Ladders as the probability of rolling $\delta \in \{ 1,2,3,4,5,6\}$ approaches 100%. We utilize Markov models, and Monte Carlo simulations in Python. We also introduce strategy to the board game by allowing the player to choose whether or not they flip a coin after each die roll where if they get heads they will advance one square and if they get tails they will go back one square. The strategy the player employs to decide when to flip the coin has a significant impact on the average duration of the game. We analyze six different non-trivial strategies.