Walk versus Wait: The Lazy Mathematician Wins

TL;DR

This paper explores Justin's decision to walk or wait at bus stops, demonstrating that the optimal strategy is to wait whenever possible, highlighting a simple yet instructive decision-making model.

Contribution

It models Justin's walk-or-wait decision at bus stops and provides a complete solution for a specific case, emphasizing the effectiveness of a lazy strategy.

Findings

Waiting at bus stops is generally optimal in the modeled scenario.

The model's solution confirms that the laziest strategy is best under certain conditions.

Complete solution provided for a special case of the decision model.

Abstract

In this recreational mathematics note, we address a simple, yet instructive question: Justin has to travel a distance of d miles along a bus route. Along this route, there are n bus stops i, each spaced at a distance of d_i from the starting point. At each bus stop, Justin is faced with a choice: to walk or to wait. If he walks on, he can still catch a bus at the next bus stop--but if a bus passes him while he walks, he is almost assured a longer wait. We model Justin's decision constraint and completely solve the model in a special case. The answer is intuitive: the optimal strategy is the laziest.