# An improved lion strategy for the lion and man problem

## TL;DR

This paper introduces an improved lion strategy for Gale's lion and man problem, which dynamically updates the center at each move, leading to better convergence and tighter bounds on game length.

## Contribution

It presents a novel strategy that updates the center dynamically, improving upon previous static approaches and providing proven convergence and superior bounds.

## Key findings

- Proven convergence of the new strategy.
- Derived upper bound on game length that improves existing bounds.
- Strategy effectively outperforms previous methods.

## Abstract

In this paper, a novel lion strategy for David Gale's lion and man problem is proposed. The devised approach enhances a popular strategy proposed by Sgall, which relies on the computation of a suitable "center". The key idea of the new strategy is to update the center at each move, instead of computing it once and for all at the beginning of the game. Convergence of the proposed lion strategy is proven and an upper bound on the game length is derived, which dominates the existing bounds.