How to eat 4/9 of a pizza

TL;DR

This paper presents an optimal strategy for the starting player in a pizza-cutting game, guaranteeing them 4/9 of the pizza, thus resolving a conjecture by Peter Winkler.

Contribution

It introduces a proven strategy for the first player to secure 4/9 of the pizza in an adjacency-restricted picking game, settling a longstanding conjecture.

Findings

The starting player can always secure at least 4/9 of the pizza.

The 4/9 share is proven to be the best possible guarantee.

The result settles a conjecture by Peter Winkler.

Abstract

Given two players alternately picking pieces of a pizza sliced by radial cuts, in such a way that after the first piece is taken every subsequent chosen piece is adjacent to some previously taken piece, we provide a strategy for the starting player to get 4/9 of the pizza. This is best possible and settles a conjecture of Peter Winkler.