Pirates and Treasure

TL;DR

This paper introduces a new two-player graph-based game involving treasure collection, proves its NP-hardness, and explores its behavior under different game sum conditions, highlighting open problems in scoring play games.

Contribution

It presents a novel game model, proves its computational complexity, and analyzes its strategic structure under various sum scenarios, extending understanding of scoring play games.

Findings

The game is NP-hard.

It exhibits both normal and misère play behaviors.

Open problem on scoring play game structures.

Abstract

In this paper we introduce a new game; in this game there are two players who play as rival pirate gangs. The goal is to gather more treasure than your rival. The game is played on a graph and a player gathers treasure by moving to an unvisited vertex. At the end of the game, the player with the most treasure wins. We will show that this game is NP-Hard, and we will also look at the structure of this game under the disjunctive sum. We will show that there are cases where this game behaves like a normal play game, and cases where it behaves like a mis`ere play game. We then leave an open problem about scoring play games in general.