The difficulty of beating the Taxman

TL;DR

This paper establishes the NP-hardness of a variant of the Taxman game through graph matching equivalence, providing a winning strategy and bounds on optimal scores.

Contribution

It introduces a novel NP-hardness proof for a Taxman game variant and derives a winning strategy with computable score bounds.

Findings

Proves NP-hardness of the game variant.

Provides a winning strategy for all n.

Derives bounds on the optimal score.

Abstract

The Taxman game has proven to be hard to solve optimally, so efforts have been made to find heuristic strategies that do well in practice. We present results on the NP-hardness of a variant of the game via an equivalence to a particular kind of graph matching problem. Furthermore this equivalence is used to derive a winning strategy for all $n$ along with efficiently computable lower and upper bounds on the optimal achievable score.