Solving the Optimal Strategy for Simplified Single-Player Qwixx

Qwixx is a quick-playing dice game that is typically played with two to five players, which consists of four colored dice and two white dice. Each player is given a scorecard with four colored rows (Red, Yellow, Green, Blue) with numbers ranging from two to twelve in each row, and each player aims to maximize their score by the time the game ends. Typically, two rows are arranged in increasing order, and the other two are in decreasing order. At a given turn, one player is the dice-thrower while the others are observers, and the game centers around crossing out numbers in rows corresponding to the colored dice picked on a given turn. The game ends when four penalties are accrued, or when two rows are “locked” after five numbers are crossed out in that row and the rightmost number in a given row is also crossed. This thesis will focus on exploring optimal ways of playing Single-Player Qwixx, with simplifications made due to the immense state space of full Qwixx. Single player Qwixx follows the same rules as regular Quixx, but it involves only one player continuously acting as the dice-thrower. The player aims to maximize their score before the game ends, either through two rows being locked or four penalties being accrued. We will focus on simplified Single-Player Qwixx played with two rows, and thus two white dice and two colored dice. First, we will create an extensible Qwixx simulator for human agents and random agents. For finding optimal play, we will create a dynamic programming agent to calculate the best move and associated expected value for any simplified single-player Qwixx game state. We will also develop a genetic algorithm that can rapidly play full four-row single-player Qwixx through an optimized rule set.