This work describes in detail how to learn and solve the Rubik's cube game (or puzzle) in the General Board Game (GBG) learning and playing framework. We cover the cube sizes 2x2x2 and 3x3x3. We describe in detail the cube's state representation, how to transform it with twists, whole-cube rotations and color transformations and explain the use of symmetries in Rubik's cube. Next, we discuss different n-tuple representations for the cube, how we train the agents by reinforcement learning and how we improve the trained agents during evaluation by MCTS wrapping. We present results for agents that learn Rubik's cube from scratch, with and without MCTS wrapping, with and without symmetries and show that both, MCTS wrapping and symmetries, increase computational costs, but lead at the same time to much better results. We can solve the 2x2x2 cube completely, and the 3x3x3 cube in the majority of the cases for scrambled cubes up to p = 15 (QTM). We cannot yet reliably solve 3x3x3 cubes with more than 15 scrambling twists. Although our computational costs are higher with MCTS wrapping and with symmetries than without, they are still considerably lower than in the approaches of McAleer et al. (2018, 2019) and Agostinelli et al. (2019) who provide the best Rubik's cube learning agents so far.

本文介绍了使用通用棋盘游戏（GBG)计算框架学习和解决魔方游戏（或谜题）的方法，详细讨论了魔方的状态表示、变换方式和使用对称性。通过强化学习训练代理，通过MCTS包装提高训练代理性能，表明MCTS包装和对称性增加了计算成本，但同时也得到了更好的效果。与已有魔方学习代理相比，该方法计算成本较低。

基于N元组强化学习的魔方学习