  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.

Machine Learning;Artificial Intelligence