  Hex is a turn-based two-player connection game with a high branching factor,
making the game arbitrarily complex with increasing board sizes. As such,
top-performing algorithms for playing Hex rely on accurate evaluation of board
positions using neural networks. However, the limited interpretability of
neural networks is problematic when the user wants to understand the reasoning
behind the predictions made. In this paper, we propose to use propositional
logic expressions to describe winning and losing board game positions,
facilitating precise visual interpretation. We employ a Tsetlin Machine (TM) to
learn these expressions from previously played games, describing where pieces
must be located or not located for a board position to be strong. Extensive
experiments on $6\times6$ boards compare our TM-based solution with popular
machine learning algorithms like XGBoost, InterpretML, decision trees, and
neural networks, considering various board configurations with $2$ to $22$
moves played. On average, the TM testing accuracy is $92.1\%$, outperforming
all the other evaluated algorithms. We further demonstrate the global
interpretation of the logical expressions and map them down to particular board
game configurations to investigate local interpretability. We believe the
resulting interpretability establishes building blocks for accurate assistive
AI and human-AI collaboration, also for more complex prediction tasks.
