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The gameplay of strategic board games such as chess, Go and Hex is oftencharacterized by combinatorial, relational structures -- capturing distinctinteractions and non-local patterns -- and not just images. Nonetheless, mostcommon self-play reinforcement learning (RL) approaches simply approximatepolicy and value functions using convolutional neural networks (CNN). A keyfeature of CNNs is their relational inductive bias towards locality andtranslational invariance. In contrast, graph neural networks (GNN) can encodemore complicated and distinct relational structures. Hence, we investigate thecrucial question: Can GNNs, with their ability to encode complex connections,replace CNNs in self-play reinforcement learning? To this end, we do acomparison with Hex -- an abstract yet strategically rich board game -- servingas our experimental platform. Our findings reveal that GNNs excel at dealingwith long range dependency situations in game states and are less prone tooverfitting, but also showing a reduced proficiency in discerning localpatterns. This suggests a potential paradigm shift, signaling the use ofgame-specific structures to reshape self-play reinforcement learning.

From Images to Connections: Can DQN with GNNs learn the Strategic Game of Hex?