Using deep convolutional neural networks for move prediction has led to massive progress in computer Go. Like Go, Hex has a large branching factor that limits the success of shallow and selective search. We show that deep convolutional neural networks can be used to produce reliable move evaluation in the game of Hex. We begin by collecting self-play games of MoHex 2.0. We then train the neural networks by canonical maximum likelihood. The trained model was evaluated by playing against top programs Wolve and MoHex 2.0. Without any search, the resulting neural network produces similar playing strength as the highly optimized Resistance evaluation function used in Wolve. Finally, using the neural networks as prior knowledge, the reigning Monte-Carlo-tree-search-based world champion player MoHex 2.0 can be enhanced.