Best way to train a board game with RL and NN?

For an assignment, we need to train a NN to be able to play Tock (a ‘go around the board’ board game). This needs to be done using RL, and we are limited to Keras and TensorFlow. We would like to avoid using a Q-table if possible, but we are not sure how to update the network’s weights and biases based on the reward. We did come across the Actor Critic method to do this, but we were wondering if there are better or simpler methods out there.