Othello: opponent mobility

[shindavid]

For each candidate move A, we can compute the number of legal moves (the "mobility") our opponent will have after making move A. We can represent this as an int in the range [1, K] using K feature planes. ChatGPT suggests this might be hard for the NN to compute on its own. I'm sort of skeptical of this suggestion - there's no recursion needed, so shouldn't a simple NN architecture easily compute it? Still, it may be worth investigating.

One option is to just create an auxiliary target for this, rather than a feature. Whether the NN can drive the loss for this auxiliary head to zero should be an indication of whether the NN can indeed learn this implicitly. We can also see whether merely adding the aux head on its own accelerates learning. My expectation is that this auxiliary loss will indeed be driven towards zero, and that adding the head does not improve learning. It would still be insightful to see this.