I'm wondering if there's a MOOC that takes you from zero to being able to build a system that learns how to play such a game, maybe focusing a bit less on the math (especially the proofs). I took Andrew Ng's course on Coursera but I feel like the gap between what I know and what's needed for this contest is huge. Am I wrong?
No, you're not wrong. That said, I don't think this is a competition aimed at people with a beginner level knowledge of machine/deep learning. I don't believe there is currently any MOOC that is going to hold your hand from 0 to expert. Given the current state of the field, I believe the only surefire path towards this level of knowledge is either university education or a /lot/ of reading.
