Is there a winning strategy of the infamous 2048 game, assuming that the computer can place down either a $2$ or a $4$ at any spot without restriction optimally? (Assume a standard $4\times4$ grid in which the goal is to get to $2048$, etc.)
Going in the positive direction, I have not done much work. However, pairing AI against AI, I have been getting results consistently around $512$, and occasionally $1024$, never $2048$, which seems to abandon the idea.
Going in the negative direction, I have tried designing an algorithm to clutter up half the board but I don't have any ideas.
Web searches either show "winning strategies" such as "keep your pile neat" which is clearly not mathematical, or show complexity theories, etc. Papers on arxiv about 2048 are either completely different results or much too weak to prove the claim.