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.

  • $\begingroup$ Welcome to Mathematics Stack Exchange! As this site is meant to be a useful repository rather than a Do My Homework forum, it's common courtesy to show what you've already tried, and really narrow down what you're struggling with. Most people here are glad to help once you've adequately motivated the problem. Quick Guide to attracting answers and preventing your question from being deleted. Good luck! $\endgroup$ Jan 27 at 18:34
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    $\begingroup$ I doubt there is a winning strategy. $\endgroup$ Jan 27 at 18:39
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    $\begingroup$ I've got a lot of winter homework :(. Jokes aside, this is obviously not a homework problem, and I'm just genuinely interested in it which is why I've brought it up. There seems to have been many similar question, but none were really satisfactory. $\endgroup$
    – Sny
    Jan 27 at 18:39
  • $\begingroup$ @VincentBatens I doubt it as well, but we haven't been able to prove it, sadly, so anything really is possible. $\endgroup$
    – Sny
    Jan 27 at 18:40
  • $\begingroup$ Ye I should have maybe copied another template, the homework part doesn't apply here. Everything else did though. I don't think this question will get an answer (see point 11 of the quick guide) $\endgroup$ Jan 27 at 18:44


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