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by vlasev
4484 days ago
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Actually, to make a 2048 you need to make two 1024s. It's unlikely that you'll make two 1024s at the same time. Similarly for the lower tiles. As a sort of upper bound you expect the game to be over in about 1024 moves and it's likely to not be much less than that. I think a more realistic number is somewhere in the 500s |
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It's been too long since I've taken any hardcore discrete math for me to reliably reason about the bounds on the number of moves required to win. All I can do is make estimates based on simplifications.
How I arrived at my estimates for the order of magnitude of the minimum number of moves required to win:
At most, you can merge 4 tiles in one move. Assuming you were doing 4 tiles every move, and the game just didn't produce twos, it'd take just 128 moves. Order of magnitude: 10^2.
Assuming exactly one merge per move, and that the game only produces twos, it'd take 1024 moves. Order of magnitude: 10^3.