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0 pointsvlasev12y ago0 comments

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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benjamincburns12y ago

I'm not sure I follow, but I think we're saying the same thing.

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.

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