I'm not sure how the math works out, but some googling suggests that 32768 is achievable in practice while 65536 and 131072 are theoretically possible but have

I'm not sure how the math works out, but some googling suggests that 32768 is achievable in practice while 65536 and 131072 are theoretically possible but have only been achieved with undos. edit: Explanation of the 131072 cap: https://puzzling.stackexchange.com/questions/48/what-is-the-largest-tile-possible-in-2048 https://puzzling.stackexchange.com/questions/48/what-is-the-... Also, in one of the answers there someone claims to have achieved 65536 in practice