Strategy and Mathematics of 2048

I've become hooked to 2048! I have managed to get the 8192 tile and my highest score so far is 109340.

My preference is to play at the top. My strategy is to fix the top line, with the biggest number in a corner. Then, I try to create a chain from that number across the top, down to the next row etc. To achieve this I group the numbers in the corner (with the highest number). 

The video below is a brilliant discussion on the strategy and mathematics of 2048 by the wonderful  +James Grime and +Steve Mould (@jamesgrime and @MouldS) - this blog is inspired by this.

2048 strategy and maths - Steve Mould

My strategy develops when I create a chain of large tiles along the top. Rather than grouping the numbers in the corner of the highest number it switches to the opposite top corner.

Other strategies:

• If the top row becomes unfixed, fix it immediately by placing tiles into it.
• If the worst happens, and the largest tile is now not in the corner. The quickest way to get it back is to work with the larger chain rather than smaller e.g. top row 4 256 64 8 try to complete from the right, rather than the left.

+James Grime discusses an interesting subgame, lowest score (most efficient) to 2048 (under 20000 is the challenge).

Calculating the lowest score possible is complicated because approximately 10% of tiles generated are 4s.

(k-1)2^k-2/5(2^(k-1))

where 2^k is the highest tile

Getting under 20000 requires a bit of luck in generating 4s. 

Interesting variations:

• 2048 - Hard (puts the tiles in the worst position)
• DIVE (prime factors)
• 2584 Fibonacci
• Doctor Who version
• All the 2048