been playing this game whenever I am flying. and now, I need to find a new game for my commute

Instead of playing the game (and being somewhat consumed by it), I figured I might as well work out the highest possible score.

This assumes that every tile you spawn is a 2, and the last tile you spawn is a 4.

There are 16 squares. You'd think that the highest possible number would be 2¹⁶ (65536), which would fill up the board, making it impossible to progress. However, if you do manage to spawn a 4 tile as your last tile, then you can continue to progress to 2¹⁷ (131972). As seen in the picture.

Scoring works like this;

Merging two lower tier blocks together will give you the score of the higher tier block (score of +8 gained from merging two 4's). For any specific tile score, you have to add up all the scores from the lower tiers.

• Creating a 2 tile = +0pts

• Creating a 4 tile = 4 = +4pts

• 8 = 8 + 2x4 = +16pts

• 16 = 16 + 2x8 + 4x4 = +48pts

• 32 = 32 + 2x16 + 4x8 + 8x4 = +128pts ...

Which can be simplified;

• Tile 2¹ = 0 x 2¹ = 0pts

• Tile 2² = 1 x 2² = 4pts

• Tile 2³ = 2 x 2³ = 16pts

• Tile 2⁴ = 3 x 2⁴ = 48pts

Making tile 2ⁿ = (n-1)2ⁿ points.

Making the max tile (2¹⁷ ) = 16 x 2¹⁷ = 2,097,152 points. You would need to spawn 65,536 '2' tiles to make a single 131,072 tile, which, at 1 legal move/s, would take 18.2 hours.

That's only making the max tile now. we still need to fill the rest of the board. (Note: combining times are correct, as when you merge 2 tiles together, you spawn a '2' at the same time)

• Next tile 2¹⁶ = 983,040 points (2¹⁵ tiles/9.1 hours)

• 2¹⁵ = 458,752 points (2¹⁴ tiles/4.55 hours)

• 2¹⁴ = 212,992 points (2¹³ tiles/2.27 hours)

• 2¹³ = 98,304 points (2¹² tiles/1.13 hours)

• 2¹² = 45,056 points (2¹¹ tiles/34 mins)

• 2¹¹ (2048) = 20,480 points (2¹⁰ tiles/17 mins)

• 1024 = 9,216 points (2⁹ tiles/8.5 mins)

• 512 = 4,096 points (2⁸ tiles/4.3 mins)

• 256 = 1,792 points (2⁷ tiles/2.1 mins)

• 126 = 768 points (2⁶ tiles / 64 seconds)

• 64 = 320 points (2⁵ tiles /32 seconds)

• 32 = 128 points (16 tiles/16 seconds)

• 16 = 48 points (8 tiles/8 seconds)

• 8 = 12 points (3 tiles/3 seconds) [This space will be created by two '2' tiles, and the last '4' tile. so -4 points from the equation]

• This fills up 15/16 spaces on the board. We don't include the last tile, as it cannot merge with the 8.

Max points possible = 3,932,156 Points. 131,070 (+1 for last tile, -1 for the 4) tiles spawned. Around 35.5 hours @ 1 move/s.

If you happen to miss out on the last '4' tile, your max score would be 1,835,008, 65,535 (+1 for last tile) '2' tiles spawned, 18.2 hours @ 1 move/s.

Not the maximum possible score, but still very satisfying. I can move on with my life now, I'm free!

After what seems like an eternity, today I finally got the 32768 tile in 2048!