Using the above heuristic would give you a board perfectly organized by value, with the largest tiles in the corner and all other tiles decreasing in value as you get farther from the largest tile. However, this method does not allow you to match any tiles, because tiles of the same value must be next to each other to be matched (and this method does not put tiles of the same value next to each other).
Smoothness refers to having tiles of the same value adjacent to each other, so that they can be matched. Once a board has become “perfectly monotonic,” it is much easier to match a bunch of tiles by making them adjacent to one another.
Using the first screenshot as an example, it is easy to see how once you have a monotonic board, applying smoothness makes matches very easy to create. In the above setting, the player could match a number of tiles that would result in the formation of a 128 tile in only a few moves:
- Down: makes the bottom 4’s adjacent
- Right: matches the bottom 4’s to make an 8
- Up: matches the new 8 and the 8 above it to make a 16
- Up: matches the the new 16 with the 16 above it to make a 32
- Left: brings the old 32 to the left so it is adjacent with the new 32
- Up: matches the 32’s to create a 64
- Up: matches both 64’s to create a 128
Once the 128 match is made, the player should remake a monotonic board by shifting the board in only two or three directions to condense larger numbers into the corner.