In my last post, I described how to play 2048 and reported the results of some simple simulations. Namely, I reported the results of two very simple strategies:
- Random play will achieve an average ending tile total (AETT) of 252 and usually the highest tile will be a 64 tile or a 128 tile (about an 85% chance of ending with one of those).
- A pure greedy strategy where the player just tries to make the largest new tile possible results in an average ending tile total (AETT) of 399 and usually the highest tile will be a 128 tile or a 256 tile (about an 87% chance of ending with one of those).
Perhaps surprisingly, there are “blind” strategies that will do even better than the pure greedy strategy. Blind strategies are strategies that ignore the current state of the board. I tried two types of simple blind strategies “biased random” and “repeating sequences”. I will summaries the results of the biased random trials in my next post.
The simplest repeating strategy would be just hitting the same key every time—down, down, down, …. Of course that does not do well. Nor would down, up, down, up, …. So the simplest repeating strategy worth trying would be down, right, down, right or some other combination of horizontal and vertical moves. I ran 100 games for every possible repeated sequence of two to four moves and found that the best of these sequences was down, right, down, left or a version of that sequence in disguise. The results are captured in the table below.
Notice that restricting your moves to only two out of the four possibilities does poorly. The Down, Left, Down, Left… strategy had an average tile total of only 44.38 at the end of the game and that strategy never created a tile above 64.
The best strategies were down-right-down-left or that same strategy in disguise (dlul, dldr, and drur are really the same strategy). Notice that this strategy does better than pure greedy which had an AETT of 399.
|move sequence||AETT||Largest Tile|