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Suppose you are playing many 2048 games, all blindfolded. As usual you can press left, right, down, or up to move the tiles. When there are no more moves the game terminates and you are told your score. This is all the information you get. What should be your strategy to maximise your average score?

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Swipe mainly in one vertical direction (ex. down) and one horizontal direction (ex. right). Since you can get stuck by doing this, occasionally, swipe left and down to free up some blocks. This way, the largest blocks appear in the bottom right (getting larger to the left).

Here is the board after using only down and right alternating. Numbers are building up toward 128 on the bottom row. No more down/right moves can be made, so the best option is to use left once then down to combine the 4's and 8's. Going once more down and continuing using only right and down will cause the numbers to continue to go up.

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With this strategy, I normally get around 2000-3500 points and get a 256 or 512 tile as the max.

With a single random game, this was the outcome (3828 points):

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Source: I played this game a lot while distracted and this seems to work pretty well.

[Sort of unrelated, but 2048 is one of the first C++ programs I wrote. Code is here: link to code.]

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    $\begingroup$ Yes, this is one of the best strategies to play the game, even without blindfolds! $\endgroup$ – shanylong Mar 15 at 13:00
  • $\begingroup$ Let's see if I understand correctly: you alternate right-down many times then you do ONE left and ONE up and repeat? Or do you do many left-up? Or do you inject left and up at random times? I would be quite interested to see what these different strategies score on average. $\endgroup$ – Dmitry Kamenetsky Mar 16 at 0:21
  • $\begingroup$ @DmitryKamenetsky : This answer does not recommend ever using UP moves. $\endgroup$ – Eric Towers Mar 16 at 6:17
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    $\begingroup$ @DmitryKamenetsky It would be a bit like this (although not sure exactly what is optiimal): Repeat "Down, right" 200 times, insert "Left, down" once, Repeat "Down, right" 200 times, etc. Since there is a possibility of no right, left, or down moves being possible, you can insert "Up, down" but very rarely. Maybe once every 10000? $\endgroup$ – eyl327 Mar 16 at 6:26
  • $\begingroup$ Do we have a proof or some experimental evidence that this is the optimal strategy? I still feel that one can do better. $\endgroup$ – Dmitry Kamenetsky Jun 4 at 7:36

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