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In the game 2048 what is the biggest tile that can be achieved, assuming a player playing optimally and tile spawning at the most optimal place?

Naively I would say that the biggest achievable tile is 65536 * 2 = 131072 because it seems that the best possible board is the following:

  4     4     8     16
 256   128    64    32
 512   1024  2048  4096
65536 32768 16384  8192

But I'm not sure if

  1. it's correct
  2. how to prove that my intuition is indeed correct.

(sorry if I should have asked on gaming.stackexchange, but this is more of a CS question than a gaming one afaict)

Absurd-Mind
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foo
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    if this is a CS question you should have asked on http://cs.stackexchange.com/ ;) – Absurd-Mind Apr 02 '14 at 06:35
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    This question appears to be off-topic because it is a theoretical CS question, not a programming question. – Raymond Chen Apr 02 '14 at 06:55
  • off, but there is no such a thing _most optimal_, there is only one _optimal_ solution. which is different from that is not _optimal_ anymore. – holex Apr 02 '14 at 08:05

1 Answers1

14

you haven't finished yet with the board you propose: you can slide to the right, going all the way down and obtaining 131072. So your analysis was correct although you missed a spot:

This will be your final board:

  4     8     16    32
 512   256   128    64
 1024  2048  4096  8192
131072 65536 32768 16384
Chris Maes
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    this is not possible, look 5 moves back and you will see that you do not have enough space to create an 8 – Bartlomiej Lewandowski Apr 02 '14 at 08:29
  • I'm sorry but I fail to see the problem: look at the position proposed by @foo in his question; suppose you have his top line and my 3 bottom lines. Then you go like this: 4 8 8 16 --> 4 4 16 16 --> 4 [] 8 32 --> 4 4 8 32 --> 4 8 8 32 --> 4 4 16 32 --> 4 8 16 32... – Chris Maes Apr 02 '14 at 08:48
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    we are talking about the theoretically best solution; "tiles spawning in the most optimal place"; the whole thing is unlikely :) – Chris Maes Apr 02 '14 at 08:55