I would like to know with what probability the number 4 appears in the grid of the game 2048. As well, is this probability the same at the beginning? I tried to find the original game's source code, but I did not succeed.

  • 7
    This strip would've been funnier if the repeating number was 4, but I remembered wrong...
    – l I
    Jun 5 '14 at 18:49
  • 21
    xkcd.com/221 where it is 4
    – mmatthews
    Jun 5 '14 at 19:45
  • 1
    @z' Only 9s appear. Only powers of two can join. Task: Score any points.
    – yo'
    Jun 5 '14 at 23:43
  • @mmatthews that was the one, i got my comics mixed up
    – l I
    Jun 6 '14 at 0:16
  • 2
    100% probability, according to xkcd
    – Kroltan
    Jun 6 '14 at 13:50

Extracted from the source code (line 71) :

var value = Math.random() < 0.9 ? 2 : 4;

Math.random() returns a number between 0 and 1. This code can be read as follows : Is the pseudo-randomly generated number strictly less than 0.9? If yes the tile value is 2, if no the value is 4. Assuming Math.random() generates numbers with uniform probability over (0,1), the code implies a 90% chance of a 2, and 10% chance of a 4.

As for your second question: Yes, the probability is the same at the beginning. When the game starts 2 tiles are generated and their value randomized with the code above.


i believe its 10% for a 4 and 90% for a 2

  • 21
    You're not wrong necessarily, but without providing any kind of source, it's just speculation. Jun 5 '14 at 22:50

I played a game and wrote how much 2 and how much 4 appeared. There were 326 times number two and 56 times number 4. So it should be abaout 17% more or less. The variation on the percentage shouldn't be more than 3%. So I would say it's between 14 and 20 percent.

I personally think that it should be 1/6 but that's just speculation...

If you want to be more precize, then just play a lot of game and wrote what you got.


I usually get a 2 65% of the time and 4 35%. It can vary, I can sometimes get alternations between the two. Sometimes the probability of the two actually swaps. You can never tell.

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