![]() It’s quite intuitive as to why the largest square should be in the corner. Why is this so? In a sense, the game requires you to build a long chain of consecutive powers of 2 to reach the next power, and one of the best ways to allow for these consecutive powers of two to easily be combined is for the consecutive powers of two to be adjacent to one another. Basic Strategy:Īn inevitable conclusion reached by anyone playing this game is that keeping the largest number in the corner is a necessary part of the winning strategy. ![]() A 4×4 grid gives us 16 units of space, while the 16384 tile requires log 2 16384 = 14 units of space, leaving us essentially 2 units of space to spare. A 4×4 grid is not a terribly large amount of space for us to create our ultimate goal, the 16384 tile. The game of 2048 is largely a game about space. What’s the point of this you ask? It’s important to understand what the game is about, what the restrictions are, so that we can devise a strategy that allows for the creation of larger tiles. A clearer explanation is available on the numberphile youtube channel: video link Of course, since the game allows for 4s to spawn, it is also possible, albeit extremely unlikely to achieve 2 17 = 131072. By induction, we can quite clearly see that the maximum possible value attainable in a 4×4 grid is 2 16 = 65536. Likewise, the maximum value you can attain in a 1×3 grid is 8, as we’ve already shown that it’s impossible to get a 8 in a 1×2 grid to combine with our first 8 to get 16. And it’s impossible to get a 4 in a single square. Why can’t we get 8 you ask? Well, quite simple, to get an 8, we’ll need two 4s. Quite clearly, in a 1×2 grid, we can only attain a maximum value of 4. What would be the largest value we can get playing in this grid? Let’s just ignore the fact that 2048 allows for 4s to spawn randomly and consider the scenario where only 2s can spawn. ![]() Suppose instead of a 4×4 grid, we only had a 1×2 grid. First, we’ll look at the theoretical maximum value attainable: Shortly after it’s release, this cap was removed, and players could attain tiles with larger values.īefore we discuss the strategy of the game, we need to look at the motivation behind these strategic maneuvers. The original version only allowed for a maximum value of 2048 to be attained the game automatically ends when the player attains a tile with the number 2048 on it. Each turn, a new tile spawns at a random location. When tiles with the same value collide, they merge to form a tile with double the original value. ![]() The player can swipe in each of the four standard directions to move all the tiles in that direction. The game is rather simple, there is a 4×4 grid with numerous tiles with powers of two on them. The free, slightly less complex 2048 rose into popularity shortly after it’s creation, while the prettier, original version did not see much success. We’ll be looking at the arguably more intricate game, 2048 today.Ģ048 was created in February 2014 by Gabriele Cirulli, based off the original game threes by Sirvo. The casual player had no trouble getting into them, and the high skill cap along with the natural competitiveness of these games propelled them into outspread popularity. 2014 saw the rise of two games, 2048 and flappy bird, both notably having simple mechanics while requiring skill to execute.
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