No points are added to the player's score for randomly appearing tiles. After all tile merges are completed, all remaining tiles on the board slide as far as possible in the direction of the player move.Įach time a pair of tiles combines, it adds the total of those tiles (the value of the new tile) to the player's score. In the case of four identical adjacent tiles (impossible in the 3x3 variant), both pairs of tiles combine into higher tiles. In the case where three identical tiles are adjacent, the two tiles closest to the edge of the board towards the direction of movement are combined, with the third tile remaining uncombined.

When there are adjacent identical tiles in the direction of movement, they merge into a tile with the sum of the two tiles. If none of the four directions are possible (no empty board spaces, and no adjacent identical tiles), the game ends.

On each turn, the player may move in any of four directions (left, up, right, or down), as long as at least one tile may slide in that direction (having an available blank space toward the direction of movement), or as long as two identical tiles are adjacent in the direction of movement. Each randomly appearing tile is a 2 with 90% probability or a 4 with 10% probability, and appears in any blank space with equal probability. At the start of the game, two tiles randomly appear within an empty grid, and after each player move, one tile randomly appears. The rules of the original game are simple: The original 4x4 version of 2048 is a single-player game created in March 2014 by Gabriele Cirulli. For each of these four objectives, the expected value (win probability or expected additional score) has been calculated for each of the four allowable moves from any achievable board position. The 3x3 variant of 2048 has been strongly solved for four objectives: Achieving a 256 tile, achieving a 512 tile, achieving a 1024 tile, and maximizing expected game score. * replace 'upper' with whatever two rows/columns are remaining, depending on your play direction.Solving the 3x3 Variant of 2048 SOLVING THE 3x3 VARIANT OF 2048 Neither of these is difficult to do consistently. If you're playing snake, your success basically boils down to being able to create 32s from the upper two rows, and then a final 64 on either edge of the upper* rows. Then you still have to factor in your success rate in creating 128 from the remaining eight tiles (not an easy drill).įortunately, the 16k tile is quite achievable. Your chance of setting up the first eight tiles successfully is 0.75 8 = ~10%, and that's just for the first eight tiles. Suppose your success rate on the 16k tile is 75%. The reason for this, of course, is that every tile on the road to 32k is equivalent to the difficulty of the 16k tile: first you have to create 16k, then you have to create 8k but with one fewer square, then you have to create 4k but with two fewer squares, etc. With perfect play the 16k is achievable over 99% of the time with careful play I estimate one could probably achieve a success rate of at least 95% on the 16k. 16k and 32k are usually not considered fake, if only for the reason that nobody who's faking ever stops at those tiles.Īs someone who has set up a 32k run once, I can assure you that not only is 16k doable, but you have to be able to do it almost on command if you want a hope of completing a 32k run.

2048 high score