Highest Tile in 2048: Can You Get 131072? The Exact Limit

The highest tile in 2048 is 131,072 (2 to the 17th power) on the standard 4x4 board, and only if a 4 appears at exactly the right moment. If every new tile were a 2, the limit would be 65,536. The highest possible score is 3,932,100.

We checked all of it with the code behind Poozee's 2048 game. Its rules engine replayed a game in which we picked every new tile, and that game made 131,072 and finished on exactly 3,932,100 points. Real play gets nowhere near: our strongest test program most often stopped at 8192.

Is there a tile after 2048?

Yes. 2048 is only the tile that wins the game. On Poozee, making it shows "You made 2048!" with two buttons, Keep going and New game. Keep going and the game carries on until the board is full and no move is left, so the next tiles are 4096, 8192, 16384, 32768, 65536 and finally 131072. The original game works the same way: its source code has a keep-playing option that "allows going over 2048".

Past 2048, every tile on Poozee has the same deep purple color, so read the number rather than the color. The labels get smaller as the numbers get longer, and even 131072 fits on a phone screen.

Why 131,072 is the highest tile

The limit comes from counting, not from luck. Here's the argument, step by step:

1. A new tile appears only after a move that changes the board. That is how Poozee's 2048 works, and the original game's source code does the same.
2. A move that changes the board always leaves an empty square. If the board was full, the only way anything could move was a merge, and a merge frees a square. So just before each new tile the board holds at most 15 tiles.
3. Merges never change the total of the tiles. Two 8s become one 16. Only new tiles add to the total: 2 or 4 each time.
4. Every tile is a power of 2, so a total needs a minimum number of tiles. 131,068 can't be split into fewer than 15 tiles (4 + 8 + 16 + ... + 65,536), because no two of those tiles can be combined into one.
5. With only 2s, the total gets stuck. It climbs 2 at a time, and at 131,070, which is 2 + 4 + 8 + ... + 65,536, the tiles need all 16 squares and no two of them match. No move is left, so the total can never pass 131,070, and no tile can reach 131,072. The highest tile with only 2s is 65,536.
6. A 4 skips the dead end. One move earlier, at 131,068 (the 15 tiles from 4 up to 65,536), a new 4 instead of a 2 takes the sum to exactly 131,072. That new 4 can merge with the 4 on the board, the 8 with the 8, and so on up to 131,072.
7. Nothing can reach 262,144. To get there, the sum would first have to be 262,140 or 262,142, and those need 16 and 17 different tiles. The first fills the board with no move left; the second needs more squares than the board has.

We didn't rely on the reasoning alone. A short program listed every total of tiles a game could ever reach under rules 1 to 4, starting from the two starting tiles. With only 2s, the largest total is 131,070, so the largest tile is 65,536. With 2s and 4s, the largest total is 262,140, and the largest tile is 131,072. The original game uses the same rules (a new tile only after a move, a 2 nine times in 10 and otherwise a 4), so the same limit applies there.

Can you actually get 131,072?

The counting argument says 131,072 is the ceiling, not that a game can reach it. Every square of the board has to be used perfectly at the end. So we looked for a game that does it.

We wrote a search that plays Poozee's 2048 while choosing every new tile itself: it tries every swipe and every empty square for the next tile, keeps the 300 most promising boards, and repeats. "Promising" means the tiles, read along a snake (the top row left to right, the next row right to left, and so on), get smaller as you go, with no gaps. New tiles are always 2s, except at the 16 moments when a 2 would leave a total that no 15 tiles can hold; there it takes a 4. Then we replayed the game it found, move by move, with Poozee's real rules engine, checking that every new tile is one the game could actually have drawn.

The replay made 65,536 after 32,800 moves, without a single 4. On move 65,533 came the first 4, right next to the 4 that move had just made:

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

That is the moment from step 6: the board holds every tile from 4 to 65,536 once, plus the new 4. It took 34 more moves to merge all the way up, and 131,072 appeared on move 65,567. The game then rebuilt everything below it and ended after 131,052 moves on this board:

  131072 65536  32768  16384
  1024   2048   4096   8192
  512    256    128    64
  4      8      16     32

Every tile from 4 to 131,072 appears exactly once, so no two neighbors match and no move is left. It's the largest board 2048 allows.

So yes, 131,072 can be made, but don't hold your breath. The chance that random new tiles land exactly as in our game is smaller than 1 in 10 to the power 100,813. Other perfect games exist, so the real odds of any game reaching 131,072 are better than that, but nobody knows by how much.

Pro tip: On Poozee, Undo takes back your last move, and swiping again draws a fresh new tile. In principle that lets you redraw a bad tile. Our perfect game still needed 131,052 moves without a single redraw, so 131,072 stays a thought experiment.

The highest possible score: 3,932,100

Your score in 2048 is set by the tiles you've built. As 2048 scoring explained shows, a tile built from 2s is worth (n - 1) times its value, where the tile is 2 to the power n, and every new 4 costs exactly 4 points (it skips the 2 + 2 merge that would have scored them).

The best board is the final board above, worth 3,932,164 points if every tile had been built from 2s. But a game can't get there with fewer than 16 new 4s: one at each of the 16 moments when a 2 would have left no room, from the one that makes 131,072 possible to the last tile of the game. They cost 4 points each, 64 in all. So the highest possible score is 3,932,164 - 64 = 3,932,100.

Two things make this exact rather than an estimate:

• The upper limit: the program that listed every reachable total also found the fewest 4s needed to reach each one, and no reachable board scores more than 3,932,100.
• A game that gets there: the replay above finished on exactly 3,932,100 points, counted by the game's own scoring.

This assumes Poozee's rules, which match the original game: a 4x4 board, every merge adds the new tile's value, and a new tile can be a 2 or a 4. If only 2s ever appeared, the ceiling would be 1,835,012 points, the board from 2 up to 65,536.

How far strong play actually gets

The perfect game had every tile handed to it. With random tiles, the picture is very different. We played seeded games with the same computer players as in is 2048 always winnable?, but this time every game kept going after 2048 until no move was left:

• Lookahead, 2 moves: tries every swipe, every square and value the next tile could take, then its own best reply, and picks the swipe that leaves the best board on average. We played 1,000 games.
• Lookahead, 3 moves: the same program, looking one swipe and one new tile further ahead. We played 500 games.

This is the biggest tile each game ended with:

The most common final tile was 4096 for the 2-move program and 8192 for the 3-move program. Neither ever made 32768, let alone 131,072. The best of these 1,500 games scored 367,352 points, under a tenth of the maximum.

Each doubling takes twice as long

The 3-move program's games show how the work piles up. Here is the median number of moves between one milestone tile and the next:

The last column explains the pattern. A new tile adds 2.2 to the board on average (a 2 nine times in 10, a 4 one time in 10), and to turn your biggest tile into the next one, you have to build a second copy of it out of new tiles. Building a second 4096 takes about 4,096 ÷ 2.2, or roughly 1,860 new tiles, one per move. The measured medians land within 2% of that every time.

So if your first 2048 took you 1,000 moves, budget about 1,000 more for 4096 and 2,000 more after that for 8192, all of it on a board with less room, because the big tiles you've already made keep their squares.

Tips for going past 2048

1. Build every new big tile in your corner. The 3-move program made its first 2048 in a corner in 493 of the 496 games that reached it, and its first 4096 in a corner in 457 of 458. The corner strategy from how to win 2048 is how you get past 2048, too.
2. Treat each new record tile as a fresh game. Making 4096 means building a second 2048 next to the first one, with one square fewer to do it in. Everything that got you the first 2048 applies again, with less room for mistakes.
3. Plan for a long game. The 3-move program's first 4096 came after a median of 1,902 moves, and its first 8192 after 3,755. Poozee doesn't save a game in progress (reloading the page starts a new one), so leave the tab open while you chase a big tile.

Pro tip: When you make 2048 on Poozee, the "You made 2048!" screen waits for you. Press Keep going rather than New game, because your best score keeps climbing as long as the game does.

Keep playing

Open 2048 on Poozee and see how far past 2048 you can get. If your games end around 1024, start with the corner strategy in how to win 2048. If they end with a big tile and no room, is 2048 always winnable? shows how strong games run out of space, and 2048 scoring explained turns your score into the tiles it took to get there.