Is 2048 Always Winnable? What 1,000 Test Games Show

Nobody knows whether 2048 is always winnable: no one has proved whether a strategy exists that reaches 2048 in every game. What we can measure is how often good play wins. In 1,000 test games played with Poozee's 2048 engine, a program that looks three moves ahead made 2048 in 991 of them (99%), while random swiping and a fixed swipe order never made it once.

So 2048 is mostly a game of skill, with a little luck left over. Even that strong program lost 9 games in 1,000, and its losses looked alike: a full board with a 1024 waiting for a partner that never arrived.

Why nobody can say 2048 is always winnable

After every move, a new tile appears in a random empty square: a 2 nine times in 10, otherwise a 4. Poozee uses the same odds as the original game's source code. A strategy that wins every game would have to survive every possible run of new tiles, including the unluckiest ones, and nobody has shown that such a strategy exists, or that it doesn't.

What we can do is measure. We played 1,000 seeded games with the code that runs Poozee's 2048 (same rules, same 2-or-4 odds), once with each of four computer players, and counted how often each one made 2048:

• Random swipes: any direction that moves the board.
• Fixed order: down whenever it can, then left, then right, and up only when nothing else moves. That's the corner rule from how to win 2048 with no thinking at all.
• Lookahead, 2 moves: tries every swipe, then 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. "Best" means many empty squares, tiles that can merge, and rows and columns in order.
• Lookahead, 3 moves: the same program, looking one swipe and one new tile further ahead.

Both lookahead programs look one move further still when 2 or fewer squares are empty, where the extra look matters most.

How often each strategy reaches 2048

The gap between the rows is the answer to "luck or skill". The same 1,000 games went from no wins at all to 917 wins just by looking ahead, and one more move of lookahead cut the losses from 83 to 9. The fixed routine, for all its corner discipline, never even made a 1024.

Pro tip: The lookahead programs never swipe without checking where the next tile could land. You can do the same: before each swipe, look at which squares it leaves empty, and ask what happens if a 2 drops into the worst of them.

Beyond 2048: how often 4096 and 8192 happen

Making 2048 is a long way from the end of the board. We let all 1,000 of the 2-move program's games, and the first 200 of the 3-move program's, keep going after 2048 until they made 8192 or ran out of moves. The table counts the games that made each tile:

Each doubling is harder than the last, because the big tiles you have already built take up squares you can't use. A program that makes 2048 in 92% of games makes 8192 in only 9%. For where these games finally end, and the largest tile any game can make, see the highest tile in 2048.

How 2048 games are lost

A game of 2048 ends only when the board is full and no two neighboring tiles match, so every lost game ends on a full board. What differs is how long it took to fill up and what is on it. Here are the lost games of each player:

Four things stand out:

• Weak play loses early, with small tiles. Random swiping filled the board after a median of 116 moves. The fixed routine kept its biggest tile in a corner in 713 of its 1,000 games and still lost every one, most often with a 256: a corner on its own is not a strategy.
• Strong play loses late, one tile short. The 2-move program's lost games lasted a median of 912 moves, and 61 of its 83 losses had already made a 1024. Those 61 games lasted a median of 439 more moves after their first 1024, while the winning games needed a median of 478 moves to turn their first 1024 into 2048. They ran out of room on the home stretch.
• The board fills up long before the end. In the 2-move program's lost games, the median board had just 1 empty square 30 moves before the end, and still 1 at 20 and at 10 moves before. Those games weren't lost to one bad swipe: a typical one spent its last 30 moves with a single free square to work with.
• The corner usually held. 66 of the 83 lost games ended with the biggest tile still in a corner. In the other 17, it had left its corner at most 30 moves before the end. When strong play loses, it is usually not because the big tile wandered off.

A lost game, up close

Here is how one of the 3-move program's 9 losses ended (game 958 of the 1,000). Twenty moves before the end, the board had one empty square, and the two 512s that could have made a second 1024 already sat apart:

  1024 512  64   2
  512  128  32   4
  64   4    2    .
  4    2    4    2

The game ended 20 moves later, after 1,089 moves and 18,692 points, on this board:

  1024 512  64   16
  512  128  32   2
  64   32   8    4
  4    2    4    2

The 1024 never left its corner. Both 512s touch it, but they don't touch each other, and two tiles can only merge when they are side by side in the same row or column. No row or column holds two matching neighbors, so no swipe moves anything. The game was two merges from 2048: 512 + 512 = 1024, then 1024 + 1024 = 2048.

Was game 958 simply unwinnable? No. The 2-move program lost it too, after 746 moves. But a 4-move version of the same program (one more swipe and one more new tile again, too slow to play all 1,000 games) played the same game and made 2048 in 987 moves.

How much of 2048 is luck?

A seed fixes the game's random numbers, so every player given the same seed gets the same run of 2s and 4s, in the same order: if the 300th new tile is a 4 for one player, it is a 4 for every player whose game lasts that long. Where each new tile lands depends on which squares are empty, so the boards drift apart, but the luck of the draw is shared. That lets us ask whether a lost game was lost to the tiles or to the decisions:

• Of the 83 games the 2-move program lost, the 3-move program won 82.
• Of the 9 games the 3-move program lost, the 2-move program won 8, and the 4-move program won the ninth (game 958 above).
• So every one of the 1,000 games was won by at least one of our programs. None was hopeless from the first tile.
• The lost games didn't get more 4s, either: 4s made up 10.1% of the new tiles in the 2-move program's lost games, and 10.0% in its wins.

That is the clearest answer we have to "is 2048 luck or skill". The difference between 0% and 99% is skill, and even a strong player's losses were games that different decisions could have won. Luck is real (a 2 landing in the one square you needed can end a game), but in our sample it never decided a game on its own.

It still doesn't prove that 2048 is always winnable. A thousand games is a sample, not every possible game, and our programs are far from perfect players.

Pro tip: If your games keep ending with a 1024 on the board, that is the strong programs' way to lose, not bad luck. The fix is room: count your empty squares every few moves, and when you are down to one or two, make the move that frees a square before the move that builds a tile.

Why do I keep losing 2048?

Compare your lost games with the table above:

1. Your games end before your first 1024. That is how the random and fixed-order players lose: the board fills up while the tiles are still small. The chain-building in how to win 2048 is what gets you past it, not a luckier set of tiles.
2. Your games end with a 1024 on the board. That is how the lookahead programs lose. A 1024 needs a second 1024 built beside it, which took a median of 478 more moves in our winning games, all of it on a board with less space. Slow down for that stretch.
3. You are not sure which tile your games die at. Your final score tells you: 2048 scoring explained shows the score that comes with each milestone tile.

Keep playing

Open 2048 on Poozee and watch your empty squares as your first 1024 takes shape. If the board locks up, the "No moves left" screen offers Undo last move, and the new tile after your next swipe is drawn fresh, so a different swipe can change the game. If you like asking whether a game can always be won, are all solitaire games winnable answers it for Klondike, and our Minesweeper 50/50 guide covers the moments where Minesweeper really is down to luck.