2048
Combine matching tiles to reach 2048, with the corner strategy that turns a luck-based game into a solvable one.
Use arrow keys or swipe to play.
A 2048 tile is worth exactly 20,480 points, whatever route you take
Every merge adds the value of the tile it creates. Building a 2n tile out of 2s means building two 2n−1 tiles and merging them, so the score satisfies S(n) = 2·S(n−1) + 2n. That solves to (n−1) × 2n exactly, and the closed form matches the recurrence at every size from a single 2 up to 65,536.
| Tile | 2s needed | Merges | Score it pays | Points per unit of tile |
|---|---|---|---|---|
| 4 | 2 | 1 | 4 | 1 |
| 8 | 4 | 3 | 16 | 2 |
| 16 | 8 | 7 | 48 | 3 |
| 128 | 64 | 63 | 768 | 6 |
| 256 | 128 | 127 | 1,792 | 7 |
| 512 | 256 | 255 | 4,096 | 8 |
| 1,024 | 512 | 511 | 9,216 | 9 |
| 2,048 | 1,024 | 1,023 | 20,480 | 10 |
So there is no such thing as making a 2048 efficiently. If every spawn is a 2, that tile costs 1,024 spawns and 1,023 merges and pays 20,480, and no route through the board changes any of those numbers. The last column is just n−1, which is why doubling the target tile slightly more than doubles the score rather than exactly doubling it. Two tiles arrive at the start and one per move after that, so a 2048 built from 2s alone needs at least 1,022 moves.
The 4 that spawns for free costs you four points
One spawn in 10 is a 4 rather than a 2, so the average spawn is worth 2.2. That 4 arrives without the merge that would normally have created it — and the merge you skipped was worth exactly 4 points. Free material, taxed on the scoreboard.
It helps in the way that matters more, though. Accumulating the 2,048 of raw material takes about 931 spawns instead of 1,024 — 9% fewer moves for the same tile. Whether that is a gift depends on whether you are playing for the tile or for the number underneath it.
The total on the board is the total ever spawned
Merging two tiles of v into one of 2v conserves the sum, and sliding moves nothing new in. So the numbers you can see add up to precisely the sum of every tile that has ever appeared: play creates nothing and loses nothing. That is worth checking rather than believing, so it is checked — 400 games of random play, and the board sum matched the spawned sum in every one.
A tile also merges at most once per move, which is the rule people misremember: a row of four 2s becomes two 4s, not an 8. And the grid has a shape rather than a score limit. Sixteen cells holding the sixteen distinct powers from 2 to 65,536 total 131,070 — two short of 217. That perfect ladder is also a dead board, because no two neighbours match. Which is the useful corollary: a full board is not a loss. A full board with no repeated neighbours is.
And random play gets nowhere near
Pressing arrow keys at random, over 400 seeded games, the best tile each game reached:
| Best tile | Games | Share |
|---|---|---|
| 16 | 3 | 0.8% |
| 32 | 25 | 6.3% |
| 64 | 159 | 39.8% |
| 128 | 182 | 45.5% |
| 256 | 31 | 7.8% |
Not once did chance produce a 512, and 2,048 is 3 doublings past 256 — each doubling needing twice the material of the last. Those games averaged 116 moves and topped out at 3,128 points, against the 1,022 moves and 20,480 points a single 2048 tile demands. The distance between those two pairs of numbers is the whole game.
How to use
- Swipe or use arrow keys to slide all tiles.
- Matching tiles that collide merge into one.
- Keep your largest tile anchored in a corner.
- Avoid moving in the direction that would dislodge it.
Frequently asked questions
What is the winning strategy?
Pick a corner, keep your largest tile there permanently, and never make a move that would shift it. Build a descending row along one edge, and use only two or three of the four directions. Most losses come from a panicked move in the forbidden direction.
Why should I avoid one direction entirely?
Because moving that way slides your anchor tile out of its corner, and a new tile can then spawn behind it. Recovering from that is usually impossible. Disciplined players use up and left almost exclusively, resorting to right only when genuinely stuck and never using down.
What is the highest tile possible?
131072 in theory on a 4 by 4 board, requiring a perfect sequence with no wasted spawns. In practice 32768 is an exceptional human result, and reaching 8192 already demands sustained careful play.
Is the game mostly luck?
Less than it feels. Tile spawns are random, but the strategy above wins consistently for players who apply it, and search-based programs reach very high tiles reliably. Luck determines how far a good player gets, not whether they reach 2048.
Where did it come from?
Gabriele Cirulli wrote it over a weekend in 2014 as a variation on an existing game called 1024, itself derived from Threes. He released it free and open source, it became enormously popular within days, and he has been open that the concept was not originally his.
Do I have to stop at 2048?
No — the game continues if you choose, and reaching 4096 or 8192 is a considerably greater achievement. The 2048 tile is a milestone the game names, not a limit it imposes.
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