Number Merge: will the next tile leave any legal move?
Check all four directions on a full board, then use one fixed position to separate a blocked swipe from a finished game.
A full Number Merge board can still have a move. A swipe that does nothing can also occur while another direction remains available. To decide whether a round has ended, ask a more precise question: can any of the four directions change the board?
That check becomes especially useful when a merge opens just one square. The next tile must fill that square, but its value can decide whether another move exists. This paper lesson follows both possible values on one fixed board and accounts for every direction.
Use a test for the whole board
Here, a legal move means a direction that changes at least one tile position or makes a merge. It need not earn points. An unchanged direction adds no tile and earns no points. After a changing move, the game adds one new tile, then checks whether any direction can still change the result.
For a board with at least one tile and at least one empty square, some direction can change it. There is a tile beside an empty square somewhere along a row or column, so movement is possible. This does not mean that every direction works or that every move is helpful.
For a full board, use this shorter test:
- Check each neighboring pair within every row.
- Check each neighboring pair within every column.
- If any such pair is equal, at least one merge is possible. If none is equal, no direction can change the board.
There are 4 × 3 = 12 horizontal pairs and 12 vertical pairs on a four-by-four board: 24 checks in total. Do not compare diagonals or wrap the end of a row into the next row. On a full board, unequal tiles cannot slide past each other to reach a distant equal value.
Start from one crowded position
Use this constructed paper board. Rows and columns count from the top-left corner. It illustrates this site's rules; it is not a claim about how often a random round reaches this position, and it cannot be loaded into the live game.
2 2 8 16 8 16 32 4 16 32 64 8 32 64 128 16
Before choosing a move, test the board. Left and Right can combine the two 2 tiles in the first row. Up and Down cannot change anything: the board has no gaps and no equal vertical neighbors. Pressing Up here would do nothing, but the round is not over because a horizontal move exists.
Play Left, then pause before the new tile
Left combines 2 + 2 into 4 and earns 4 points. The other three rows stay put. Before the spawn, the board is:
4 8 16 · 8 16 32 4 16 32 64 8 32 64 128 16
Only R1C4 is empty. The new tile must go there. Its only orthogonal neighbors are R1C3, holding 16, and R2C4, holding 4. The game chooses a 2 with probability 90% and a 4 with probability 10%.
Check the other 22 neighboring pairs once: every one is unequal. Filling R1C4 changes only its two incident comparisons. That lets us finish the calculation without rescanning all 24 pairs separately for each outcome.
Follow both possible outcomes
A new 2: the board is finished
4 8 16 2 8 16 32 4 16 32 64 8 32 64 128 16
The new 2 matches neither 16 on its left nor 4 below it. All 24 neighboring pairs are unequal, and there are no gaps. Left, Right, Up, and Down all leave the board unchanged. The game has no moves left.
Some equal values still touch diagonally: the 8 at R1C2 and the 8 at R2C1, for example. That does not create a legal move. A direction processes rows or columns, and there is no empty square that could rearrange this full board first.
A new 4: two directions remain
Replace only R1C4 in the last diagram with 4. It now matches R2C4 directly below. Up and Down can merge that vertical pair into 8, earning 8 points. Left and Right still cannot change the full board because no horizontal neighboring pair is equal.
| New tile | Changing directions | Ends now? |
|---|---|---|
| 2 | None | Yes |
| 4 | Up, Down | No |
Conditional on this starting board and choosing Left, the chance of ending immediately after the spawn is therefore 90%. The chance that at least one more changing move exists is 10%. The two outcomes are not equally likely merely because there are two of them.
Surviving this check does not promise a long round. The next changing move adds another random tile and needs a fresh test. The four points already earned by Left are the same in both outcomes, so this immediate score alone cannot reveal whether a move remains.
Fill a small paper ledger
Cover the outcome table and copy three columns onto paper: new value, equal neighboring pairs, changing directions. Fill one row for 2 and one for 4. Count only horizontal or vertical neighbors. Then compare your entries with the table.
Check your ledger: how many equal neighboring pairs are there in each outcome?
With a new 2 there are zero, so no direction changes the board. With a new 4 there is exactly one, R1C4–R2C4, so Up and Down work. Two directions can use the same pair; that does not make it two distinct pairs.
Change R2C4 from 4 to 2 in the original starting board. After Left, what is the chance of ending immediately?
It becomes 10%. The single empty square is still R1C4, but its neighbors are now 16 and 2. A new 2, probability 90%, creates a vertical pair and leaves Up and Down available. A new 4, probability 10%, creates no equal neighboring pair, so the full board is finished. The remaining comparisons stay unequal.
Does pressing the blocked Up on the original board give you another chance at a random tile?
No. The original Up leaves the board unchanged, so it triggers no spawn. You must choose a changing move such as Left or Right. An ineffective swipe neither proves game over nor rerolls the next tile.
Keep the conclusion local
For your own board, first distinguish an unchanged swipe from a board with no available direction. When the board is full, check its orthogonal neighbors. When a chosen move leaves a single gap, inspect the values beside that gap and weight each spawn by the actual rules.
The 90% and 10% calculations apply only to the two paper positions described here and their specified Left move. They do not measure the overall chance of losing a random round, compare every strategy, or promise a route to 2048. The useful result is a repeatable check of whether another move exists.