Number Merge: can the next tile break your plan?
Check all ten spawns on one board, distinguish an 80% surviving merge from a 2% bonus, and test your predicted Up points.
A pair can look ready to merge and still be interrupted before your next move. Number Merge adds a new tile after every changing slide. If that tile lands between the pair, a plan based only on the board before the spawn can fail.
This lesson counts every possible first spawn on one fixed board. It separates the chance that a particular merge survives from the chance of earning a bonus elsewhere. You can choose an outcome and check your own predicted points in the exercise below the lesson.
Make one plan explicit
Use this constructed teaching board. Rows and columns count from the top-left corner; dots are empty squares. It is not the random two-tile board used at the start of a live game.
4 4 4 16 · · · · 8 128 256 512 16 32 64 128
Our plan is Left, followed by Up. First Left merges the first two 4 tiles into 8 and earns 8 points. The remaining 4 cannot join that new 8. Before the first spawn, the board is:
8 4 16 · · · · · 8 128 256 512 16 32 64 128
The two 8 tiles in column 1 have one empty square between them, at R2C1. Without a tile in that gap, the next Up will combine them into a 16 and earn 16 points from that pair. The question is specific: will those two original 8 tiles combine on our next Up?
Count the empty squares after the slide
There are five places for the first spawn: R1C4 and all four squares in row 2. The game chooses uniformly among these empty squares. It then chooses a 2 with 90% probability or a 4 with 10% probability.
Each position therefore has probability 1/5, or 20%. A particular position receiving a 2 has probability 1/5 × 9/10 = 18%; that position receiving a 4 has probability 1/5 × 1/10 = 2%. The ten position-and-value outcomes are not equally likely.
The gap that blocks the original pair
If either a 2 or a 4 appears at R2C1, column 1 becomes 8, new tile, 8, 16. It is full, and no equal neighboring pair exists there. Up cannot remove that new tile or let either 8 pass through it.
For example, here is Up after a new 2 at R2C1, stopping before the second spawn:
8 4 16 512 2 128 256 128 8 32 64 · 16 · · ·
This Up earns zero points. It still changes other columns, so the live game would add another tile afterward. The diagram deliberately stops before that second spawn to keep the first decision visible. A 4 at R2C1 also blocks the 8 pair and earns zero on Up.
At the other four first-spawn positions, column 1 stays 8, empty, 8, 16. Up combines its two 8 tiles. Thus the chance that this particular merge survives is 4/5 = 80%, and the chance it is blocked is 1/5 = 20%. Both possible new tile values give the same answer to this question.
A different question needs the tile value
Now ask how many points the whole Up move earns. Most successful outcomes earn 16, but a new 4 at R2C2 creates a second merge. Column 2 becomes 4, 4, 128, 32, so its first two values combine into 8 for another 8 points.
16 8 16 512 16 128 256 128 · 32 64 · · · · ·
The whole Up earns 16 + 8 = 24 points in that outcome. A new 2 at the same position does not match the existing 4, so Up earns only 16. The bonus case has probability 1/5 × 1/10 = 2%, not 1/10 = 10%. Counting it as one of ten equally likely outcomes would give the wrong weight.
Keep a complete outcome table
Each row represents one possible first-spawn position. Every 2 case in the table has probability 18%; every 4 case has probability 2%. Points count only the following Up, before its new tile, and exclude the first Left's 8 points.
| First spawn | If new 2 | If new 4 | Original 8 pair |
|---|---|---|---|
| R1C4 | 16 | 16 | Combines |
| R2C1 | 0 | 0 | Blocked |
| R2C2 | 16 | 24 | Combines |
| R2C3 | 16 | 16 | Combines |
| R2C4 | 16 | 16 | Combines |
The whole move earns 0 points with probability 20%, 16 points with probability 78%, and 24 points with probability 2%. The weights add to 100%. The 78% comes from four successful 2 cases, worth 4 × 18% = 72%, and three ordinary successful 4 cases, worth 3 × 2% = 6%.
Optional: what an average can tell you
The expected immediate points from this particular next Up are 0 × 0.20 + 16 × 0.78 + 24 × 0.02 = 12.96. This is a probability-weighted average across outcomes, not a number the score counter can award in one move. Each actual Up here earns 0, 16, or 24.
That average is conditional on starting from this board, playing Left, and then committing to Up regardless of the first spawn. In real play you can inspect the new tile and change your plan. This calculation does not compare all possible policies or prove that Left followed by Up gives the best long-term score.
Predict an outcome before revealing the answer
In the spawn exercise below, choose a position and value, enter the points you expect from the next Up, then choose Check prediction. It shows the board after your chosen first spawn and the board after Up. Reset exercise clears your prediction. The exercise is deterministic because you choose the outcome; it does not load or alter the random live game.
Self-check: a 2 at R2C2
Up earns 16 points, because column 1 combines the two 8 tiles. Column 2 is 4, 2, 128, 32 and has no equal neighboring values, so it contributes no merge points. Changing that chosen 2 to a 4 raises the whole Up to 24.
Self-check: a 4 at R1C4
Up still earns 16. The new 4 belongs to column 4, whose nonempty values are 4, 512, 128. It cannot combine with the 4 in column 2 during an Up move; columns are processed separately.
Use the method on your own board
Name the merge you hope to make next. First calculate the chosen slide without a new tile, then list its empty squares. For each possible spawn, check whether the planned merge remains and whether the new value creates another merge. Keep an event probability, such as the survival of one pair, separate from the points of the whole move.
A blocked merge here does not mean game over. Other moves and later merges may still be available. Conversely, an 80% chance of keeping this pair is not a guarantee of a good final score. These exact percentages apply to this fixed board and this site's spawn rules; a different board, value distribution, or direction needs a fresh count.