- +
Constructive. Two equal tiles with the same phase merge into the next value: |8⟩ + |8⟩ → |16⟩, and likewise for two − tiles.
- ✕
Destructive. Two equal tiles with opposite phases cancel out, |8⟩ − |8⟩ = 0. Both vanish, you get points for the released energy, and the board gets space.
- Z
Z tile. Push any tile into it, or it into a tile, and that tile's phase flips: Z|v⟩ = −|v⟩. The Z tile is used up.
- H
H tile. It splits a tile of 4 or more into two halves with opposite phases, |2v⟩ → |v⟩, −|v⟩. The − half appears in a free cell. Good for building the anti-tile that cancels a blocker.
- ⚠
Careful: − tiles merge with each other too. A big −|64⟩ can wipe out your |64⟩.
- ★
Goal: make a |2048⟩. Either phase counts, because a global phase can't be measured.