About

This tool is a rigorous implementation of the sliding block puzzle paradigm, specifically designed to test spatial reasoning and long-term planning. Unlike simple arcade games, 2048 operates on a deterministic grid where entropy increases with every move. The risk of gridlock (where no valid moves remain) grows exponentially as the number of distinct values on the board increases.

Success requires maintaining a monotonic gradient of values - keeping the highest value tiles, such as 1024 or 2048, anchored in a corner. This minimizes the fragmentation of the available 4×4 workspace. The game ends when the grid density reaches 100% and no adjacent tiles satisfy the merge condition v_i = v_j.

Formulas

The Merge Condition

Two tiles merge if and only if their vector positions allow collision and their scalar values are identical:

{

v_new = v₁ + v₂ = 2⋅v₁if v₁ ≡ v₂

Scoring Algorithm

The total score S is the summation of the value of every merged tile produced throughout the game:

S = N∑k=1 merge_value_k

Where N is the total number of merge events.

Reference Data

Tile Value (2ⁿ)	Probability	Hex Color	Rarity Tier
2	90% (Spawn)	#eee4da	Common
4	10% (Spawn)	#ede0c8	Uncommon
8	Merge Only	#f2b179	Regular
16	Merge Only	#f59563	Regular
32	Merge Only	#f67c5f	Intermediate
64	Merge Only	#f65e3b	Intermediate
128	Merge Only	#edcf72	Advanced
256	Merge Only	#edcc61	Advanced
512	Merge Only	#edc850	Expert
1024	Merge Only	#edc53f	Master
2048	Merge Only	#edc22e	Legendary

Frequently Asked Questions

Yes. The theoretical maximum tile on a 4x4 grid is 131,072 (2^17). However, reaching this requires perfect play and spawning 4s exactly when needed to execute the final merges.

The "Corner Strategy" is the most effective. Keep your highest value tile in one corner (e.g., bottom-right) and never move it. Build a snake-like chain of descending values connected to it. Only swipe in two directions (e.g., Right and Down) unless absolutely forced.

After every move, the game identifies all empty cells set E. One cell is chosen uniformly at random from E. The value is 2 with a probability of 0.9 (90%) and 4 with a probability of 0.1 (10%).

Yes. This implementation uses LocalStorage to persist the grid state and score instantly after every move. You can close the tab and resume exactly where you left off.

You lose if the grid is full AND no adjacent tiles have the same value. If you have empty squares, you cannot lose yet. This tool checks for "Game Over" only when valid moves = 0.