How the 2048 AI Solver Works: Expectimax Explained

By LK Forge  ·  6 min read  ·  Updated Jul 2026

When you turn on Autoplay, the board is handed to a small search algorithm that plays 2048 far better than a casual human. It memorises nothing and follows no fixed script — it re-scores the entire board every single move. We also ran its exact search code headless for 250 full games to see how well it really plays: it reaches the 2048 tile in about 70% of games, pushes on to 4096 in roughly 30%, and — honestly — essentially never reaches 8192. Here is exactly how it decides, and where it hits its ceiling.

The Core Idea: Expectimax Search

2048 is a game against chance: you choose a direction, but the game then drops a new tile on a random empty square. The right tool for games like this is expectimax search. It builds a tree that alternates two kinds of layers. On a max layer the AI tries each of the four moves and keeps the best. On a chance layer it considers where a new tile could appear — a 2 with 90% probability or a 4 with 10% — and averages the results, weighted by probability. By looking several layers deep, the solver does not just grab the move that looks good now; it picks the move whose likely future is strongest, even accounting for unlucky spawns. That distinction is why expectimax handles 2048's randomness far better than a greedy one-move-ahead approach.

The Heuristic: Scoring a Board

Search needs a way to score a board it cannot play all the way out. The whole evaluation is one line — three terms added together:

score = positional + empties × 200000 + smoothness × 4000

• Positional (corner-snake) — each square has a fixed rank, and its tile value is multiplied by 4^rank. Because the weights grow as powers of four, a big tile in the top-ranked corner dominates everything else, so the search is strongly rewarded for stacking value toward that corner in snake order.
• Empty squares — every blank cell is worth a flat 200000. That number is deliberately huge: empty space is what keeps future moves legal, so a nearly-full board is scored as almost worthless no matter how large its tiles.
• Smoothness — for each pair of horizontal/vertical neighbours the heuristic subtracts |log2(a) − log2(b)|. Neighbours one doubling apart (mergeable) cost almost nothing; a 2 sitting next to a 512 is punished. Jagged boards score lower.

Those weights are why the AI keeps its largest tile pinned in a corner without ever being told to — it simply scores those boards higher. This is the snake rank map it uses (darkest = highest weight, the corner everything flows toward):

Ranks boustrophedon ("snake") down to the bottom-right corner. Each rank r contributes 4^r, so the corner is worth 4× its neighbour, 16× the next, and so on.

Searching Deeper When It Matters

Looking further ahead costs time, and the cost explodes with every empty cell because each blank is a branch on the chance layer. The solver makes two pragmatic trades to stay fast enough to run live in your browser:

• Adaptive depth. It counts empty squares and picks its search depth from them: >8 empties → depth 3, >3 → depth 4, otherwise → depth 5. When the board is wide open there is little danger and far too much branching to go deep; as it fills up and mistakes get fatal, the search looks further ahead.
• Bounded chance branching. On a chance layer it samples at most 6 of the empty squares (chosen at random) instead of expanding all of them. Averaging over 6 representative spawns is close enough to the true expectation to play well, while capping the branching factor that would otherwise make depth-5 search hang.

Those two knobs are the entire reason it feels instant — in the benchmark it spent about 0.5 ms per move — and they are also the reason it plateaus, which we will get to.

From Score to Move

Putting it together, each turn the solver tries all four directions in the order down, right, left, up (a mild tie-break bias toward the bottom-right corner), runs expectimax over each resulting board, and plays the direction with the highest expected score. The AI Hint button runs that search once and reports the winning direction; Autoplay just repeats it on a timer until you stop it or the board locks up.

How Well Does It Actually Play?

Claims like "wins almost every time" are easy to write and easy to disprove, so we measured it. We lifted the solver's exact search and board code out of the page, played 250 complete games to game-over with no human input, and recorded the largest tile each game reached. Results:

250 self-play games, standard spawn odds (90% "2", 10% "4"). Median game length ~1,650 moves; ~0.5 ms of thinking per move.

So the honest headline is roughly a 70% win rate to 2048 — strong, watchable, and well clear of casual human play — but it is not a superhuman bot. Notice the cliff between 4096 (about 1 game in 3) and 8192 (never). That wall is not mysterious; it is a direct consequence of the two speed trades above.

The result is a live, watchable run of the corner-snake strategy — the exact pattern the strategy guide teaches — executed move after move in front of you. Turn on Autoplay and you can literally watch the snake weights and the empty-square bonus fight it out in real time.

Read next: the corner-snake strategy · or the full strategy guide.