| --- |
| license: mit |
| pretty_name: "2048 Solver Benchmark (expectimax depth sweep)" |
| language: |
| - en |
| tags: |
| - "2048" |
| - expectimax |
| - game-ai |
| - search-depth |
| - benchmark |
| task_categories: |
| - other |
| size_categories: |
| - n<1K |
| configs: |
| - config_name: depth_sweep |
| data_files: data/2048-benchmark.json |
| --- |
| |
| # 2048 Solver Benchmark — Expectimax Depth Sweep |
|
|
| By **[LK Forge](https://lkforge.com)**: privacy-first browser tools & games, nothing to install, nothing uploaded. |
|
|
| How well the [LK Forge 2048 Solver](https://lkforge.com/games/2048/) plays as a function of |
| search depth. The shipped engine is an **expectimax search with a corner-snake heuristic**, |
| plus **probability-threshold pruning and a transposition table** (the pruning/table approach |
| follows [nneonneo's canonical 2048-ai](https://github.com/nneonneo/2048-ai)). Self-played |
| headlessly at fixed depths 1–6 plus the shipped adaptive setting. |
|
|
| - **How the solver works:** https://lkforge.com/games/2048/blog-how-the-ai-solver-works.html |
| - **Full write-up:** https://lkforge.com/blog/2048-expectimax-depth-benchmark/ |
| - **Try it:** https://lkforge.com/games/2048/ |
| - **Producer:** [LK Forge](https://lkforge.com) — client-side AI games, solvers, and tools. |
|
|
| ## Headline numbers |
|
|
| - **Below a 3-ply lookahead the solver never reaches 2048** — 0% of games at depth 1 and depth 2. |
| - **Depth 3 is the threshold:** reach-2048 jumps to **66%**, and the mean score jumps six-fold |
| (from ~4,400 to ~29,600) for that one extra ply. |
| - **Quality climbs to 97% reach at depth 5**, but a depth-6 move costs about **83× more compute** |
| than depth 3 for a shrinking gain. |
| - **The shipped adaptive engine reaches 2048 in 94% of 300 games** (depth 4 on an open board, rising to |
| depth 7 when it is nearly full), pushes to 4096 in **70%**, and breaks **8192 in 9%**, at 1.8 ms/move. |
| A separate 250-game run of the same engine measured **92.8%** reach-2048 — corroborating within |
| sampling error. |
|
|
| ## Files |
|
|
| - `data/2048-benchmark.json` — per-depth reach-rates (1024/2048/4096/8192), mean/median score, and |
| mean ms/move for fixed depths 1–6, plus the adaptive run and a headline summary. |
|
|
| ## Method |
|
|
| - **Engine:** the exact shipped engine (`public/games/2048/solver-core.js`), self-played headlessly — |
| the numbers describe the search the game actually runs. |
| - **Reach-rate** = share of games that reached that tile at least once. |
| - **Spawns:** standard 90% "2" / 10% "4" tile spawns. |
| - **Samples:** depths 1–4 and adaptive are 300 games each; depth 5 is 100 games, depth 6 is 30 games |
| (each move there is far slower), so those percentages carry wider error bars. |
| - Tile spawns use a seeded PRNG so the run is re-runnable. The search itself is deterministic — it |
| expands every empty cell rather than sampling — so all game-to-game variance comes from the random |
| spawns, and reach-rate is a distribution, not a single fixed value. |
| - Timing is mean milliseconds per move on one laptop. Measured **23 September 2026** (reworked engine). |
|
|
| ## Reproduce |
|
|
| ```bash |
| node scripts/benchmark-2048-depth.mjs |
| # or: GAMES=300,300,300,300,100,30 DEPTHS=1,2,3,4,5,6 node scripts/benchmark-2048-depth.mjs |
| ``` |
|
|
| The same engine is published as a standalone, MIT-licensed repo that reproduces the adaptive run: |
|
|
| ```bash |
| git clone https://github.com/lucian-devops/2048-ai-solver && cd 2048-ai-solver |
| node benchmark.js 250 # ~20 minutes: ~2 ms/move, ~3,000 moves per game |
| ``` |
|
|
| ## Citation |
|
|
| > LK Forge (2026). *2048 Solver Benchmark — Expectimax Depth Sweep.* |
| > https://lkforge.com/blog/2048-expectimax-depth-benchmark/ |
|
|
| Everything runs client-side, no login, no tracking. |
|
|
