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"producer": "LK Forge",
"tool": "2048 AI Solver",
"url": "https://lkforge.com/games/2048/",
"method_url": "https://lkforge.com/games/2048/blog-how-the-ai-solver-works.html",
"benchmark_url": "https://lkforge.com/blog/2048-expectimax-depth-benchmark/",
"engine": "expectimax search with a corner-snake heuristic, probability-threshold pruning and a transposition table (pruning/table approach follows nneonneo's canonical 2048-ai); the exact shipped engine (public/games/2048/solver-core.js), self-played headlessly",
"measured": "2026-09-23",
"metric": "self-play reach-rate per tile, mean and median score, and mean milliseconds per move, by fixed search depth",
"tiles_tracked": [1024, 2048, 4096, 8192],
"spawns": "standard 90% '2' / 10% '4' tile spawns",
"notes": "reach_*_pct is the share of games that reached that tile at least once. Depths 5 and 6 use 100 and 30 games (vs 300 for depths 1-4 and adaptive) because each move is far slower, so their percentages carry wider error bars. Tile spawns use a seeded PRNG; 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 rather than a single fixed value. Timing is mean ms/move on one laptop. These numbers reflect the reworked engine (probability-threshold pruning + transposition table, Sept 2026); the site's separate 250-game run of the same engine measured 92.8% reach-2048, corroborating the 94% here within sampling error.",
"fixed_depth_runs": [
{ "depth": 1, "games": 300, "reach_1024_pct": 3, "reach_2048_pct": 0, "reach_4096_pct": 0, "reach_8192_pct": 0, "mean_score": 4366, "median_score": 3636, "ms_per_move": 0.002 },
{ "depth": 2, "games": 300, "reach_1024_pct": 4, "reach_2048_pct": 0, "reach_4096_pct": 0, "reach_8192_pct": 0, "mean_score": 5117, "median_score": 4544, "ms_per_move": 0.008 },
{ "depth": 3, "games": 300, "reach_1024_pct": 91.7, "reach_2048_pct": 66.3, "reach_4096_pct": 13.3, "reach_8192_pct": 0, "mean_score": 29648, "median_score": 28680, "ms_per_move": 0.044 },
{ "depth": 4, "games": 300, "reach_1024_pct": 88.3, "reach_2048_pct": 66, "reach_4096_pct": 15.3, "reach_8192_pct": 0, "mean_score": 29990, "median_score": 31416, "ms_per_move": 0.203 },
{ "depth": 5, "games": 100, "reach_1024_pct": 100, "reach_2048_pct": 97, "reach_4096_pct": 66, "reach_8192_pct": 5, "mean_score": 61019, "median_score": 67432, "ms_per_move": 0.919 },
{ "depth": 6, "games": 30, "reach_1024_pct": 96.7, "reach_2048_pct": 86.7, "reach_4096_pct": 60, "reach_8192_pct": 0, "mean_score": 51914, "median_score": 60280, "ms_per_move": 3.667 }
],
"adaptive_run": {
"description": "the shipped default: search depth 4 when the board is open (more than 8 empty cells), rising to depth 7 when it is nearly full",
"games": 300,
"reach_1024_pct": 99,
"reach_2048_pct": 94,
"reach_4096_pct": 70.3,
"reach_8192_pct": 9,
"mean_score": 62529,
"median_score": 60644,
"ms_per_move": 1.844
},
"headline": {
"reach_2048_depth_1_or_2_pct": 0,
"reach_2048_depth_3_pct": 66.3,
"reach_2048_depth_5_pct": 97,
"adaptive_reach_2048_pct": 94,
"adaptive_reach_8192_pct": 9,
"cost_multiplier_depth_3_to_6": 83,
"summary": "Below a 3-ply lookahead the solver never reaches 2048. Depth 3 is the threshold (66%); quality climbs to 97% at depth 5. The shipped adaptive engine reaches 2048 in 94% of games (corroborated by a separate 250-game run at 92.8%), 4096 in 70%, and breaks 8192 in 9%, at 1.8 ms/move."
}
}
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