checkers stringclasses 5
values | 1 stringclasses 7
values | 2 stringclasses 7
values | 120 stringclasses 2
values | 96.3 stringlengths 2 9 | 2.5 stringlengths 1 8 | 546.2 stringlengths 2 5 | 151 stringlengths 2 6 |
|---|---|---|---|---|---|---|---|
checkers | 2 | 3 | 120 | 64.2 | 25 | 100.3 | 1297 |
checkers | 3 | 4 | 120 | 57.1 | 20.8 | 49.1 | 4031 |
checkers | 4 | 5 | 120 | 62.5 | 31.7 | 88 | 15645 |
checkers | 5 | 6 | 120 | 62.9 | 35.8 | 91 | 49528 |
checkers | 6 | 7 | 120 | 63.8 | 25.8 | 97.2 | 181183 |
chess | 1 | 2 | 120 | 86.7 | 23.3 | 320.7 | 15200 |
chess | 2 | 3 | 120 | 86.3 | 19.2 | 314.6 | 59662 |
chess | 3 | 4 | 120 | 78.8 | 29.2 | 225.1 | 307045 |
connect4 | 1 | 2 | 120 | 100 | 0 | 952.8 | 30 |
connect4 | 2 | 3 | 120 | 51.3 | 15.8 | 8.6 | 231 |
connect4 | 3 | 4 | 120 | 53.8 | 7.5 | 25.9 | 566 |
connect4 | 4 | 5 | 120 | 57.9 | 12.5 | 55 | 1296 |
connect4 | 5 | 6 | 120 | 51.3 | 9.2 | 8.6 | 2537 |
connect4 | 6 | 7 | 120 | 57.9 | 7.5 | 55 | 5747 |
game | from_depth | to_depth | games | score_pct | draw_pct | elo | ms |
othello | 1 | 2 | 120 | 97.5 | 0 | 610.4 | 629 |
othello | 2 | 3 | 120 | 71.7 | 3.3 | 159.7 | 4683 |
othello | 3 | 4 | 120 | 79.2 | 0 | 229.4 | 16609 |
othello | 4 | 5 | 120 | 73.3 | 0 | 174 | 73872 |
othello | 5 | 6 | 120 | 65 | 1.7 | 106.6 | 270455 |
Negamax Search-Depth Scaling — What Is One Ply of Search Worth?
Measured strength gain, in Elo per extra ply of search depth, for four
depth-limited negamax + alpha-beta board-game engines: Connect 4, Checkers,
Othello, and Chess. Strength is defined as a fixed search(state, {maxDepth: N})
depth — a deterministic, hardware-independent knob — so every number reproduces from a seed.
- Full write-up: https://lkforge.com/blog/search-depth-scaling/
- Playable engines: https://lkforge.com/games/connect4/ · /games/checkers/ · /games/othello/ · /games/chess/
- Producer: LK Forge — client-side AI games, solvers, and tools.
Headline numbers (120 games/step, seed 20260819)
The single biggest gain is almost always the first extra ply — depth-1 is a near-random blunderer:
| Game | 1 → 2 ply (Elo) | After the first ply |
|---|---|---|
| Connect 4 | +952.8 | collapses to near-noise (+9 to +55/ply, odd/even parity wobble) |
| Othello | +610.4 | bounces (no clean decay) |
| Checkers | +546.2 | plateaus around +90/ply |
| Chess | +320.7 | exception — 2→3 ply is nearly equal (+315); huge branching leaves plenty to discover even shallow |
Files
data/elo-per-ply.csv— one row per adjacent depth step:game, from_depth, to_depth, games, score_pct, draw_pct, elo, ms.
Method
- Strength = search depth. Deterministic search ⇒ hardware-independent, seed-reproducible results.
- Because the search is deterministic, games are diversified with random openings played with both colours (each opening played twice, sides swapped, so first-move advantage cancels). Draws score ½.
Elo per step = 400 · log10(p / (1 − p))from the colour-balanced scorep.
Reproduce
Byte-identical engine snapshots and the harness are published alongside the study:
node negamax-harness.mjs --game othello --openings 60 # full ladder for one game
node negamax-harness.mjs --game chess --pair 2 --openings 60 # a single depth step (3 -> 4)
Citation
LK Forge (2026). What Is One Ply of Search Worth? — Negamax Search-Depth Scaling. https://lkforge.com/blog/search-depth-scaling/
Everything runs client-side, no login, no tracking. Full method and interactive charts on the write-up above.
- Downloads last month
- 25