Blending the learned value with the hand-written one

Mix the learned board value with the hand-written heuristic, and see whether the combination beats either alone.

The intuition

Two evaluators were available at this point: a learned n-tuple value trained from half a million games, and a hand-written "phase horizon" heuristic that reasoned about the rise clock directly. They disagree about positions, and they disagree for different reasons — one from data, one from a human's model of the game. The standard move is to add them: value = heuristic + c × learned, and tune the single number c.

If the two evaluators make uncorrelated mistakes, the blend should be steadier than either. This experiment tested that in the cleanest possible way: one coefficient, chosen on one set of games, then frozen and measured on a different set.

How it works, step by step

1. Load the trained native n-tuple checkpoint into the TypeScript engine.
2. Calibrate the two evaluators onto a common scale, because a learned sum of weights and a hand-written score are not in the same units.
3. Try four blend coefficients — 0 (heuristic only), 0.25, 0.5, and 1 (learned only) — on a small set of tuning games.
4. Freeze the winning coefficient.
5. Play the frozen policy on a separate fixed 64-game development probe, with a depth-2 expectimax and three chance samples.

What happened, in plain English

The tuning games preferred pure learned value — the more of the learned evaluator in the mix, the better the tuning score, right up to using it alone. So the "blend" that won the tuning stage was not a blend at all.

Worse, when that frozen choice was played on the fixed probe it scored about 217,000 points a game, below the roughly 232,000 the native learned-value search had already recorded on the same probe. Running the same idea through a different implementation lost ground, and mixing in the heuristic never helped at any coefficient. It was recorded as a rejected theory.

The technical record

Status in the experiment index: rejected, ledger-recorded — "the frozen blend trailed learned-value search alone."

From the ledger: tuning means for learned-value coefficients 0, 0.25, 0.5, and 1 were 173,413.5, 186,019.75, 187,391.375, and 190,087.25 respectively, on the 0x5d70... tuning games. Coefficient 1 won and reached 217,332.672 on the fixed 0x4d70... 64-game probe, below the native n-tuple-only depth-2 result of 232,107.156 on the same probe.

Configuration: 8 training games, 24 scale-calibration games, 64 probe games, depth 2, three chance samples, 100,000 work units, 500-move cap.

Limitations. The tuning cohort is very small, the probe range was already burned, and the ledger records only the four coefficient means — no per-game data, dispersion, or paired bounds. The ledger does not state which level bonus these figures use.

Source: main.ts.

What this taught us, and what is still open

The experiment rules out this specific linear blend of these two specific evaluators at these four coefficients. It does not rule out combining a learned and a hand-written signal in general — later approaches in the repository kept trying, usually by letting a learned scalar break ties rather than by adding it into the value.

The more useful observation is procedural: the tuning set picked a coefficient that then underperformed on held-out games. With eight tuning games that is exactly what one should expect, and it is a small illustration of why the repository's benchmark ladder insists on separate cohorts for choosing and for confirming.