Gray throughput

Stop trying to score and start trying to keep up — clear numbered discs and open covered ones fast enough that the board never fills.

The intuition

There is a piece of arithmetic in this game that has nothing to do with strategy. A board has 49 cells. Every five drops, five numbered discs land on it and a rise pushes in a row of seven covered discs. Twelve discs arrive per cycle, so a board that is not slowly filling up must remove twelve per cycle too:

and every one of those seven covered arrivals has to be opened before it can be cleared at all:

This policy is that arithmetic turned into an objective. It does not ask "how many points is this move worth"; it asks "does this move keep me at, or above, the replacement rate" — and it pays a surplus bonus for clearing or revealing more than the requirement, not merely for clearing or revealing.

How it works, step by step

1. Read the position — board, next disc, rise clock.
2. Simulate each legal column over a few stratified guesses about what the hidden gray numbers would show, then continue for a short horizon.
3. Score the resulting board with thirteen state features: occupancy, total covers, solid and cracked counts, how much cover load sits high, load above the safe band, peak and mean height excess, pressure from the coming rise, low-number caps and adjacent low caps, and two topology terms for whether covers are exposed and numbers are still live.
4. Score the move with seven transition features, dominated by the two surplus terms — clears above 2.4 per move and reveals above 1.4 per move.
5. Blend the immediate value with the continuation value and play the best column.

The companion tune.ts fits the twenty weights with a cross-entropy method on complete games from a training seed range, then replays the frozen champion on a separate calibration range.

What happened, in plain English

Pushing harder on gray discs made the board look better and did not make the policy live longer. The retained sentence is that stronger gray weights improved exposure — how much of the covered population was attackable — but not the sustainable rate of cracks and reveals, and not the score.

That is a more interesting failure than it first appears. It says the deficit is not caused by the policy failing to value reveals highly enough. Wanting reveals more does not produce more of them.

What this taught us, and what is still open

• Naming the right objective is not the same as reaching it. This lab encoded the correct conservation law and still could not satisfy it. The later exploratory work reached the same wall from the other side: no legal policy tested has achieved flow balance (finding 06, which carries two published correction notices and should be read with them).
• Exposure is a decoupled measurement. Making covers attackable and actually converting them into reveals came apart here. Any successor should report both, because improving the first is easy.
• What was ruled out is this weight family, tuned this way. The conservation objective itself is now the organizing idea of a separate research line, lifetime objective.