Lifetime objective

Judge a move by how much longer the game will still last, rather than by how many points it scores right now.

That sounds like a slogan until you count the points. When this repository instrumented 64 games of its strongest policy and attributed every single point to its source, 94.3% of the score was the flat 17,000-point bonus for surviving another row rise, 5.7% was chain reactions, and 0.0% was the 70,000-point bonus for emptying the board, which never happened once. Final score and moves survived correlated at r = 0.9995 (finding-01, a development-tier exploratory finding; the same run is written up on the score decomposition page).

So a Drop7 Hardcore score is survival time wearing a different unit, and the million-point target is really a survival target. Points arrive at a measured 3,423 per move, and the same finding puts the lifetime a one-million-point average needs at about 294 moves. The reference policy's games last 94.

The picture: twelve discs arrive every five moves

Here is why the game ends. Both boards below are the repository's own rules engine, playing a real game; nothing is drawn by hand.

Every five moves, five placed discs plus seven risen gray discs — twelve discs — enter a board that only has 49 cells. Nothing else adds material, and the only way material leaves is a numbered disc clearing. The arithmetic is therefore exact and unforgiving: a policy survives indefinitely only if it sustains

• 2.400 numbered clears per move (12 ÷ 5), and
• 1.400 gray discs revealed per move (7 ÷ 5).

The reference policy sustains 1.973 and 1.090: a structural deficit of about 18% and 22%. Its board fills up, and then it dies. That deficit, not a shortage of spectacular chain reactions, is what ends its games (finding-01).

What every approach in this family does

1. Take a policy: the reference depth-4 search, a hand-written rule, a planner, or a candidate with something learned bolted into it.
2. Play whole games with it, paired against a comparator on the same random seeds, so the two policies face identical luck.
3. Report three numbers besides the score: numbered clears per move, gray discs revealed per move, and the occupancy slope: how many of the 49 cells the board gains per five-move cycle. The slope is just the conservation law integrated: a board drifts by 12 − 5 × clears-per-move cells per cycle, so a positive slope is a policy that is losing, however good its tactics look on any single move.
4. Ask whether the mechanism moved, not just the mean. A score gain with no movement in the flow rates is treated here as unexplained rather than real.

That last rule is what makes this family a family. Score in this game is heavy tailed: one lucky game can swamp 63 ordinary ones, while a flow rate is averaged over every move of every game and is far better determined. Several of the results below were decided on the flow rates when the score deltas could not be separated from zero.

What happened

Three things, and none of them is the one the family was hoping for.

The target is physically reachable. A planner that is allowed to cheat — it reads the hidden numbers under the gray discs and plans exactly against a fixed future — holds the required clear rate for 6,000 consecutive moves and never dies. That settles a real question: Drop7 Hardcore is a control problem with a solution, not an arithmetic impossibility. It is also, emphatically, not a policy; see the flow ceiling page, where the cheating is labelled on every number.

No legal policy tried here got near it. A planner with the same objective and the same look-ahead but no access to the hidden numbers closes only a small part of the gap, and the part it cannot close grows exactly as the board fills up and there is more hidden information to be ignorant of. Every one of those games ended.

Small, bounded corrections to the reference search worked better than replacing it. The two positive results in this family are both of that shape: a better handling of the game's randomness (reveal sampling) and a learned survival estimate mixed into the reference search's board-scoring function at half weight (learned leaf). Both are worth tens of thousands of points on 64 paired games. Neither is worth hundreds of thousands, and the target needs hundreds of thousands.

Every approach in the family

The measurements that started it

• Score decomposition — counts where each point came from, and finds that a score is a stopwatch.
• Flow ceiling — asks whether any line of play can sustain the required clear rate, using a clairvoyant planner that reads the hidden board. Answer: yes, but only that planner did.
• Suite validation — tests whether a cheap 128-position benchmark predicts whole-game strength, and finds that at the horizon it was minted with, it does not.

Bounded changes to the reference search

• Reveal sampling — the search had one dial governing two different coin flips; separating them is worth about as much as a whole extra move of look-ahead.
• Risk calibration — turns the reference search's baked-in constants into dials that can be swept.
• Leaf reweight — makes the nineteen weights in the hand-written board-scoring function runtime data, so refitted weight vectors can be tested.
• Rollout veto — looks twenty-five moves ahead with a weak player and overrules the search only on a clear disagreement.

Learning something

• Sibling corpus — the training-data generator: every public position a game visited, labelled with how many moves that game still had left.
• Afterstate net — the survival network trained on that corpus.
• Learned leaf — blends a learned survival estimate into the reference search's board scorer, and measures what a network at that position is actually allowed to cost.
• Planner distillation — tries to compress the expensive legal planner into a small network, with every legal move at every position labelled.

Machinery the rest of the family runs on

• Scenario engine: a rules simulator in which every hidden number and every future disc is fixed in advance, which is what makes a clairvoyant optimum well posed at all.
• Fast engine: the same rules about three times faster, proven to make byte-identical decisions.
• Common: the shared harness that runs a cohort, enforces seed leases and writes the result artifacts.
• GPU: the environment and benchmarks for the machine's integrated GPU, including two host defects that had to be worked around.

What this taught us, and what is still open

• The objective is now a number, not a slogan. "Play better" became "hold 2.400 clears and 1.400 reveals per move, at around 20 occupied cells". That is a far more testable target than a score.
• Flow rates are the cheap early statistic. They move before the score does and they are averaged over thousands of moves instead of dozens of games.
• Chain building is real and is not the lever. A cheating planner told to maximise points instead of survival earned 1.75 times the points per move — and died in less than half the time, ending with a lower mean score (finding-06).
• Still open: nothing legal has been shown to hold flow balance. The measurements say the missing ingredient is reasoning about what is under the gray discs, rather than averaging over guesses of it, and no candidate in this family does that yet.

For the wider picture see the research status, and for the ideas these pages assume, the concepts primer and the glossary.