Constructive planning

The idea

A move can score nothing today and set up a lot three moves from now. A planner that asks only "which column scores the most right now?" never makes that move, because building scores zero on the turn it happens. Constructive planning asks a different question: what should the board look like a few moves from now, and which column heads there?

In Drop7 the thing to build is a reservoir: a stack of high-numbered discs that cannot clear yet, arranged so that one later event sets all of them off at once. The event these planners aim for is the rise, the row of gray discs pushed in under the board every fifth drop. The rise usually threatens the player, because it takes a row away. Here it is the trigger.

A small example

Dominoes on a table. Each turn you either stand one domino at the end of a line, which pays nothing, or tip the line yourself, which pays one point per domino that falls and leaves the table empty. Every sixth turn the table gets bumped: the whole line falls, and you are paid for it as if you had tipped it.

A player who judges each turn by what it pays sees a zero for standing a domino and a one for tipping a single domino, so they stand, tip, stand, tip. Over six turns that earns three points. A player who plans for the bump stands five dominoes in a row, takes five zeros, and collects five points when the table shakes on turn six.

Two things about the toy carry over to Drop7. The payoff needs the line intact when the bump arrives: if something knocks it over on turn three, five turns of patience bought nothing. And the bump is on a public schedule, so the plan can be timed to it. The rise is the same kind of event, and the number of drops left before it is one of the four things a policy is allowed to see.

How it works

The planners on this site differ in detail but share a shape, which the family page gives in four steps.

1. Name a target. Write down what a good board looks like a cycle from now. The constructive spectrum planner's target has four parts: a spread of column heights, covered discs still reachable at the edges, safe caps on top of each column, and stored high discs whose trigger conditions overlap.
2. Look further than one move. Simulate to the end of the current five-drop cycle, and often through the next one, over sampled futures rather than a complete tree.
3. Score the end of the plan by the target, in score-like units so the rise bonuses inside the horizon still count, and ignore the points collected on the way.
4. Keep a tactical guard. A conventional search supplies the shortlist of columns the planner may choose between, or refuses structural moves when the board is close to dying.

The same instinct has been tried without simulation: the vertical reservoir policy names the shape of a good stack in hand-written features, and the vertical ladder term adds a stored-energy bonus to the reference search's leaf. Two labs make the plan itself the unit of choice: cycle abstraction picks one of five intentions for a whole cycle, and rise-option QD builds the machinery for an option, a plan held across a cycle instead of re-decided every move.

In Drop7

Here is the mechanism on a real board. A disc clears when the unbroken line through it is exactly its own number, and gray discs count toward that line. Four 6s stacked on a gray row make a run of five, so the fourth drop scores nothing. Then the rise pushes a new gray row in underneath, the run becomes six, and all four clear at once.

The engine records 28 chain points for that clear, on top of the 17,000-point rise bonus (family page).

Planning the cycle forward worked against a weak comparator. On 32 paired games, the constructive spectrum planner averaged 266,695.5 points against 157,198.1 for the one-move-ahead fair search, and won 25 of the 32 (constructive spectrum, ledger-recorded). Reading the structure off a still board did not. On its 128-game tournament the vertical reservoir policy averaged 160,498.1 points against the same comparator's 178,554.4 (vertical reservoir, ledger-recorded); the viability controller lost its 32-game screen too.

Attaching the planner to the four-move reference search made things worse. Used only as a tie-break between that search's top two near-equal columns, it averaged 283,286 points against exact depth-4's 372,870.5 on four fitting games, a quartet and not a cohort (constructive spectrum). On 32 fitting games a twelve-move continuation beat a seven-move one, and seventeen was much worse than both. Cycle abstraction is task-record only, and rise-option QD has never played a game.

What it cannot do

It cannot tell a promising structure from a still image. The two policies that read structure off the visible board lost to a one-move-ahead search, and the research status records why: boards that look alike can have very different futures depending on how their triggers and covered discs evolve across the rises.

It cannot override a deeper search on close calls. Each time the planner's signal was injected into the depth-4 reference as an override, it switched on unstable comparisons between near-equal columns and lost ground. The ledger keeps the idea alive as a feature or an option inside a larger policy, and its look-ahead is a sampled continuation that does not get more trustworthy by running longer.

Every comparison here is a screen against the one-move-ahead search, a much weaker comparator than the depth-4 reference, and nothing from this technique has been measured on a protected or final cohort. The open question the family leaves is whether comparing sibling columns across more than one cycle can be made affordable and stable enough to test properly.