A small board can still have an enormous turn.

There is a delightful lie that small-board games tell programmers: the board is only eleven by eleven; surely we can just calculate it.

OverGrid politely disagrees. A turn is not a click on a square. It is a three-piece construction: each physical piece can rotate into several genuinely different cube shapes, each shape can sit at many origins and elevations, the combined construction must be legal, and its value depends on captures, height awards, black tiles, future access, and the opponent’s next public hand. The board is compact. The turn is not.

The first mistake would have been to search a convenient sliver

The first deterministic solver used a fixed construction budget. That is necessary for a responsive browser opponent, but it creates a quiet obligation: the prefix must be representative.

Our original 400-construction prefix was deterministic all right. It was also geometrically lopsided: it could spend its early attention on one transform of the U piece. A move that was legal and tactically obvious from another orientation might simply arrive after the budget ran out. That is not evaluation. It is a queueing accident wearing a lab coat.

The repaired opening traversal still stops at 400 candidates, but it deliberately spreads the sample across 19 U-piece origins and 12 orientations. That is not exhaustive search, and it does not claim to be optimal. It is a much better answer to the narrower question: did each kind of physical move get a chance to audition?

The first integrity rung

The earliest arena was intentionally tiny: one Standard-map seed, both seat orders, a 12-turn horizon, and a 400-construction budget. It produced four reproducible replay hashes and no invalid moves or failures. Every decision used exactly the declared 400 constructions—19,200 across the rung.

That is a good result, but only for what it measures. It establishes that the reducer, candidate generator, and arena can agree on legal, repeatable play. It does not establish that Ender is stronger than Bean, that seat two is advantaged, or that a horizon leader would win a complete game.

The distinction sounds fussy until one remembers how easy it is to optimize an accidental property of a search order. A solver can be deterministic and still be systematically myopic. Reproducibility tells us the same error will happen twice; it does not make the error wise.

Board sequenceRepresentative search must compare materially different footprints.

Follow the marked cells from position to reply to result.

Your territoryRival territoryObjectiveYour lineTheir reply

1. State 1Position

   Your captured home and soft frontier touch a broad neutral lane.

2. State 2Wasteful overlap

   Useful columns

   2

   Three columns sit over territory you already own; only two columns reach forward.

3. State 3One anchor, four forward

   Useful columns

   4

   One cube anchors the construction while the remaining footprint opens the lane.

A search budget is a contract

The eventual design principle was pleasantly unglamorous:

1. Generate a broad, legality-checked set of complete constructions.
2. Make the order representative across pieces, orientations, and regions.
3. Score only what fits inside the declared deterministic budget.
4. Keep the best completed legal move as the fallback.
5. Spend deeper reply work only when it has a specific job to do.

This is why “800 candidates” means something in the AI lab. It is not a mystic difficulty number. It is an auditable work limit: the same public state, profile, and seed receive the same candidate supply and the same decision. No wall-clock panic button gets to quietly choose a different move because someone opened another tab.

<details> <summary>Method note: what the early rung did and did not hold fixed</summary>

The phase 0–3 integrity configuration crossed both seat orders and used zero seeded variety. It did not cross maps, starters, homes, or enough gameplay seeds for comparative inference. All four games were intentionally censored at turn 12; their “leaders” are snapshots, not winners. The complete research record and later corrected measurement boundaries live in the AI Lab.

</details>

The candidate set is part of the policy

An evaluator cannot choose a move it never receives. This became one of the project’s most durable lessons: improving weights, adding a reply search, or inventing a personality cannot compensate for a candidate generator that fails to present the relevant geometry.

That is why the early work treated candidate coverage as an integrity property, not a performance trick. Later experiments can argue about height conversion, risk, denial, or closure. First the solver must be looking at the right family of moves.

The next question was therefore not “can we search everything?” It was much more useful: when two already-good constructions disagree, can a cheap, public, deterministic look at the opponent’s reply resolve the tie?

The player-facing orientation exercise is Rotate the whole hand, not just the piece you like.