Petra once left an obvious height capture on the board. The evaluator did not prefer a subtle positional sacrifice. The search had simply failed to offer the tactical construction inside its bounded candidate supply.

That incident reframed the compute question. An AI does not become stronger merely because its budget grows from 250 to 800. It becomes stronger when the extra work exposes meaningfully different legal plans—especially the plan a human can already see.

The live opponents use 250 complete legal constructions at a three-to-six-player table and 800 in a standard duel. Those numbers are deterministic work contracts, not difficulty labels. More importantly, neither is exhaustive: the candidate order decides which parts of a much larger legal space the evaluator is allowed to see.

Figure 1 · Work contract250 and 800 answer different table-size questions.Configured complete-construction budgets · not comparative strength data
3–6 players250

Keep a full round responsive as more players and intervening turns change the board before the AI returns.

Shared bounded census
Two-player duel800

Spend more attention where the same opponent replies immediately and a direct response can settle a close construction choice.

Shared bounded census

Both are deterministic limits over complete legal constructions. Neither is an exhaustive count, a difficulty score, or a win-rate promise.

First, a number is not a search tree

The unit matters. OverGrid does not budget a vague “move” or a raw orientation. It budgets a complete legal construction: all three dealt cube pieces, with their orientations, resting positions, support, connectivity, overlap, terrain, and scoring consequences checked together.

That is already a deliberately bounded view. On one reproducible Standard-duel opening—9 × 9 board, seed 101, hand U/W/T—the rules admit 330,437 distinct legal full-turn constructions. Eight hundred is not an exhaustive census of that position, and 250 is not one either. The point of the candidate order is to make the bounded sample representative enough that a consequential family of constructions has a fair chance to appear.

The scoring values change which candidate should win; they do not shrink the raw geometry. Height, captures, black-tile clearance, and routes make a fixed prefix more valuable—and more dangerous—because a conveniently ordered sample can hide the move that actually matters.

That was the original lesson of bounded search: a deterministic prefix that sees the wrong transforms is just a reproducible blind spot.

Same legal reality, different table cadence

At a six-player table, a bot that takes an expensive private tour through every imaginable construction does not get to preserve that imagined board. Five intervening turns will rewrite the frontier before it returns. The responsive question is: can this player receive a strong, repeatable legal choice without holding up the room?

At a duel, the opponent’s next turn is the immediate consequence of yours. That makes some near-ties worth inspecting more carefully. Eight hundred constructions give the selector a deeper representative menu before it decides whether one bounded public reply is useful. It does not grant the AI the opponent’s unrevealed hand, a future deal, a personality oracle, or a guess at the RNG cursor.

The same distinction applies to humans. A four-player plan needs resilience through several changing turns; a duel plan may justify a more precise question about the reply right in front of you.

Ender spends compute where the board makes it legible

Ender is the special case, but not the loophole. In a duel, it begins with the 800-construction unit and can select one to eight public-board ordering beams. Quiet states use less. A large deficit, tactical pressure, or decisive ending earns more.

Figure 2 · Ender in a duelMore work is a situational tool, not a permanent setting.Public-state adaptive plan · 800 constructions per beam

DevelopmentPublic reason: normal-development

4 × 800 = 3,200
The ordinary duel setting: more than a quick glance, less than a panic search.

The beams are alternate orderings of one legal candidate supply, not parallel games, hidden opponent models, or client-side solver threads.

These are not eight JavaScript workers racing in the browser. They are alternate public consequence orderings over the same legal candidate supply, deduplicated and evaluated in one deterministic policy. The client renders the result; it does not run the search.

The public triggers are deliberately boring: score margin, territory remaining, a final-round flag, and the observed size of the last opponent swing. That is a feature. The same board state, profile, and game seed should produce the same work budget and the same decision—not a different move because the player’s laptop was having a dramatic afternoon.

More candidate work has failed before

This is not a sermon against calculation. It is a warning against treating it as a coupon code for intelligence.

In an early six-game paired reply screen, a worst-case two-ply policy spent 2.83× the mean compute of one-ply and lost 405 score. The failure was conceptual: its selected “worst” opponent reply often harmed the opponent’s own position merely to be spiteful. More work amplified a bad model of the opponent.

Later, the targeted near-best reply check was cheaper and more promising: only constructions close to the shallow best were eligible. Its 30-game, 20-turn panel gained score and capture totals at 1.33× compute—but those games were horizon-capped, so that is directional evidence, not a win-rate claim. The longer probe produced too few natural endings to crown a champion.

Figure 3 · What the number does not buyA larger census can find more candidates; it cannot make an absent signal wise.Research constraint · supported by earlier bounded-search and reply-search screens
  1. GenerateRepresentative complete legal constructions
  2. MeasurePublic territory, height, capture, and route effects
  3. CompareUse a bounded reply only to resolve a close question
  4. VerifyReplay, cross homes/starters, then test fresh schedules

The early reply experiments showed why this matters: a 2.83× wider worst-case search lost score in a small paired screen. Extra calculation changed the wrong decision rule, not the game’s truth.

Responsive is a measured property

The budget contract makes three things auditable: candidate constructions, bounded reply checks, and deterministic work receipts. Wall-clock timing is still useful product telemetry, but it is not allowed to silently truncate an arm in an experiment or decide a different live move on a slower machine.

We do not yet have a held-out result saying 250 is globally optimal for multiplayer, that 800 is globally optimal for duels, or that Ender’s 6,400-construction decisive-endgame pass improves match-point win rate. Those are research questions. A credible answer needs exact paired schedules, crossed homes and starters, naturally resolved games, replay verification, and a compute comparison that counts every extra candidate and reply.

For now, the live claim is narrower and sturdier: OverGrid makes its compute visible, puts it behind public-state rules, and refuses to confuse a larger number with a smarter opponent.

The table-size strategy this suggests is developed separately in Fast expansion is not control.