Ending a game is a rule, not a shortcut

An arena can make a policy look wonderfully decisive by declaring the game over just before its opponent gets the chance to be decisive back.

That is not a hypothetical failure mode. We built two plausible ways to stop late capture carousels; one was too eager, the other too timid. Both were rejected.

The tempting rule

Late games can look ridiculous in a log. Most ordinary territory is owned, the same frontier changes hands, and the turn count keeps clicking upward. We wanted the engine to recognize a sustained transfer war and adjudicate it rather than burn a fixed horizon.

The first version had a very human appeal: when occupancy was high and three rounds were transfer-heavy, call it. It worked magnificently on the narrow operational metric. In 192 exact v4-to-v5 pairs, turn caps fell from 77 to 6.

That is the kind of chart that makes an engineer reach for the green marker. Then we asked the question that decided whether the rule was acceptable: what would the original game have done?

What the v4 continuation did	What v5 did instead	Games
Natural completion	Preserved the natural finish	75
Natural completion	Adjudicated early	40
Turn cap	Adjudicated	71
Turn cap	Still capped	6

The rule was not finding already-settled games. It preempted 34.8% of the natural finishes in this paired panel.

A faster ending can change the winner

The first rule’s apparent leader agreed with the fully observed continuation only 76.6% of the time. Among the 40 games that would naturally have finished, the eventual winner agreement was 70.0%. Its worst policy slice was 59.1%.

Those are not confidence intervals around a small positive effect. They are a red light.

[DISCARDED] The three-round transfer-war rule. It solved caps by taking over games that were still strategically alive.

The useful diagnosis was subtler than “recaptures are bad.” The adjudicated boards averaged 95.1% occupancy with only 3.5 ordinary tiles remaining, and 78.0% of transfers revisited a cell. High occupancy was necessary for this sort of rule—but plainly not sufficient. A three-round fight over the last few cells can still contain a real tactical reversal.

Then we overcorrected

Version six required a much more conservative six-round signal. It was safe in the way a locked emergency exit is safe.

It preserved all 115 natural v4 finishes in the same 192-game calibration, and all five of its adjudications matched the eventual v4 leader. But it resolved only 5 of 77 prior caps. 72 games, or 37.5% of the panel, still hit the horizon.

[DISCARDED] The six-round transfer-war rule. It fixed the false-positive problem by barely intervening at all.

The right research conclusion was not “choose v5” or “choose v6.” It was that an engine finish condition must be treated as game rules research, with its own continuation oracle and fairness gates—not slipped into an AI benchmark as a harmless performance optimization.

Board sequenceAn ending rule must preserve every owed reply.

Follow the marked cells from position to reply to result.

Your territoryRival territoryObjectiveYour lineTheir reply

1. State 1Trigger now

   Owed replies

   R → G → Y

   Score at trigger

   Blue +10

   Blue takes the final neutral while red, green, and yellow are still owed turns.

2. State 2Replies reverse the lead

   Projected finish

   Blue −15

   The trigger score looked safe, but three scoring replies leave blue behind.

3. State 3Trigger later

   Owed replies

   R only

   Projected finish

   Blue +20

   After the round advances, an equivalent finish leaves only one rival reply.

4. State 4But waiting has a price

   Guardrail

   secure access first

   Delay only when the route stays yours; otherwise a rival may trigger first or strand the cell.

Endings are part of fairness

The calibration made a durable protocol rule: report territory completion, flip-war adjudication, turn caps, and failures separately. A cap is right-censored, not a loss. A horizon leader is an observation, not a winner. And an adjudication cannot be allowed to occur at a boundary that gives one player fewer owed turns than another.

This is a slightly less romantic takeaway than “our AI found a new tactic.” It is also more valuable. Before we can ask whether a policy closes games well, the engine has to know what a fair closure is.

The player-facing endgame routine now lives separately in Close the board, not just the score.

<details> <summary>Methods and limits</summary>

The phase-27 and phase-29 panels each used 192 exact paired/triad continuations. Schedule, provenance, seeded choices, checkpoint prefixes, replay, scoring, and termination evidence all passed with zero mismatches. Version four served as the continuation reference for this historical calibration. It is not a proof that any currently shipped rule is ideal, and it does not estimate a named AI’s win rate.

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