Tie-breaking

Every policy in this repository ends up with two columns it likes exactly equally. The rule it uses to pick between them is arbitrary — and this program measures whether "arbitrary" is harmless.

The intuition

Here is a position that is symmetric down the middle. A 3 is coming, and columns 1 and 5 are mirror images of each other:

Dropping the same 3 into column 5 does the identical thing on the other side — the same two discs cleared, the same 14 points, the same single crack — and leaves the exact mirror image of the board above:

3

Real ties are rarer than mirror images, but near-ties are everywhere: two moves whose scores differ by less than the noise in the evaluation. Whichever column the loop reaches first wins them all, so a fixed order like "left to right" is a silent, permanent bias in the policy. If that bias is worth a few percent of score, then a comparison between two candidates that use different orders is partly measuring the order.

How it works

1. Play complete games with a simple one-move-ahead policy: for each legal column, play the move a few times with different imagined reveals, average the immediate points plus a hand-written board score, and keep the best.
2. The comparison is strict — a later column has to be better, not equal, to displace an earlier one — so the order in which columns are visited decides every exact tie.
3. Run the whole thing four times, changing only that order: left-to-right, centre-outwards, edges-first, and a paired order.
4. Then, as a second family, run three deterministic rules that use no evaluation at all: always play the lowest legal column; prefer a column whose new height would equal the disc's number (a guaranteed vertical clear); or prefer the column already holding the most copies of that number. Each falls back to the lowest column, centre-first.
5. Report mean score, mean moves and best score for each of the seven variants over the same games.

Everything it reads is public. It is not a candidate policy: the point is the spread between the variants, not the level any of them reaches.

What happened

No retained result. The experiment index lists this source as support-only and repository-verified, and audit 04 §B.2 lists it among the sources whose question has no lane and no retained output. Nothing in this repository records how large the tie-breaking effect is.

What can be said without a run: the fixed order matters enough that the repository standardised on one. The native search policies use the centre-first order 3, 2, 4, 1, 5, 0, 6, and the fair depth-4 audit (audit 02) refers to positions that "fall through to kColumnOrder tie-breaking" as a normal, frequent event rather than an edge case.

The technical record

Status: support-only — repository-verified. No ledger entry, no task record, no retained output.

Defaults in main.ts: 64 games from seed 0x1d700500, four imagined reveals per candidate column, a 1,000-move cap. Orders tested: left = 0…6, center = 3,2,4,1,5,0,6, edge = 0,6,1,5,2,4,3, paired = 0,1,6,5,2,3,4. Rule policies: shortest, vertical, grouped. The evaluator is evaluateHeuristic(..., "combined") from src/core/typescript/heuristic.ts, and the tie is resolved by the strict value > bestValue comparison, i.e. first-in-order wins.

Reading the output correctly: these are seven variants of a weak one-move policy, so their absolute scores say nothing about the strength of any research candidate. Only the difference between the seven rows is the measurement, and 64 games is a small cohort for a heavy-tailed score.

Source: main.ts.

What this taught us, and what is still open

• A fixed column order is a real degree of freedom in every policy here, not a formality, and near-ties are common enough for it to have an effect.
• Nobody has recorded how big that effect is. This is one of the cheapest unanswered questions in the repository: seven complete-game arms on a documented seed range, no training, no model.
• The result that would matter most is not on the weak policy above but on the depth-4 reference: if changing only its tie order moves its mean by an amount comparable to the differences experiments are gated on, then some past gate decisions were partly measuring column order.