Letting a long look-ahead overrule the search

The reference search sees four moves. This candidate looks twenty-five moves ahead with a much weaker player, and is allowed to overrule the search when the long view disagrees strongly enough.

It was tested on 32 paired games and it lost — not narrowly, and not only on score. It made the game's two survival flow rates worse, which is the one thing it could not afford to do.

The intuition

A four-move look-ahead is very good at not dying in the next four moves and completely blind to a board slowly filling up over the next thirty. The idea here is a division of labour: keep the strong short-range search as the default, and add a second opinion that trades accuracy for reach.

The second opinion works like this. Take each column you could legally play. Imagine seven possible futures — seven sequences of discs and hidden numbers. Play each column forward for twenty-five moves in each future, using a fast two-move search to make the intervening decisions. Now you have seven paired comparisons for every column against the column the reference chose. If a challenger wins consistently enough across all seven, take it; otherwise stay with the reference.

The seven futures are shared across all the columns, and each future is seeded from the visible board alone — never from the game's seed — so the comparison is between columns rather than between lucky and unlucky imagined futures.

How it works, step by step

1. Input. The visible board, the visible next disc, and the drops remaining before the next rise. The imagined futures are generated from a hash of the visible position, so nothing about the real game's randomness leaks in, and the score, level and move number are structurally unreachable by the continuation player.
2. Default. The unmodified reference: full-width, four-move fair expectimax with five chance samples. Its chosen column is the incumbent.
3. Routing. The long look-ahead only runs when the board is already tall — when some column holds four or more discs. In the recorded cohort that fired on 77.3% of decisions.
4. Challengers. Every other legal column. There is no shortlist and no width limit.
5. Continuation. For each column and each of the seven futures, play the column, then let a fresh two-move search play the next twenty-four moves. Add up the points; if the line dies, charge it the same large death penalty the reference uses; if it survives all twenty-five moves, add one leaf score for where it ended up.
6. The veto test. A challenger replaces the incumbent only if it passes all four conditions: it survives at least as many of the seven futures; it clears at least as many numbered discs on average; its paired advantage over the incumbent clears a confidence bound across the seven futures; and the reference search itself does not rate it worse than the incumbent by more than one row-rise bonus.
7. Output. A column — the best passing challenger, or the reference's own column if none passes.

What happened

It was rejected on every one of its five preregistered conditions. On 32 games played by both, the reference averaged 339,290 points and 98.66 moves; the candidate averaged 292,780 points and 86.34 moves. Game by game it lost 19, won 9 and tied 4, and the confidence bound on the difference sat around −92,000 — comfortably on the wrong side of zero.

The rule genuinely fired: 68 vetoes across 2,137 opportunities, so this is not a policy that quietly did nothing. Three games drew no vetoes at all, and in all three the two arms produced exactly identical games, which is a free check that the fallback works. Attributing the whole cohort's loss to the vetoes that caused it gives an average of about −21,900 points per veto taken — and individual vetoes were near coin flips with a strongly negative mean, one game gaining nearly 300,000 and another losing over 440,000.

The decisive part is not the score. It is that the candidate cleared fewer discs and revealed fewer gray discs per move than the policy it was trying to improve. For a long look-ahead to buy survival it has to buy flow, and this one sold it — despite one of the four veto conditions being an explicit demand for more clears. The estimate of a column's clear advantage, measured twenty-five moves deep under a two-move continuation, did not transfer to a game that was actually going to be played by the four-move search. The rollout was measuring a different policy's future.

The technical record

Source: finding-03-rollout-veto-17k. Run validity valid; scientific outcome fail; evidence tier development (SCREEN, 32 paired whole games); provenance reproduced, executed in this checkout. Seed lease SEEDLEASE-A51D-VETO, cohort 0xa51e0000–0xa51e001f, 600-move declared cap, 8 threads. 0 runner failures, 0 illegal moves, 0 score-identity violations, 0 censored games in either arm.

Gate frozen in PREREGISTRATION.md before any cohort seed was read.

Arm	Mean	Median	Min / max	Mean moves	Clears/move	Reveals/move
fair depth-4 (comparator)	339,290	257,270	120,279 / 725,934	98.66	2.0200	1.1308
rollout veto (candidate)	292,780	250,794	120,286 / 799,183	86.34	1.9515	1.0749

Statistic	Score	Moves
Paired mean delta	−46,510.5	−12.31
Paired median delta	−9,264.0	−2.00
One-sided 95% bootstrap lower bound (20,000 resamples)	−91,924.6	−24.34
Wins–ties–losses	9–4–19	7–9–16
Paired delta standard deviation	159,175	—

An exact one-sided sign test on the 28 non-tied games gives p = 0.0436. All five preregistered conditions failed: positive mean score delta, positive bootstrap lower bound, positive mean move delta, at least 20 score wins of 32, and flow rates not below the reference's.

Mechanism counters: 2,763 decisions, 2,137 routed, 12,314 alternatives scored, 103 passing all four conditions, 68 vetoes taken. The binding condition is the confidence test on the paired return, which rejected 12,203 of 12,314 alternatives (99.1%) — because a single imagined future in which one column dies and another does not moves the difference by the whole million-point death penalty, so the spread across seven futures is enormous relative to the mean. A diagnostic on one probe game puts the number of futures the estimator would actually need at roughly 16 to 51, against the 7 in use.

An ablation ran the whole cohort again with the pre-correction band of 7,000 points instead of 17,000 on the fourth condition. It tripled rejections on that condition (720 to 2,266) and changed the number of vetoes actually taken by one (68 to 67); 29 of 32 games were identical between the two bands, and both bands failed all five conditions. The audit's specified repair was applied, measured, and did not rescue the mechanism.

Runtime, and why the original was shelved for the wrong reason. The historical version was paused on a projected 15,341 seconds against a 2,700-second ceiling. Measured here, the long look-ahead adds about 1.92 times to total decision CPU and 1.61 times to arm wall time — a factor of two, not a factor of six. The runtime gate was never the real obstacle. These timings were taken on a heavily contended machine (other jobs held 20 to 70 of 32 logical CPUs throughout); the absolute seconds are upper bounds and are not benchmark-grade, and only the ratios transfer.

Correctness. The port is proven byte-identical to the frozen historical source at the rollout level: a canonical digest of per-column mean return, surviving futures, mean clears, legal-action count, transitions, calls, work and nodes over 10 public states matched over 80 digest lines. That gate caught a real transcription error on its first run. Self-tests cover corrected scoring, repeat determinism, horizontal-reflection equivalence, blindness to score, level and move index, legality, and seed-lease containment. No cross-engine TypeScript parity sweep was run for this candidate, which is a weaker claim than full engine parity.

Other limitations as recorded. n = 32, with a paired delta standard deviation of 159,175 — enough to decline promotion, not enough to quantify how much worse the mechanism is. One machine, one compiler. The cohort and probe seeds are now permanently development data; no protected or final seed was touched.

What this taught us, and what is still open

Ruled out: this exact configuration — twenty-five moves, seven futures, danger threshold of four discs, a two-move continuation, the confidence test as written, every legal column as a challenger, at both settings of the fourth condition, on 32 fresh paired games.

Not ruled out: the family. A valid negative rejects a configuration, not an idea. Two live alternatives survive it. The first is simply that seven imagined futures is too few to decide anything — the estimator is under-sampled by something like two to seven times, and cost grows linearly in the number of futures, so the cheapest honest next test is more futures over a shorter horizon, preregistered as a new configuration rather than as a repair of this one. The second is harder: even the vetoes that were accepted made realized flow worse, which under-sampling alone does not explain. A continuation player that is much weaker than the policy that will really be playing may simply be answering the wrong question.

The wider lesson is about single spectacular games. This cohort contains a +299,746 game and a −446,294 game side by side. That is what a one-game result from this policy looks like, and it is why the repository counts means over paired whole games, not best games.