Depth-4 search and long outcomes

The strongest dependable policy here looks four of your own moves ahead. These experiments ask what a move looks like when you keep playing for twenty-five — five complete rise cycles — and whether anything useful can be brought back from that far out.

Everything in this family is a legal public-information policy or an offline study of one. There is no privileged information anywhere on these pages; for that, see oracle and curriculum research.

What "four moves" misses

A rise happens every five drops. A four-move search therefore usually does not see even one full cycle, and it never sees what its choice does to the next one. Structures in this game are built and released over several cycles: a column stacked to prepare a long run, a covered disc kept reachable, a low number left where the rise will make it useful. Those pay off well outside a four-move window, and a shallow search values them at whatever its leaf evaluator happens to say.

The two things you can do with a longer look

Use it directly. Keep depth-4 search as the default, and only when the board is dangerous, replay every legal column forward for 25 moves under seven shared imagined futures. If some alternative is clearly better across all seven, take it; otherwise keep depth 4. That is the rollout veto.

Learn it. A 25-move replay of every column at every position is far too slow to play with, so train a model on those replays and use the model instead. That is the long-outcome family, the sibling network on the 200-move panel, and — as a sanity check on whether the learning machinery works at all — compressing depth-4 search itself.

Every one of these keeps exact depth-4 search as the fallback, so a failure costs nothing but time.

What happened, in plain English

The long look does contain information the shallow search cannot see. The learned models predict survival over a 100-move horizon strikingly well. But predicting survival is not choosing a column, and every attempt to convert the long-outcome signal into a ranking of the seven available moves ranked them worse than a plain, much cheaper exact search — the sibling trap in its purest form.

The direct version has a more dramatic history. One single game — one — scored 404,047 points and lasted 250 moves where depth 4 scored 159,616 in 105. That number was shelved for being far too slow rather than for being wrong, and it sat in the repository for a long time as the most tempting unexploited result in it. It has since been retested properly, at corrected scoring, on 32 paired games. It does not reproduce; on that cohort the veto is significantly worse than plain depth 4, and it degrades exactly the clear and reveal rates that would have had to improve for it to work.

The record behind those sentences

• Single pilot, ledger-recorded, one game: seed 0x3ded0000, stock fair depth 4 scored 159,616 in 105 moves; the veto scored 404,047 in 250 moves. Recorded at the time as "only one pair, not statistical evidence", and paused for missing its runtime ceiling by a wide margin (projected 15,340.599 seconds against a 2,700-second limit).
• finding-03 reports the corrected-scoring retest, reproduced in this checkout: 32 paired games, run validity valid, scientific outcome fail, evidence tier development. Fair depth 4 averaged 339,290 points / 98.66 moves; the veto averaged 292,780 / 86.34. Paired mean delta −46,510.5 points, one-sided 95% bootstrap lower bound −91,924.6, wins–ties–losses 9–4–19. Clears per move fell 2.0200 to 1.9515 and reveals per move 1.1308 to 1.0749.
• Learned long-outcome rankers: the auxiliary survival head reaches Pearson correlation around 0.85 on held-out data while top-move accuracy falls below exact depth-2 search — 27.79% for exact depth 2 against 25.99% and 23.94% for the two learned capacities (ledger-recorded; this comparison predates the scoring correction and uses the historical 7,000-point level bonus).
• The reference figure every candidate is measured against: fair depth 4, 308,295.578 points over 90.031 moves on the recorded 64-game cohort (status, detailed ledger).

What this taught us, and what is still open

• A single spectacular game is not evidence. Scores here are heavy-tailed; finding-03 found a +299,746 game and a −446,294 game side by side inside one 32-game cohort. That is what a one-game result from this policy actually looks like.
• Rejecting a configuration is not rejecting the family. The retest ruled out one exact configuration — horizon 25, seven futures, danger height 4, a depth-2 continuation — at both of the two value bands that were argued about. It did not rule out a longer look done differently, and it identified the single most likely defect: the return estimate is under-sampled by roughly two to seven times at seven futures.
• The continuation policy matters as much as the horizon. A move chosen because it looks good under 25 moves of depth-2 play is then executed in a game that will be played by depth-4. The estimator was measuring a different policy's future.
• Still open: a cheaper exact veto that preserves the original intervention decisions (experiment index, "what remains genuinely open"), and a scenario count high enough for the return test to mean what it claims.