Perfect-information oracle

A planner that is handed the entire future of a game — every disc that will arrive and every hidden gray number — before it plays, so we can measure how long a game could last if uncertainty were removed.

Its own source file says it in capitals: upper-bound diagnostic only. It is not a policy, it cannot be entered in any comparison with a real policy, and it is not even a proof of the best possible cheating play, because it prunes.

Why anyone would build this

Before spending months teaching a program to play well, it is worth knowing whether the target is reachable at all. The qualification standard is a mean above one million points, and the strongest legal search averages roughly a third of that. Two very different worlds are consistent with that gap:

• the simulator simply does not permit long games, and a million-point average is arithmetically out of reach; or
• long games exist and are common enough, and the difficulty is entirely one of choosing well under uncertainty.

Removing uncertainty separates the two. If a planner that knows everything still cannot survive, the objective is impossible. If it survives easily, then every point of the gap is attributable to not knowing — which is the problem the rest of the repository works on.

How it works, step by step

1. Start a game from a seed. The harness knows the game's future disc stream and the reveal stream that turns gray discs into numbers.
2. At each move, plan by beam search over that known future: expand every legal column, apply the actual next disc and the actual reveals rather than averaging over what might happen, keep the best few thousand resulting positions, and repeat for a fixed number of plies. The file's defaults are depth 12 and beam width 512, with a 500-move cap; the runs used in later experiments configure it down to depth 4 and beam 128.
3. Rank the surviving plans by the score they accumulate, and play the first column of the best one.
4. Advance one real move and re-plan. Dying is charged an enormous penalty, so the planner is effectively told to survive first and score second.

Because chance has been replaced by fact, there are no chance nodes here at all — the whole thing is a plain search over a known sequence. That is exactly what makes it illegal: a real player choosing between seven columns does not know which of them the next four discs will reward.

What happened, in plain English

It survives, comfortably. In a twelve-game cohort it reached the 500-move cap in every single game and averaged over a million points, while public depth-3 search on the same games averaged about 133,000 and lived about 90 moves. In a separate sixteen-game matched audit at a much smaller beam it still hit the 200-move cap in all sixteen and won every paired game.

So the answer to the question the oracle was built to ask is: long games exist. What it did not, and cannot, show is that any of that is available to a player who must guess. The family page collects the several attempts to transfer it, all of which failed.

Three limitations belong in the same breath as the numbers. The cohorts were censored at a move cap, so those means are lower bounds on the oracle's own play and not comparable with uncensored games. They were scored with the historical 7,000-point level bonus, which the ledger preserves as Sequence- scored evidence and not as evidence for the Hardcore target. And the beam prunes, so this is a reachable ceiling, not the true perfect-information optimum.

The technical record

Cohort	Configuration	Result	Evidence
Seed 0x3d700000, one game	receding beam over the realized tape	2,079,579 points, stopped by the 500-move cap	ledger-recorded
0x3d950000...0b, 12 training-only games	depth 4 / beam 128, 500-move cap	capped in all 12; mean 1,058,931.5 under the historical 7,000-point level bonus; paired public depth 3 averaged 132,979 points / 90.5 moves	ledger-recorded
0x3d70f000...0f, 16 games	depth 4 / beam 128, 200-move cap, matched against public depth 3	oracle 429,182.5 points, capped in all 16, won every pair; depth 3 90,273 / 63.625 moves; clears and reveals per move 2.354 / 1.386 against 1.792 / 0.960	ledger-recorded, historical 7,000-point seeds

The clear and reveal rates are worth noting on their own. The status summary records roughly 2.4 numbered clears and 1.4 reveals per move as the region associated with stable long games, treating those as diagnostic targets from limited runs rather than proven thresholds. The oracle's 2.354 / 1.386 sits essentially in that region while public depth 3, at 1.792 / 0.960, does not.

Records: experiment index "Oracle and curriculum research" (completed, ledger-recorded diagnostic); ledger, sections "Privileged-future oracle distillation" and "Privileged topology audit". Source: perfect-information-oracle/main.ts.

What this taught us, and what is still open

• The million-point objective is not blocked by the rules of the simulator. Whatever else is hard, that is settled.
• The gap between the oracle and legal search is a measure of the value of information, not a measure of how much better a legal policy could be. Later work (audit-05 §5.4) measured how much of the oracle's edge survives when the real tape is taken away, and the answer was: not much, and what remains is visible as board quality rather than as move preference.
• The oracle remains useful as a generator: the positions it reaches are the input to the state curriculum and the topology audit. Whether those positions are worth practising from is still unmeasured.