Oracle and curriculum research

Let a planner cheat — show it the hidden gray-disc numbers and the discs that are still to come — then try to teach an ordinary player, who sees only the screen, to play the way the cheater did.

A cheating planner is called an oracle or a teacher — the idea, and the line it must never cross, are explained in cheating on purpose and the glossary. It is never a player. Its scores are produced with information a real player cannot have, so they belong on a different scale entirely: they are an upper bound on what the simulator makes possible, and a source of labelled examples. Every page in this family is about one of two questions — how much is that hidden information worth?, and can any of its advantage be handed across the boundary to a legal policy?

Where the boundary sits

The middle column is the whole design problem. A teacher can be as strong as we like; what determines whether the exercise works is whether the reason for its move is visible in the narrow slice of information that crosses to the student.

How this family works, in general

1. Play games with a privileged planner. In this repository that is a receding-horizon beam search over the game's realized future — see the perfect-information oracle.
2. Record, at each position, the public view only, plus the teacher's choice or some summary of what the teacher's positions looked like.
3. Train something on that: an action classifier (distillation, DAgger), a board-shape classifier (topology), a hand-built feature family (accessible energy), or a set of restart positions to practise from (state curriculum).
4. Freeze it, and make it play complete games through the public interface, against unchanged fair search, on games it has never seen.

One page here is the odd one out. The hindsight planner reads no hidden information at all — it invents futures from a hash of the public board and plans as if each invented future were certain. It sits in this family because it fails for the same reason the oracle cannot be copied.

What happened, in plain English

The cheating planner is enormously strong. On twelve training-only games it hit the 500-move cap in every one and averaged more than a million points — under the historical 7,000-point scoring, and censored by the cap. That answered the first question: the simulator does contain million-point structure, and long games are mechanically possible.

Nothing has yet crossed the boundary. Every attempt — copying the teacher's moves, copying them again on the student's own positions, learning what an oracle-visited board looks like, turning the oracle's stable board features into a scoring term, restricting that term to statistically tied moves — produced either a weak held-out label or an apparent gain that reversed when more complete games were played. Two independent measurements say why, and they agree: the oracle's advantage is mostly knowing the tape, not judging the board better.

The record behind those sentences

• Single upper-bound check: 2,079,579 points at the 500-move cap on seed 0x3d700000 (ledger-recorded; one game).
• Twelve training-only games 0x3d950000...0b at depth 4 / beam 128: capped in all twelve, mean 1,058,931.5 under the historical 7,000-point Sequence-style level bonus; paired public depth-3 play averaged 132,979 points and 90.5 moves (ledger-recorded).
• Sixteen-game matched audit: oracle 429,182.5 points, 200-move cap in all 16, winning every pair, against depth 3's 90,273 and 63.625 moves; clears and reveals per move 2.354 / 1.386 against 1.792 / 0.960 (ledger-recorded, historical 7,000-point seeds).
• Action distillation: training cross-entropy 0.480 against held-out top-1 0.218, top-2 0.386, cross-entropy 3.282 — and the ledger notes the oracle and behaviour holdouts were "similarly weak", so this is not merely the student visiting unfamiliar boards.
• audit-05 §5.4 collects four independent measurements of the same question and concludes the oracle's advantage is "overwhelmingly … exploitation of the realised tape", with a real but non-actionable residue that shows up as state quality, not as action preference. §4 of the same audit classifies seventeen failed learned models by failure mode; the oracle distillations are classed as representation/information-gap failures.
• Sources: experiment index "Oracle and curriculum research"; ledger sections on privileged oracle distillation, the privileged topology audit, accessible energy, and synthetic-tape hindsight optimization.

What this taught us, and what is still open

• A ceiling is not a curriculum. Knowing a million points is reachable told us the objective is not impossible. It did not supply a single usable move.
• State quality and action quality are different measurements. A separate discriminator (in the n-tuple family) separated oracle-visited boards from fair boards on public features alone at held-out area-under-curve 0.925 / 0.915, and the very same scalar, used to rank moves as a near-tie tie-break, lost games to plain depth-3 search — 253,798.9 against 301,101.1 points (ledger-recorded, quoted in audit-05 §2.4). This is the sibling-ranking problem in its privileged-teacher form.
• Optimism in a label is a trap. A target realized on a lucky future is not a function of the public board, so the best a public model can fit is the average lucky outcome — an over-confident survival estimate, worst exactly on the cluttered boards where confidence kills.
• One cheap measurement is still missing. The restart curriculum re-scores every oracle position under independent public futures, but audit-05 §5.4 records that the aggregate fair-relabelled survival was never reported. Nobody has published what an oracle-visited board is worth to a fair player. That number decides whether practising from oracle positions is worth anything at all, and it has never been run.