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Cheating on purpose: oracles, teachers and students

Privileged programs measure the value of hidden knowledge and try to teach that advantage to a legal policy.

A Drop7 player sees a board, the disc about to drop, and how many drops remain before the row rises. That is all. Several programs in this repository see much more: the number under every gray disc, and the exact sequence of discs the game will deal next. They are allowed to, because they are never going to play.

The split matters because researchers cross it during training. The results show what happened each time this project tried to teach a blind player what a sighted one knows.

The line: what a legal policy may read

The methodology states the deployable policy as a function of exactly four things:

(visible board, visible next disc, moves until rise, terminal flag) -> column

and lists what it must not inspect: the game or origin seed, future numbered discs or covered-disc reveals, a future random tape or oracle action, accumulated score, level, or absolute move number, and any history that cannot be reconstructed from the public state. That list is the information boundary. A program that reads anything on it is disqualified as a policy, regardless of how well it scores.

The reason is not purity. It is that the target is a claim about playing the game, and a program that knows the future is not playing the same game.

The same position, seen twice

next disc31 drop until the next riseWhat the player seesand the only thing a legal policy may read33317314What a privileged planner seesthe same board with the answer key filled in334643176632147575722211One position, two information statesEvery gray disc already has anumber; the game fixed it when therow appeared. The player never seesit until two clears land beside it.Here 16 discs are covered and 1 ofthem is already cracked.Possible answer keys for this board:7^16 = 33,232,930,569,601The planner is handed the one that is true.Position played by the engine in latent mode from figure seed 0x5eed031b, after 19 moves(level 4). A figure, not gameplay evidence.
Left: the position as the game shows it, with fifteen solid grays and one already cracked. None of their values are visible. Right: the same position with the answer key filled in. The covers are removed, but the game is unchanged. Every gray disc's number was fixed when its row appeared.

Both boards are the engine's own output. The figure was produced by playing a short game through the TypeScript engine in latent mode, where each covered disc is given a predetermined number instead of drawing one at the moment of reveal. The same position can therefore be exported twice: once as the player sees it and once as the answer key.

Notice the size of what is hidden. Sixteen covered discs, each independently one of seven numbers, is more than thirty-three trillion possible answer keys. The player has to choose a column without knowing which one is true. The privileged planner is handed it.

Why build a cheater at all

Two reasons, both diagnostic.

To find the ceiling. If a planner that knows everything still cannot survive, the difficulty is in the game, not in the uncertainty. If it thrives, the gap between it and the best public policy is a measurement of what the hidden information is worth. That gap is an upper bound on what any amount of public reasoning could recover.

To produce labels. A privileged planner can be run offline over thousands of positions and asked, for each one, which column would you have played? Those answers become training data for a public model. The privileged inputs are thrown away; only the public board and the teacher's answer are kept.

Both uses are allowed only during training and diagnosis. The methodology says: "Privileged planners may inspect future randomness to generate labels. Such an experiment is an oracle or teacher experiment until a separate public student is frozen and evaluated without those inputs."

Teacher, labels, student, blind evaluation

1 · Privileged teacherreads the board, the next disc,the rise clock —and the hidden gray numbersand the future disc tape.Runs offline only.2 · Labelsfor each public position:the column the teacherpreferred, or the value itassigned. The privilegedinputs are not stored.3 · Public studenttrained to reproduce thelabels from public inputsalone: board, next disc,rise clock, terminal flag.Then frozen.4 · Blind evaluationthe frozen student playsfresh unseen games throughthe public interface, pairedagainst fair D4, judged onwhole-game mean score.information boundaryonly public inputs past hereThe teacher is never a result.Its score measures how much the hidden information is worth. Only box 4 can produce apolicy number, and only if nothing privileged reached box 3.
The teacher's score is never a policy result; only the frozen student's blind games are. If any privileged input reaches box 3 through a feature, filter, or tuning decision, the whole pipeline reverts to a diagnostic.

What the ceiling turned out to be

The privileged planner is extremely strong. In the retained topology audit, an analysis-only future-aware planner was run to a 500-move cap on twelve training-only seeds. It reached the cap in all twelve games and averaged 1,058,931.5 points. The public depth-3 search on the same paired cohort averaged 132,979 points and 90.5 moves.

That number needs four qualifications:

  • it was scored with the historical 7,000-point level bonus, not the corrected 17,000-point Hardcore bonus this project's target uses;
  • every game was censored at 500 moves, so the mean is a lower bound on a quantity that is not the target quantity;
  • it is twelve games; and
  • it is an oracle. The ledger's own sentence is the right one: this "establishes that a million points is mechanically attainable in the simulator, but it is not evidence for a deployable policy: the oracle sees the realized future disc and reveal streams."

A million points therefore exists inside these rules. Nobody has shown that a blind player can find it.

What happened when the teaching was tried

Oracle and long-outcome teachers show the same pattern:

Privileged future-aware planners, D4 distillation, 25-move outcomes, rollout vetoes, and curriculum data were used to build better labels. They found predictive signal, but students usually lacked enough diverse successor data, failed held-out sibling ranking, or were too slow to improve complete games. Oracle strength is an upper-bound teaching signal, not a legal policy result.

The clearest example is the native oracle-distillation lab. Its teacher was excellent. Its labelled roll-ins reached the 200-move label cap and averaged 829,516.75 points, and the student fitted those labels well during training. On held-out whole games, it collapsed: top-1 agreement with the teacher was 0.218 against a preregistered floor of 0.30. The diagnosis in the ledger is "strong seed-tape/state-distribution overfit". The teacher's choices, it turned out, were not recoverable from the public state at all: two positions that look identical to a player can call for different moves depending on covers the student cannot see.

The frozen hybrid was still screened on eight games and appeared to win. It gained 21,978.75 points and 5.25 moves, enough to unlock its preregistered confirmation. On the disjoint 16-game confirmation it lost badly: minus 62,274.25 points and minus 18.125 moves per game. An eight-game win that reverses on sixteen is exactly what a heavy-tailed score distribution produces when you look at too few games.

The technical record
  • Ceiling. Privileged topology audit (approaches/oracle-curriculum/topology/oracle-topology-audit.cpp), ledger-recorded diagnostic. On fresh historical 7,000-point Sequence-scored seeds 0x3d70f000...0f, public depth 3 averaged 90,273 points and 63.625 moves; the privileged depth-4/beam-128 oracle averaged 429,182.5 points, reached the 200-move cap in all 16 games, and won every pair (clear/reveal rates 2.354/1.386 per move versus 1.792/0.960). Separately, on twelve training-only seeds 0x3d950000...0b at a 500-move cap, the same oracle reached the cap in all twelve games and averaged 1,058,931.5 points with the historical 7,000-point bonus; paired public depth 3 averaged 132,979 points and 90.5 moves. A single earlier TypeScript perfect-information run scored 2,079,579 points and reached the 500-move cap on seed 0x3d700000. It was one game by an oracle.
  • Distillation. approaches/oracle-curriculum/oracle-distillation/oracle-distill.cpp, rejected, ledger-recorded. 5,110 fitted labels and 1,629 held-out labels; whole games form the split; a hard boundary drops the game seed, future tape, reveal RNG, score, level and move count before the 614/128/128/7 sparse network. Oracle fitting roll-ins reached the 200-move label cap and averaged 829,516.75 points. Training cross-entropy reached 0.480, but held-out top-1/top-2 accuracy was 0.218/0.386 and held-out cross-entropy was 3.282 against fixed gates of 0.30/0.55/1.75. Screen on 0x3d7e0000...07: exact behavior 261,871.875 points / 79.25 moves, hybrid 283,850.625 / 84.5, both paired 95% lower bounds negative. Confirmation on 0x3d7f0000...0f: exact behavior 249,816.875 / 75.375, hybrid 187,542.625 / 57.25; paired deltas −62,274.25 points and −18.125 moves with lower bounds −118,363.971 and −33.322. The hybrid switched on 18.45% of confirmation moves.
  • Both entries are in the experiment history and the experiment index under oracle and curriculum research; the summary paragraph quoted above is §5 of the research status summary.
  • The figure position was generated by web/scripts/generate-oracle-scenario.ts from the figure/scripted seed domain (0x5eed****). It consumes no seed lease and is not gameplay evidence.

What this taught us, and what is still open

The oracle did its job. It proved the simulator contains long, high-scoring games and measured a large gap between knowing the future and not. No form tried here transferred that advantage across the boundary. The list includes distillation, DAgger, topology summaries, accessible-energy features, synthetic tapes, and oracle-manifold features.

The strategy landscape draws the conclusion as a rule for whoever tries next: "Future distillation should first show that its public features predict oracle preferences across whole held-out games before it is allowed to control moves." Predicting the teacher on positions the teacher visited is not the test; predicting it on whole games nobody has seen is.

There is a second reason these students struggled, and it is not about privilege: a student trained on the move that was actually played has no information about the six moves that were not, which is exactly what it is asked to rank at play time. That is the sibling trap, and it applies to every teacher, privileged or not.

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