---
title: Accessible energy
family: oracle-curriculum
summary: Turn the board properties that separate a future-reading planner's positions from ordinary ones into a handful of readable numbers, and let a legal search use them.
status: rejected
evidence: ledger-recorded
reads: public
---

Take the board properties that reliably separate a future-reading planner's
positions from an ordinary search's positions, write them down as a handful of
readable quantities, and let a completely legal search use them.

<EvidenceLabel status="rejected" evidence="ledger-recorded" reads="public" />

<Callout title="Where the privileged information is, and is not" tone="info">
The privileged planner appears only in the *design history* of these features:
the directions came from the split-half-stable list produced by the
[topology audit](/approaches/oracle-curriculum/topology). The fitting
continuations, the ranking, and the deployed policy read nothing but the public
board: the source file says privileged oracle tapes "are unavailable to
training roll-ins, ranking continuations, and the deployed policy". What this
page describes is a legal policy built with a privileged hint about *where to
look*.
</Callout>

## The intuition

"Energy" here means potential that is actually *usable*. A 7 sitting in a column
of height two is worth something: a run of seven can still be built through it.
The same 7 buried under three rows with no reachable trigger is dead weight that
will ride the board upward until the game ends. A board's score tells you
nothing about the difference; a human player feels it immediately.

The feature family tries to make that feeling explicit, in a few groups:

- **stored unfired numbers** — high numbers still capable of firing;
- **trigger readiness**: how close a run is to completing, directly or after a
  reveal;
- **cover access**, whether covered gray discs can still be reached and cracked;
- **debt** — projected occupancy, dead low numbers, low caps and congested
  adjacent ones, which are the ways a board quietly becomes unplayable.

## Two experiments, in order

**The residual.** Calibrate the existing evaluator first, then fit a small ridge
regression on top of it, on positions produced by ordinary depth-3 play. Split
by *source game*, never by position. Then use the improved evaluation inside the
search.

**The root prior.** After the residual lost games, the same frozen model was
re-used in a deliberately conservative way. The leaf evaluator was left
completely unchanged. Three independent chance-sampling salts produce three
complete valuations of every legal column; an alternative is admitted only when
a one-sided 95% paired lower bound *fails to establish* that it is worse than
the search's own pick. Accessible energy then ranks only inside that admissible
set, and if only one column is admissible, the exact search's action is
returned untouched. The design intent is a tie-break, not a policy.

## What happened

**The prediction improved. The games got worse.** On held-out positions, adding
the energy residual raised the accuracy of picking the best of the available
columns from about 23% to about 31%, and pairwise ordering from about 49% to
about 52% — modest but real. Then it played eight complete games against
unchanged depth-3 search and lost seven of them, scoring roughly a quarter less.
Under the protocol, confirmation seeds were never opened.

**The safety valve was not safe.** The confidence-set version was supposed to be
nearly a no-op: change the move only when the statistics genuinely cannot tell
two columns apart. In practice it switched **44% of all decisions** — it
admitted about a third of all non-reference alternatives, and averaged nearly
three admissible columns per move. That is not a tie-break; that is a different
policy. It lost about 15,000 points and 12 moves per game, and its realized flow
— clears, reveals and waves per move — fell across the board while its work per
move roughly tripled.

The mechanism of the second failure is worth separating from the first. Nothing
about the energy model *learned* anything new between the two runs; what failed
was the calibration of "statistically indistinguishable". Three sampling salts
were not enough to establish that a column was worse, so a great many columns
that were in fact worse were declared eligible.

<TechnicalDetails>

**Residual** (rejected; ledger-recorded). 601 held-out action successors:
calibrated score-prediction R-squared 0.580 to 0.615; within-position top-action
accuracy 22.9% to 31.3%; pairwise ranking 49.2% to 52.2%. Stored energy was the
strongest feature group. Complete-game gate on fresh historical 7,000-point
Sequence-scored seeds `0x3e890000...07`: exact depth 3 averaged 112,318.5 points
and 77.125 moves; the residual-guided search averaged 85,768 and 60.625, losing
seven of eight pairs. Confirmation seeds were not read.

**Root prior** (rejected; ledger-recorded). Screen on fresh `0x3e930000...07`:
exact depth 3 averaged 105,767.875 points / 73.125 moves; the root prior
averaged 90,300.75 / 60.875 — paired losses of 15,467.125 points and 12.25
moves. The confidence set switched **214 of 487 decisions (43.94%)**, admitted
31.90% of non-reference alternatives, and averaged 2.828 admissible actions.
Realized clears / reveals / waves per move fell from 1.885 / 1.032 / 1.405 to
1.725 / 0.910 / 1.244, while work rose from 53,395 to 158,522 units per move.
The reserved `0x3e940000...0f` confirmation was not read, and the admission
threshold was **not** retuned on the failed screen.

The ledger's own conclusion after the first failure: energy "may only be
reconsidered as a conservative root tie-break among actions that repeated search
samples cannot distinguish", which is precisely what the second experiment
tested, and it failed on the calibration of that phrase.

[`audit-05`](/docs/exploratory/audit-05-optimistic-curriculum) §4 classifies the
residual as a distribution-shift failure and the root prior as an
objective-mismatch failure: "calibration, not learning, failed".

Records: [experiment index](/docs/research/experiment-index) "Oracle and
curriculum research"; [ledger](/docs/research/history) sections
"Accessible-energy residual" and "Accessible-energy confidence-set root prior".
Sources: `accessible-energy-lab.cpp`, `accessible-energy-root-prior.cpp`.

</TechnicalDetails>

## What this taught us, and what is still open

- **Interpretable features do not escape the ranking problem.** These were
  hand-designed, split-half validated and readable, and they still improved
  prediction while losing games. Compare
  [ranking siblings](/learn/concepts/ranking-siblings): the failure is not about
  neural networks, it is about what the data supports.
- **"Only when statistically tied" needs its own evidence.** A confidence set is
  a claim about power. With three sampling salts it admitted a third of all
  alternatives. Any future conservative-override design should report its switch
  rate *before* its score.
- **Cost is part of the result.** Tripling the work per move to lose points is a
  worse outcome than losing points cheaply, and the ledger records both.
- **Still open:** the feature family itself was never tested as an input to a
  learned ranker trained on *every* legal sibling, which is the data structure
  later work argues is the missing ingredient
  ([status](/docs/research/status), open work).