Accessible energy

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.

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, in plain English

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.

The technical record

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 §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 "Oracle and curriculum research"; ledger sections "Accessible-energy residual" and "Accessible-energy confidence-set root prior". Sources: accessible-energy-lab.cpp, accessible-energy-root-prior.cpp.

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: 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, open work).