Hindsight planner

The problem

Uncertainty is what makes this game hard, and averaging over it honestly is expensive: the tree multiplies at every gray-disc reveal and every new disc. Fair expectimax pays that cost in full. The alternative every planning textbook offers is determinization: replace the uncertainty with a handful of specific, fully specified futures, solve each of those easy deterministic problems well, and average the answers. It parallelises perfectly, and it lets each individual plan look far ahead. Whether a legal, public version of that trade is worth making in Drop7 had not been measured.

Proposed solution

Invent seven complete futures for the current board, plan each one as though it were already known, average the results, and play the column that comes out best. The futures are invented from a hash of the visible board itself, and every legal column at that position gets the same seven, so the comparison between columns is paired.

The policy reads only the public position: the visible board, the visible next disc and the moves until the next rise. The real game seed and the real future never enter it, and the clairvoyance lives entirely inside the invented tapes, where the planner is allowed to make later moves that depend on knowing the tape it is planning in. That last freedom is the known risk in this design, and the experiment was registered to find out what it costs.

How it works

1. Hash the current public board to a seed. Every legal column at this position gets the same seven invented futures.
2. For each column and each invented future, run a deep search, depth 8 with a beam of 64, that treats the invented future as certain: the discs arrive in the order the tape says, and the gray discs reveal the numbers the tape says.
3. Summarise the seven values for each column with a blend of the mean and the lower quartile, so a column that is excellent in three futures and fatal in four is not rewarded for its average.
4. Play the best column, which is the output at every position, and throw all seven futures away. Next move, hash the new board and invent seven fresh futures.

What happened

On its fresh four-game screen the hindsight planner averaged 51,500.5 points and 37.5 moves, where an ordinary depth-3 search averaged 107,076 and 72.5 on the same games (rejected, ledger-recorded, ledger section "Synthetic-tape hindsight optimization"; historical 7,000-point scoring, archival). Four games is a screen, and under the protocol the confirmation seeds stayed closed once it failed, so there is no larger cohort to quote.

The ledger's diagnosis is explicit: "tape-specific later decisions make the per-tape root values incompatible and overoptimistic: the familiar strategy fusion failure of determinization."

What we learned

Strategy fusion is the name for what went wrong, and it is worth stating in the game's terms. Each of the seven plans is coherent on its own. The plans are incompatible with one another, because each responds to information the player will never have, and averaging incompatible plans produces a number that is systematically too high. The bias is largest on cluttered boards, where a favourable reveal is the only thing that saves you, which is where over-confidence kills.

Optimism does not require privileged information. This policy reads nothing it should not, and it still smuggles the answer key in through its own internal model. The rules here cover fair chance handling for that reason, as well as what a policy is allowed to read. A separate oracle diagnostic swept the number of imagined futures from one up to 1,024 and found quality rising to 256 and then falling, so more machines make the same estimator converge more faithfully on the wrong objective; those are oracle measurements, from a planner that reads hidden values, and they are not policy evidence (finding-12 §3, and what more compute buys).

What survives is the paired-futures machinery. Giving every column the same imagined futures is good practice and is reused throughout the long-outcome experiments; it was the clairvoyant continuation inside each tape that broke this one. The open question is whether a determinized planner whose continuations are restricted to public information at every step behaves any better, which is the design of the fair planner studied later under lifetime objectives, legal by construction and expensive by construction.

Agent contextRecords and provenanceopen ↓close ↑

Records: experiment index "Oracle and curriculum research", rejected, ledger-recorded, "strategy fusion made the public root ranking worse"; ledger section "Synthetic-tape hindsight optimization".

Configuration: seven synthetic tapes per root, built from a canonical public-state hash; an independent depth-8, beam-64 clairvoyant continuation per tape; a mean and lower-quartile blend to select the root action. The real game seed and the realized future are not inputs. Screen cohort 0x3e8b0000...03, four games; confirmation seeds not read.

audit-05 §4 lists this as failure 3 of 17, primary mode "objective mismatch" with "representation / information gap" secondary, and calls it "exactly the owner's 'best possible outcome' generator, made public and fair, and it is the single worst result in the corpus". §5.4 uses it as one of four independent measurements showing that the privileged oracle's advantage is its tape rather than its judgement: take the tape away from the oracle's own algorithm and it falls far below the public baseline it was supposed to beat.

Agent contextFull results tableopen ↓close ↑

Screen on fresh seeds 0x3e8b0000...03, four games, historical 7,000-point Sequence scoring, archival:

Arm	Mean score	Mean moves
Exact depth 3	107,076	72.5
Hindsight planner	51,500.5	37.5

Confirmation seeds were not read.

Agent contextValidity, gates and limitationsopen ↓close ↑

The implementation passed determinism, metadata-blindness, reflection, chance-stratification and legality self-tests under an optimised -Werror build and under ASan/UBSan, and stayed inside a 153,713-transition decision bound.

Four games is a screen. It is enough to reject a policy that loses about half the score and about half the lifetime, and it certifies nothing about the size of the gap. Under the protocol the confirmation seeds stay closed once a screen fails.

Agent contextScoring modeopen ↓close ↑

The screen ran under historical 7,000-point Sequence scoring, archival. The absolute point totals are not corrected 17,000-point Hardcore evidence and are not compared with corrected figures elsewhere on this site; the paired direction on the same four games is what the rejection rests on.