---
title: Hindsight planner
family: oracle-curriculum
summary: Imagine seven complete futures, play each as if it were certain, and average the results. The policy is legal but misuses uncertainty.
status: rejected
evidence: ledger-recorded
reads: public
kind: strategy
technique: determinization
featured: true
---

## 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](/approach/fair-expectimax/reference) pays that cost in full.
The alternative every planning textbook offers is
[determinization](/learn/glossary): 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](/docs/research/history) 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](/docs/exploratory/finding-12-fair-planner-ceiling-extended) §3, and
[what more compute buys](/learn/concepts/does-more-compute-help)).

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](/approach/d4-long-outcome); 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](/approach/lifetime-objective), legal by
construction and expensive by construction.

<AgentContext summary="Records and provenance">

Records: [experiment index](/docs/research/experiment-index) "Oracle and
curriculum research", rejected, ledger-recorded, "strategy fusion made the public
root ranking worse"; [ledger](/docs/research/history) 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`](/docs/exploratory/audit-05-optimistic-curriculum) §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.

</AgentContext>

<AgentContext summary="Full results table">

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.

</AgentContext>

<AgentContext summary="Validity, gates and limitations">

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.

</AgentContext>

<AgentContext summary="Scoring mode">

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.

</AgentContext>