---
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
---

Imagine seven complete futures for the current board, plan each one perfectly as
though it were already known, average the results, and play the column that
comes out best.

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

<Callout title="This one is legal, and it still fails like an oracle" tone="info">
Unlike the rest of this family, the hindsight planner reads **no hidden
information**. Its seven futures are invented from a hash of the public board
itself; the real game seed and the real future never enter it. It sits here
because it fails for exactly the reason the
[perfect-information oracle](/approaches/oracle-curriculum/perfect-information-oracle)
cannot be copied, and because it produced the worst measured result in the
repository, which makes it the most instructive failure in it.
</Callout>

## Why it looks like a good idea

Uncertainty is what makes this game hard. Averaging over it without optimism, as
[fair expectimax](/approaches/fair-expectimax/reference) does, is expensive: the
tree multiplies at every gray reveal and every new disc. The alternative that
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.

## How it works, step by step

1. Hash the current public board to a seed. Every legal column at this position
   gets the *same* seven invented futures, so the comparison between columns is
   paired.
2. For each column and each invented future, run a deep search — depth 8 with a
   beam of 64: that treats that 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, and throw all seven futures away. Next move, hash the
   new board and invent seven fresh futures.

## The flaw, in one sentence

Inside each invented future, the planner is allowed to make *later* moves that
depend on knowing that future, so the value it reports for a column is not "how
good is this column", it is "how good is this column **if I am also allowed to
respond to information I will not have**".

That is called **strategy fusion**, and it is the same defect that makes the
perfect-information oracle unbeatable and useless. Each individual plan is
coherent; the plans are incompatible with one another, and averaging
incompatible plans produces a systematically over-optimistic number. Worst of
all, the bias is not uniform: it is largest exactly on cluttered boards where a
favourable reveal is the only thing that saves you: the boards where
over-confidence is fatal.

## What happened

It lost half the game. On its fresh four-game screen, ordinary depth-3 search
averaged about 107,000 points and 72.5 moves; the hindsight planner averaged
about 51,500 points and 37.5 moves — less than half the score and roughly half
the lifetime. Under the protocol the confirmation seeds were never opened. 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."

There is a striking follow-up elsewhere in the repository. A later study swept
the number of imagined futures from 1 up to 1,024 and found quality *rising*
until 256 and then **falling**: with few futures, sampling noise accidentally
masks the planner's bias, and with many futures the noise disappears and the
planner converges faithfully on the wrong objective. That is written up in
[is more computation the answer?](/learn/concepts/does-more-compute-help), and
it means this is not a result you can fix by buying more machines.

<TechnicalDetails>

Screen on fresh historical 7,000-point Sequence-scored seeds `0x3e8b0000...03`
(four games): exact depth 3 averaged **107,076 points and 72.5 moves**; the
hindsight planner averaged **51,500.5 and 37.5**. Confirmation seeds were not
read. The implementation passed determinism, metadata-blindness, reflection,
chance-stratification and legality self-tests, and a 153,713-transition decision
bound.

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 / lower-quartile blend to select the root action. The real game seed
and realized future are not inputs.

[`audit-05`](/docs/exploratory/audit-05-optimistic-curriculum) §4 lists this as
failure 3 of 17, primary mode "objective mismatch", 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 the *tape*, not
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.

Records: [experiment index](/docs/research/experiment-index) "Oracle and
curriculum research"; [ledger](/docs/research/history) section "Synthetic-tape
hindsight optimization". Source: `hindsight-planner.cpp`.

</TechnicalDetails>

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

- **Optimism does not require privileged information.** A perfectly legal policy
  can smuggle it in through its own internal model. This is why the repository's
  rules talk about *fair chance handling*, not only about what the policy is
  allowed to read.
- **The estimator, not the budget, was wrong.** The K-sweep above turns that from
  an opinion into a measurement: more compute made the same estimator converge
  more faithfully to a worse answer.
- **What survives.** Common random numbers across siblings — giving every column
  the same imagined futures — is genuinely good practice and is reused
  throughout the [long-outcome experiments](/approaches/d4-long-outcome). It was
  the clairvoyant *continuation*, not the shared tape, that broke this.
- **Still open:** a determinized planner whose continuations are themselves
  restricted to public information at every step. That is precisely the design of
  the fair planner studied later under
  [lifetime objectives](/approaches/lifetime-objective), which is legal by
  construction and expensive by construction.