---
title: Turning the reference search's constants into dials
family: lifetime-objective
summary: Makes death penalty, search depth, and chance samples configurable to test which settings improve survival.
status: completed
evidence: reproduced
reads: public
---

The strongest policy in this repository has a handful of numbers baked into it
that nobody had ever varied. This approach makes three of them adjustable
without changing anything else, so they can be swept and measured instead of
assumed.

<EvidenceLabel status="completed" evidence="reproduced" reads="public" />

Two sweeps have been run through it. The first: the one the approach is named
after — is a **valid negative**: the death penalty is at its stop and is not a
lever. The second is a **replicated positive**: the number of chance samples was
too small to represent the game's own randomness, and fixing it was worth about
a third more score.

## The intuition

At the bottom of its look-ahead, the search puts a number on every board it can
reach. A board where the game is over gets a fixed, very large negative number —
the *terminal utility*, set to −1,000,000. Every other board gets a score from a
hand-written [leaf evaluator](/learn/glossary), and in practice those come out
between roughly 200 and 11,000.

So the death penalty is about a hundred times larger than the entire spread of
everything else. The decision rule is effectively: **first avoid dying within
four moves; only then prefer the nicer-looking board**. Given that surviving is
where 94% of the points come from
([score decomposition](/approaches/lifetime-objective/score-decomposition)),
that constant is the single number pointed most directly at the objective — and
it had never been swept. Perhaps the search was too timid, or not timid enough.

The second dial is subtler. At a [chance node](/learn/concepts/chance-vs-choice)
the search has to average over the next disc, which is equally likely to be any
of seven values. The frozen reference averages over **five** representative
samples. Five buckets cannot cover seven equally likely outcomes, so some disc
values get no weight at all: the same ones, every time, at every node. That is
not noise that cancels out; it is a fixed bias built into every estimate the
search makes.

## How it works, step by step

1. **Input.** Exactly what the reference reads: the visible board, the visible
   next disc, and how many drops remain before the next rise. Nothing else.
2. **Reuse, not reimplementation.** The leaf evaluator, the chance
   stratification, the board canonicalisation, the cache keys, the column
   ordering, the work accounting and the legal fallback are the unmodified
   frozen code, included as a library. Only the depth-limited driver is
   rewritten, so that three constants become command-line options.
3. **A parity gate before any game is played.** At its default settings the
   parameterised driver must pick the identical column as the frozen reference
   on every move. Recorded result: **50 moves compared, 0 mismatches.**
4. **Paired sweeps.** Each setting plays the same ordered list of game seeds as
   the reference, so scores can be compared game by game rather than as two
   separate averages.
5. **Output.** A column, and per-game records through the family's
   [shared harness](/approaches/lifetime-objective/common), including the
   survival-flow rates that the whole family watches.

## What happened: the death penalty

**Nothing at all, in the direction that mattered.** Making death fifty times
more expensive produced byte-identical games: same scores, same lifetimes, 0
wins, 64 ties, 0 losses. The search is already as risk-averse as the constant
can make it. Moving the other way, towards recklessness, only cost, and it cost
in an instructive shape: at a penalty of −100,000 the policy cleared slightly
*more* discs per move and still died *sooner*. Throughput is not the objective;
throughput sustained without dying is.

That closes a cheap hypothesis. The gap between a 94-move average and the
roughly 294 moves a million-point average would need cannot be bought by
re-pricing death.

<TechnicalDetails title="The technical record — terminal utility">

Source: [`finding-04-terminal-utility-saturated`](/docs/exploratory/finding-04-terminal-utility-saturated),
status exploratory, **evidence tier `development`**, recorded as a valid
negative result. Six arms, 64 paired games each, seeds
`0xa51d0000`–`0xa51d003f` on the exploratory development lease `SEEDLEASE-A51D`,
2,000-move cap, common seeds across arms.

| Terminal utility | Mean score | Mean moves | Clears/move | Paired delta vs reference | W–T–L | 95% lower bound |
| ---: | ---: | ---: | ---: | ---: | :---: | ---: |
| −50,000,000 | 321,992 | 94.06 | 1.973 | 0 | 0–64–0 | 0 |
| −10,000,000 | 321,992 | 94.06 | 1.973 | 0 | 0–64–0 | 0 |
| −3,000,000 | 321,992 | 94.06 | 1.973 | 0 | 0–64–0 | 0 |
| −1,000,000 *(frozen)* | 321,992 | 94.06 | 1.973 | 0 | — | — |
| −300,000 | 321,652 | 93.98 | 1.973 | −340 | 1–62–1 | −1,039 |
| −100,000 | 320,161 | 92.92 | 1.987 | −1,831 | 4–29–31 | −4,563 |

The identical-game result at magnitudes at or beyond 1,000,000 is exact and
needs no statistics. The −300,000 and −100,000 deltas are single-cohort
estimates. Only the terminal utility was varied; the leaf weights are frozen, and
a jointly re-tuned leaf could in principle move the saturation point, which is
what the [leaf reweight](/approaches/lifetime-objective/leaf-reweight) work went
on to test, using this same parameterised search as its base.

</TechnicalDetails>

## What happened: the number of chance samples

**Averaging over seven disc values instead of five was worth about a third more
score**, and it replicated on a second, previously unread set of games. On the
confirmation cohort the seven-sample search scored 398,498 against 297,327, and
lasted 114.66 moves against 87.16. Median, lower quartile and minimum all
improved, so this is not one lucky long game; and the survival-flow rates moved
in the direction the mechanism predicts, closing roughly a fifth of the gap to
the clears and reveals per move that indefinite survival requires.

The more interesting part is that this is an **interaction, not a "more samples
is better" result**. With the biased five-sample estimator, adding a fourth move
of look-ahead bought nothing measurable. With the exact seven-sample estimator,
the fourth move was worth about 86,000 points. Depth and estimator quality are
complements. That offers a mechanism for one of the repository's most repeated
conclusions: that deeper search is not automatically stronger because every
historical depth experiment sat on top of the same biased estimator.

It is also not free: the exact estimator costs 3.82 times the work per move at
the same depth, and a variant one move shallower with the exact estimator ties
the frozen reference at an eighth of the work.

<Callout title="A trap that has already produced one wrong conclusion" tone="warn">
The frozen search carries a work limit sized to sit just above five-sample
depth-4 search. Seven samples need 3.7 times that. Left at the frozen limit, a
seven-sample run silently hits the ceiling and falls back to a completed
three-move search, so a naive comparison measures a shallower search and
reports it as a chance-sampling result. Every arm here declares its limit
explicitly.
</Callout>

<TechnicalDetails title="The technical record — chance samples">

Source: [`finding-05-chance-strata`](/docs/exploratory/finding-05-chance-strata),
status exploratory, **evidence tier `development`, replicated across two
independent cohorts for the headline arm**. Positive result. Same parity gate
(50 moves, 0 mismatches).

| Comparison | Delta score | 95% lower bound | Delta moves | W–T–L | Verdict |
| --- | ---: | ---: | ---: | :---: | --- |
| depth 4: 7 samples − 5 samples | +101,171 | +47,457 | +27.50 | 41–0–23 | significant |
| depth 3: 7 samples − 5 samples | +7,276 | −45,961 | +2.42 | 34–0–30 | not significant |
| 7 samples: depth 4 − depth 3 | +86,172 | +26,468 | +22.39 | 40–0–24 | significant |
| 5 samples: depth 3 − depth 4 | +7,723 | −42,743 | +2.69 | 35–0–29 | not significant |

Cohorts: a first cohort on `0xa51d0000`–`0xa51d003f`, whose seeds had already
influenced other decisions and therefore cannot serve as confirmation
(+71,138, lower bound +5,826); and a **confirmation cohort on previously unread
seeds** `0xa51d1000`–`0xa51d103f` (+101,171, lower bound +47,457). 64 paired
games each.

Confirmation cohort detail: mean score 297,327 versus 398,498; mean moves 87.16
versus 114.66; clears per move 1.9489 versus 2.0571; reveals per move 1.0697
versus 1.1549; 0 censored games and 0 score-identity violations in both arms;
games at or above one million: 0 versus 2.

Cost, at fixed depth 4: work per move 1,296,034 versus 4,956,614, a ratio of
3.824 against a predicted 3.79. Depth 3 with seven samples costs 156,834 per
move and ties depth 4 with five samples (+14,999, 95% lower bound −31,029,
32–0–32).

**Limitations as recorded.** 64 paired games per arm; only the headline arm is
replicated, and every other row of the interaction table rests on a single
cohort. Seven samples makes the *next-disc* expectation exact, but gray-disc
reveals are still sampled, so the reveal expectation is not exact — whether
reveal sampling is now the binding bias was tested separately in the
[reveal sampling](/approaches/lifetime-objective/reveal-sampling) work. No
fixed-time comparison is reported. And the headline mean of 398,498 is far below
the 1,050,000 the frozen protocol requires before a candidate may even be
frozen: **no protected or final seed was opened or is justified by this
result.**

</TechnicalDetails>

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

Two constants, two opposite outcomes, and the difference between them is the
lesson. The risk constant was saturated: it had no reachable setting that
changed a decision, so no amount of tuning could have helped. The sample count
was biased: it was systematically wrong in a way that no amount of extra depth
could average away. Sweeping a constant is cheap; assuming which way it will go
is not.

The negative result also narrowed the search for the remaining headroom. The
search already minimises death within its horizon as its first priority, and its
horizon is four moves against a rise every five. Whatever is missing has to live
in the long-horizon content of the leaf evaluator, not in the search's appetite
for risk.

Still open, and cautionary: whether the depth gradient keeps climbing once the
estimator is exact. A later, still in-progress test in the
[fast engine](/approaches/lifetime-objective/fast-engine) approach reports the
fifth move of look-ahead *reversing* rather than continuing the gain, on interim
partial cohorts. Read that record's own caveats before quoting it.