---
id: CB-WP-0025
kind: product
title: "Could we have won: a path out of a lost game, and how hard the game actually is"
status: done
state_hub_workstream_id: "a866982f-94e7-432b-b0d5-2fefb781a574"
---

# Purpose

```
structural tier  L   (creates a new capability — a search over game state,
                      and a measurement the engine does not currently take;
                      both produce numbers ground-game will tune against)
chaos            d8 = 6  → no override
declared tier    L
```

Declaration 8 of chaos window 2. Tier L: separate survey, **adversarial
review**, ADR, then spec, then code.

## Two remarks, and why they are one pass

> *"I had a game where we lost and in this case I would have liked to know
> if and how we could have won… the best path is not computable I guess so
> a path to win is fine."*

> *"Do we have difficulty estimations? If so we should show them. It will
> help tuning the game. I felt it was too easy but then we lost, so who
> knows."*

They are the same machine asked two questions. *Was this game winnable?*
is a search from a recorded state. *How hard is this game?* is that search
run over many deals and counted. Building the second without the first
gives a win-rate with no witness; building the first without the second
gives one anecdote per game.

**"I felt it was too easy but then we lost, so who knows" is the finding.**
The maintainer cannot calibrate the game from play, and that is precisely
the gap `ground-game` is currently blocked in: **GROUND-WP-0005**
*(Difficulty tiers (threshold ratio) and optional Pressure dial)* is active
with **both its tasks in `wait`**. Tiers cannot be set without a measured
baseline, and clay-borg is the thing that can measure. This pass is what
unblocks it — which is the design-instrument aspect CB-WP-0022 is in the
middle of stating, arriving with a concrete demand.

## What already exists, so the survey does not re-find it

The state is replayable (`replay.rs`, `make replay-test`); the move space
is enumerable (`legal_commands`, narrowed by CB-WP-0023 so branching is
real rather than inflated by inert moves); bots exist (`bot.rs`); and the
threshold is public (`OutcomeView`). **A search needs no new persistence
and no new rules** — which is why D6 put it in `games/ground` with no new
crate and no port.

## What makes this hard, and must not be waved through

**Settled by [ADR-0013](../decisions/ADR-0013-could-we-have-won.md).** The
declaration framed the central risk as *a path computed with the deck
known is a path the players could never have found*, and asked the ADR to
choose between an omniscient, an information-respecting, and a bounded
search.

**D1 dissolved the choice**: strategy fusion is a defect of aggregating
over determinizations to *choose a move*, and after the game there is one
world — so a line found in it is executable in it. **D2** keeps the
declaration's real concern by marking each move `visible`/`hidden` rather
than by refusing to search.

The second warning here — *"one win rate over one bot policy is not the
difficulty"* — was right, and **the survey made exactly that error
anyway**; see T02.

## Task: survey

```task
id: CB-WP-0025-T01
status: done
priority: high
state_hub_task_id: "556cfd24-5992-4cc0-be90-0b60e989b5bb"
```

`research/CB-RES-0008-*.md`, with `tier: L` and the chaos roll recorded
(`loop-lint` checks both).

Per §Step 1 the survey is done when it can name a **benchmark-to-beat**
per dimension. Four were asked for: retrospective solvers in
hidden-information games (and their known failure, strategy fusion); *a
path to win* as a **witness** rather than a proof; difficulty as a measured
quantity in co-operative games; and the **per-node cost**, measured on our
machine — the runnable-baseline option applies, since a search that cannot
finish while the player is looking at the page is a different feature.

**Done 2026-08-05.**
[CB-RES-0008](../research/CB-RES-0008-could-we-have-won.md), with a
runnable baseline (`games/ground/examples/difficulty-baseline.rs`).

> **Everything this record originally claimed was withdrawn by T02 the
> same day.** Kept as a pointer rather than rewritten, because a claim
> retracted silently is how three earlier wrong premises survived
> (ADR-0012 D5).

**Claimed:** a greedy bot wins 200/200 at five and six seats, so the game
is too easy there; the points-to-threshold ratio rises with seat count and
explains the curve; `legal_commands` costs 112–161 µs, so exhaustive
search is out; and all of this explains the maintainer's report.

**Withdrawn:** the win rate is `GreedyPolicy`'s, not the game's (C4 —
`FirstLegal` scores 0% on the same deals); the ratio is identical at 3p
and 4p, which differ by 12.5 points (C2); the cost figure was wrong by
30–50× and exhaustive search is affordable (C1, C6); and the maintainer's
losses were 3-player games on the pre-ruling deal (C5).

**What survives:** the harness exists and runs, the 6/9/12 arithmetic is
right against `Problems.csv`, and the branching widths (4.7–9.1) hold. See
[CB-RES-0008](../research/CB-RES-0008-could-we-have-won.md) for the
corrected text and
[the response](../history/260805-could-we-have-won-response.md) for the
full accounting.

## Task: adversarial review

```task
id: CB-WP-0025-T02
status: done
priority: high
state_hub_task_id: "bdd9fc97-4706-4d8e-b286-91ff53339680"
```

Tier L requires it. Exactly one round: challenge, then response, trail in
`history/`, unpolished. Four attempts required: that the honest version is
unaffordable; that a witness misleads more than it helps; that the
difficulty number is a bot benchmark in a difficulty costume; and that
this is CB-WP-0022's job rather than a separate capability.

**Done 2026-08-05.** Trail:
[challenge](../history/260805-could-we-have-won-challenge.md),
[response](../history/260805-could-we-have-won-response.md).
Separate agent, as in CB-WP-0022.

**Six of seven conceded. The survey's headline finding is WITHDRAWN.**

**C4 kills it and the reviewer ranked it fourth.** A `FirstLegal` policy —
`legal[0]`, no heuristic — scores **0% at five and six seats** where greedy
scores 100%, and **77.5% at two** where greedy scores 66%. Two
unsophisticated agents span the whole range, so *"too easy at 5–6 seats"*
was about `GreedyPolicy`, not GROUND.

**C1**: the node cost was wrong by 30–50× — the timer bracketed whole
games — and **the tell was in my own output**, falling as branching rose.
**C6**: exhaustive search is *not* out, which changes T03's premise.
**C3**: the finding failed the admissibility rule this project wrote nine
hours earlier. **C2**: 3p and 4p share deal, threshold and ratio and differ
by 12.5 points. **C5**: `lib.rs:2487` contradicts the "explains the
maintainer" claim — his losses were 3-player on the pre-ruling deal,
unwinnable at 6 against 7.

**T06 was pointed at GROUND-WP-0005, which is blocked on this number.**
Sending it would have been the fifth wrong premise to reach ground-game.
**Both tier-L reviews here have now caught a false headline that every
gate passed.**

## Task: decide

```task
id: CB-WP-0025-T03
status: done
priority: high
state_hub_task_id: "055630a1-56e0-4ad4-8796-35f444313371"
```

`decisions/ADR-0013-*.md`. (ADR-0012 is CB-WP-0022 T03's.) At minimum:
which question the solver answers and what it is called in the UI; the
**information boundary** and whether it is structural or promised; the
**bound**, and what *no path found* means against it; whether difficulty
is one number or a table, and of what; and **where it lives** — the tier
was declared L assuming a new capability port, and if there is none, say
so.

**Done 2026-08-05.**
[ADR-0013](../decisions/ADR-0013-could-we-have-won.md), seven decisions.
**Two of them are not what T03 was written expecting**, because the review
moved the ground under both.

- **D1 — strategy fusion does not apply, and that is why this is
  affordable.** Fusion is a defect of *aggregating over determinizations
  to choose a move*. **After the game there is one world**: the deal is
  known, so a search over it produces a line executable in the only world
  there is. The survey treated fusion as this pass's central obstacle; it
  is an obstacle to a *playing* engine, which we are not building.
- **D4 — difficulty is the WINNABLE FRACTION, not any bot's win rate.**
  C4 killed the bot rate: two trivial policies span 0–100% on the same
  deals, and improving the bot would make the game "easier" without a rule
  changing. The solver supplies a policy-independent measure — *over N
  deals, in what proportion does a winning line exist* — which is a
  property of the deal distribution and the threshold, and is what
  GROUND-WP-0005 actually needs. **The bot rate never was.**

**D2** searches `GroundState` — the survey's view-only boundary is not
implementable, since a view cannot fold events — and moves the guarantee to
a checkable per-move `visible`/`hidden` marking from `project()`. **D3**
bounded exhaustive over the last K rounds, with *"no winning line found in
the last K rounds"* normative, never *"unwinnable"*. **D5** makes the
harness an instrument before any figure is quoted (C3). **D6** no new
crate and no port — **the L declaration was an over-declaration, recorded
as one**. **D7** the node cost is disputed 5×; T04 benchmarks it and
neither existing figure may be cited.

## Task: specify

```task
id: CB-WP-0025-T04
status: done
priority: high
state_hub_task_id: "7c3ca25d-0001-44ef-a07d-0ab2d51b09a5"
```

`specs/` — extend `MetricsAndScenarios.md` or add a capability spec as the
ADR directs, with metrics, because a spec without them is prose.

Candidates, to be argued not adopted: **witness checkability** (every
emitted path replays to `group_success` — a hard gate, not a metric, since
a path that does not replay says the opposite of the truth); **search
cost** at the chosen bound; and **difficulty resolution** — the smallest
threshold difference the measurement can distinguish, with its N, which is
more useful to `ground-game` than any rate with no error bar.

Per `ground-game`'s ruling (GROUND-WP-0004 T02), **any arithmetic finding
this produces ships a runnable reproduction and a row-level table** — never
a summed figure. A difficulty number is arithmetic, and it is exactly the
kind that has already gone wrong twice.

**Done 2026-08-05.**
[specs/RetrospectiveAnalysis.md](../specs/RetrospectiveAnalysis.md) v1.0,
and `games/ground/benches/search.rs` for D7's disputed number.

**The benchmark's own first fixture was defective — the same defect class,
one layer down.** A fixed stop at step 20 put 2p and 4p where seat 0 had
**no legal commands**, so it timed an empty `Vec` (~120 ns) and silently
skipped `validate_fold`. It now advances to a real branch **and asserts
it**.

Measured at real decision points (table in
[RetrospectiveAnalysis §3.1](../specs/RetrospectiveAnalysis.md)):
`legal_commands` 4.06–4.76 µs, `clone` 378–639 ns, `validate+fold`
**0.5–3.8 µs**.

**`clone` is in there because a search must copy state per branch**, and
`iter_batched` excludes setup from timing — leaving the budget on an
unmeasured span, which is precisely C1's mistake.

**The affordability conclusion drawn here was itself falsified by T05.**
It projected joint branching and concluded `K = 2` holds at two to four
seats. The real search exceeded 2×10⁶ nodes at **two**. See T05's record
and [RetrospectiveAnalysis §3.1](../specs/RetrospectiveAnalysis.md) —
a projection from branch widths is not a timing of a search, and this
pass has now made that mistake twice.

**§4.1 is a normative prohibition**, not a preference: a single-policy win
rate may not be reported as a difficulty. The spec carries the measured
reason — greedy 100% vs first-legal 0% on identical deals.

## Task: build the witness

```task
id: CB-WP-0025-T05
status: done
priority: high
state_hub_task_id: "5f1cbda3-7427-4f23-8c67-b2e216b987a8"
```

The search, the bound, and the replayable path. Wire it to the ending page
so a lost game can be asked the question — the page CB-WP-0024 T01 is
already reworking, so land that first or expect a conflict.

**A game that was won is not asked the question.** The feature exists for
a loss.

**Controls:**
- every emitted witness replays to `group_success` through the existing
  runner — asserted, not spot-checked;
- a deal constructed to be unwinnable returns *none found*, and the test
  says which construction makes it so;
- the information boundary is mutation-provable: relax it, and a test
  naming *that* boundary goes red. If it cannot be mutated, it was a
  comment rather than a rule.

**Done 2026-08-05.** `games/ground/src/search.rs`, five tests.

**The first traversal was wrong and the diagnostic hid it.** It branched
on *the first seat with any legal command* and stopped there, so a later
seat never acted if an earlier one was already selected. Restructured
around what the rules oblige: a seat without a selection **must** select
(GR-R02) and nothing else can happen first; after Reveal the optional
actions branch freely, and the aggregate rejects `Resolve` until the
obligatory ones are done — **so the search needs no phase logic of its
own.**

**And my rewind was off by one round**, replaying the round it was meant
to search — which is why the first run reported 3 nodes and looked fine.

**The measurement falsified the spec's own projection at two seats, where
§6 predicted four**: 2p `K=1` exhausted in 8,103 nodes (~29 ms), 2p `K=2`
cut at 2,000,000 nodes (~5 s), 3p `K=2` won in 41 nodes.

The projection assumed a joint product per round; the search explores
sequential per-seat decisions, so orderings multiply the tree far beyond
`width^seats`.

**The asymmetry is the operative finding.** *Finding* a win is cheap;
*proving none exists* needs exhaustion. So the **witness feature is
affordable now** and the **winnable fraction is not**, because its
negative half must exhaust every deal it counts.

## Task: measure the difficulty, and hand it to ground-game

```task
id: CB-WP-0025-T06
status: done
priority: high
state_hub_task_id: "723feae8-1ed4-4dd4-9330-8ec84625e5d9"
```

Run the measurement, ship it as a `make` target beside the other
instruments, and send it to `ground-game` against **GROUND-WP-0005**,
which is active with both tasks waiting on exactly this. Per CB-WP-0022
T06 it lands as a **file in their repo under their workplan**, not only an
inbox entry — *the message that sat unread for four days is the baseline
to beat*.

**Controls:**
- the number regenerates from a single command, and `facts.toml` carries
  it if anything else quotes it (§Single source of fact — `make
  facts-check`);
- the report carries the row-level table the ruling requires;
- **the seed range and policy are in the number's name**, not in a
  footnote.

**Done 2026-08-05.** `games/ground/examples/difficulty.rs`, `make
difficulty`, wired into `make self-tests`, and
[a report file in ground-game](../../ground-game/workplans/GROUND-WP-0005-clay-borg-difficulty-260805.md)
under GROUND-WP-0005 with a hub message pointing at it.

**The report opens with the retraction**, because what this task was
written to send was withdrawn by T02 and GROUND-WP-0005 is blocked on
exactly that number.

Winnable-from-round-5, 60 seeds: **60% / 93% / 100% / 100% / 100%** at
2/3/4/5/6 seats, beside greedy / random / first-legal rates and the spread
between them. Full table in the report and in `make difficulty`.

**`spread` justifies the whole redesign** — 71.7 to 100.0 points between
three trivial policies. No single rate says anything about the game, and
the table now shows that rather than asserting it.

**The confound is stated in the tool's own output**: `winnable` is
conditioned on greedy's play up to the final round. Presenting it as a
property of the deal would repeat this pass's error in a subtler form.
**No threshold changes are proposed.** The instrument can fail (spec §5),
and `difficulty-baseline.rs` is marked superseded.

Registered as **F16, `inconsistent`, `withdrawn`**, with `difficulty.rs`
as its reproduction.

## Task: evidence

```task
id: CB-WP-0025-T07
status: done
priority: high
state_hub_task_id: "2616e06c-5d88-4680-be18-4452515dff21"
```

`evidence/CB-EV-*.md` (**CB-EV-0024** — CB-EV-0023 went to CB-WP-0024).
Was the maintainer's game winnable; what the
honest search cost against the omniscient one; whether the difficulty
measurement moved `ground-game`; what tier L cost against what it caught;
and CB-WP-0024's cost by re-running the instrument.

**Done 2026-08-05.**
[CB-EV-0024](../evidence/CB-EV-0024-could-we-have-won.md).

- **The maintainer's question is answered.** 3p seed 7 was winnable — a
  10-move line, found in 41 nodes, replays to `group_success`. 2p seed 7
  was **not**, exhaustively, in 8,103 nodes. **The witness feature works;
  the difficulty half is where the trouble was.**
- **Five of nine defects came only from the review**, four from execution
  — and all four of those were in work written *after* it.
- **The wrong-denominator family now has five instances and no control.**
- **The 5–6 seat rows point the opposite way from the withdrawn claim**;
  neither reading is established, and the evidence says so.
- **Tier L was an over-declaration** (no port) **and paid for itself
  anyway** — the review is L-only, and without it a false number reaches a
  blocked repo.
- **Chaos window 2 will close with zero overrides**, making its retirement
  condition untestable.

**Not done, and named rather than quietly dropped:** the witness is **not
wired to the ending page**, so the browser cannot yet ask the question.
That is the maintainer-facing half of remark 2.