clay-borg/evidence/CB-EV-0024-could-we-have-won.md

# CB-EV-0024 — could we have won

CB-WP-0025 T07. Tier L (structural L declared; **there was no port —
D6 records it as an over-declaration**; chaos d8=6 → no override).
Declaration 8 of chaos window 2. Closed 2026-08-05.

**Delivered:** [CB-RES-0008](../research/CB-RES-0008-could-we-have-won.md)
with a runnable baseline, an adversarial review that withdrew its
headline, [ADR-0013](../decisions/ADR-0013-could-we-have-won.md),
[RetrospectiveAnalysis.md](../specs/RetrospectiveAnalysis.md),
`games/ground/src/search.rs`, `benches/search.rs`,
`examples/difficulty.rs`, `make difficulty`, and a report to
GROUND-WP-0005 that opens with a retraction.

---

## 1. Was the maintainer's game winnable?

The question the pass exists for. **Yes, and the tool answers it.**

For 3-player seed 7, searched over the last round: a **10-move winning
line**, found in 41 nodes, which replays through `validate`/`fold` to
`group_success`. For 2-player seed 7 — a game greedy lost — the search
returns **`NoneFound { exhausted: true }` in 8,103 nodes**: no winning line
existed in the final round. That is a real negative, not a budget cut, and
the type keeps the two apart.

**The feature works. The difficulty half is where the trouble was.**

## 2. What the review cost against what it caught

Second tier-L review in this project, second time it caught a false
headline that every automated gate passed. `make all` was green
throughout.

| caught | by |
|---|---|
| the headline finding was about `GreedyPolicy`, not GROUND (C4) | **only the review** |
| the node cost was 30–50× too high (C1) | **only the review** |
| exhaustive search is not out (C6) | **only the review** |
| the finding failed our own admissibility rule (C3) | **only the review** |
| the maintainer's losses were misattributed (C5) | **only the review** |
| the benchmark's fixture timed an empty `Vec` | building it |
| the traversal skipped later seats; the rewind was off a round | building it |
| `K=2` is not exhaustible at two seats | **running it** |
| the winnable fraction is still greedy-conditioned | writing it down |

**Five of nine from the review, four from execution.** The four that
execution caught were all in work written *after* the review, which is
some evidence that the review's discipline transferred rather than that
the remaining errors were easier.

**The reviewer under-ranked their own best challenge.** They put C4
fourth. Measured, it is the one that kills the finding — and I said so in
the response rather than accepting their ranking, which is the correct use
of a review: material to check, not a verdict to adopt.

## 3. The error family, now with five instances

CB-EV-0019 §1 named it: *this project's arithmetic errors are not in the
arithmetic.* A number computed correctly against the wrong base, span, or
subject.

| # | pass | the wrong thing |
|---|---|---|
| 1 | CB-WP-0021 | `csv` cost against AM-4a, which never sees the code |
| 2 | ground-game report | *"12 in the file"* — a sum with no deal table |
| 3 | CB-WP-0018 | SOLVE's inertness attributed to the wrong condition |
| 4 | **this pass, C1** | a timer bracketing whole games, divided by decisions |
| 5 | **this pass, C4** | a win rate attributed to the game, not the policy |

**And two projections published in place of measurements**, both in this
pass: the survey's `7.4^15` hand-wave, and the spec's joint-branching
estimate that the real search exceeded at *two* seats where §6 predicted
four.

**`facts-check` catches copies that disagree. Nothing catches a number
computed correctly against the wrong denominator**, and after five
instances that is a standing gap rather than a run of bad luck. Naming it
is what this file can do; closing it is not this pass's.

## 4. What the difficulty measurement actually shows

`make difficulty`, 60 seeds:

| seats | winnable | greedy | random | first-legal | spread |
|---|---:|---:|---:|---:|---:|
| 2 | 60% | 60.0% | 5.0% | 76.7% | 71.7 |
| 3 | 93% | 88.3% | 6.7% | 25.0% | 81.7 |
| 4 | 100% | 93.3% | 6.7% | 30.0% | 86.7 |
| 5 | 100% | 100.0% | 3.3% | 0.0% | 100.0 |
| 6 | 100% | 100.0% | 3.3% | 0.0% | 100.0 |

**The `spread` column is the finding.** 71.7 to 100.0 points between three
trivial policies. It is the evidence for the prohibition in
RetrospectiveAnalysis §4.1, and it is why the withdrawn headline was
meaningless rather than merely imprecise.

**The 5–6 seat rows point the opposite way from the withdrawn claim.**
`first-legal` scores 0% where greedy scores 100% — the widest spread in
the table. Whatever is happening at five and six seats makes *play matter
more*, not less. The survey read 100% as "trivially easy"; the panel
suggests "high variance in what an agent must get right". **Neither is
established**, and saying so is the honest state.

**The winnable fraction is still not policy-free**, and the tool says so
in its own output: it is *"winnable from where greedy got to"*, because
searching from round 1 is unaffordable. Presenting it as a property of the
deal would be this pass's own error in a subtler form — which is exactly
how a corrected project reintroduces a defect, so it is stated in the
code, the spec, the report and here.

## 5. Tier L's cost, and the over-declaration

**The tier was declared L on the assumption of a new capability port.
There is no port** — the search uses `validate`, `fold`, `legal_commands`
and `project`, so it lives in `games/ground` (D6). By the structural
trigger this was an **M**.

**And the L weight paid for itself anyway**, twice: the adversarial review
is L-only, and without it a false difficulty claim reaches a repo that is
blocked waiting for exactly that number. **That is an argument the tier
table does not currently make** — the trigger asks *does this create a
port*, when the question that predicted value here was *will this pass
produce a number someone else acts on*. Recorded for whoever revisits
§Loop tiers; not proposed as a change from one instance.

## 6. Chaos window 2

**Declaration 8 of 12.** Structural L (over-declared), d8 = 6, no
override.

**Eleven declarations, no 8 rolled.** The window will close with **zero
overrides**, so its retirement condition — *retire if an override changes
nothing twice running* — is **untestable**. Window 1 closed with two
overrides at d4 and both changed the outcome.

**The d4 → d8 cut bought rarity at the cost of evidence**, and CB-EV-0015
did not price that. At d8 over twelve declarations the expected count is
1.5, so zero is unremarkable *as a sample* and damning *as a design*: a
mechanism that produces no data in a full window cannot be evaluated by
the window. **This is the second window's headline finding about the loop
itself** and belongs in whatever closes it.

## 7. Cost

CB-WP-0024's cost, by re-running the instrument: `make cost`. Not inlined
(§Single source of fact), and see CB-EV-0019 §4 — the chain breaks beyond
roughly four passes and still has no bound.

## Open after this pass

- **Search from round 1** would remove the greedy confound. Needs
  transposition or move-ordering; neither built.
- **Difficulty resolution** — the smallest distinguishable threshold
  change, with its N — is required by the spec and not yet supplied.
- **The witness is not wired to the ending page.** T05 built the search;
  the browser cannot yet ask it. That is the maintainer-facing half of
  remark 2 and it is not done.
- **The wrong-denominator family has no control** (§3), at five instances.
- **The chaos window's retirement condition is untestable** (§6).