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 with a runnable baseline, an adversarial review that withdrew its headline, ADR-0013, 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.

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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).