clay-borg/decisions/ADR-0013-could-we-have-won.md

ADR-0013: answer the retrospective question, and measure difficulty with the solver rather than with a bot

status: accepted date: 2026-08-05 decided by: agent, under the standing loop authorization tier: L (structural L — a new analysis capability whose numbers ground-game will tune against; chaos d8=6 → no override). Tier L: separate survey, adversarial review, then this document. references: CB-WP-0025, CB-RES-0008, challenge / response, ADR-0012 (admissibility), GameDesign.md, GROUND-WP-0004 T02, GROUND-WP-0005 (blocked on D4)

Context

The maintainer asked two things: "we lost — could we have won, and how?" and "do we have difficulty estimations?"

The survey answered the second and was wrong. It measured GreedyPolicy winning 200/200 at five and six seats and called the game too easy there. A FirstLegal policy — legal[0], no heuristic — scores 0% on the same deals. Two unsophisticated agents span the whole range, so the measurement was about the policy.

That failure is not incidental to this ADR; it determines D4.

The premise that changed, and it changes the algorithm

The survey said exhaustive search was impossible and reached for determinized sampling, which carries strategy fusion. Both halves were wrong.

• Its per-node cost was 30–50× too high (a timer bracketing whole games). Corrected: ~3–4 µs per legal_commands call, with the exact figure still disputed (§D7).
• Bounded exhaustive search is affordable: measured ~3 s over the last two rounds at three seats.

Joint branching, treating the table as one co-operative agent — the product over seats of the measured per-seat branching:

seats	per-seat mean	joint per round	last 2 rounds
2	4.7	~22	~5×10²
3	7.4	~405	~1.6×10⁵
4	9.1	~754	~5.7×10⁵

Against a ~10⁵–10⁶ node budget, the last two rounds are exhaustively searchable at two, three and four seats. Five rounds is not, at any seat count.

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D1 — answer the retrospective question, and say so in those words

Three questions were on the table (CB-RES-0008 §3). The tool answers:

"Given the deal as it actually was, was there a line of play that reached the threshold — and here is one."

Strategy fusion does not apply to this question, and that is the whole reason it is the affordable one. Fusion is a defect of aggregating over determinizations to choose a move: the search picks different actions in states the player cannot distinguish. After the game there is one world. The deck is known, the deal is known, and a search over that single world produces a line that is executable in it — because it is the only world there is.

The survey treated fusion as an obstacle to this pass. It is an obstacle to a playing engine. We are not building one.

What remains true is that the line may have been unfindable at the time, and D2 handles that by annotation rather than by refusing to answer.

On screen it is called "was this deal winnable?" — never "how you should have played". The distinction is the honest content of the feature, and a label that overclaims turns a true answer into a false lesson.

D2 — run on GroundState, and mark each move's information dependence

The survey's preferred guarantee was structural: search a GroundView so the boundary cannot be crossed. It is not implementable — a view cannot fold events, so a search needs a state it may not see. The survey said so in §6 and was right to.

Decision: search GroundState — legitimate here, because post-game the deal is public (solution_discard already is, and the game is over) — and move the honesty guarantee to something checkable:

Every move in an emitted witness is marked visible or hidden. A move is visible if, at the point it is played, everything it depends on was in the acting seat's projection: the target Problem face-up, the Solution in that seat's own hand. Otherwise hidden.

So a witness reads "you could have won — but two of these six moves needed a card you had no way to know was coming." That is a more useful answer than either extreme, and it is computed from project(), which already exists and is already tested.

Falsifier: if a witness is emitted whose moves are all marked visible but which no seat could actually have chosen, the marking is wrong and D2 has failed. A test constructs exactly that case.

D3 — bounded exhaustive over the endgame, K rounds, and honest wording

Exhaustive search over the last K rounds, with the table treated as one co-operative agent choosing joint selections. K = 2 by default, which the measurements put inside budget at 2–4 seats.

• The bound is rounds, not nodes or seconds, because rounds are what a player understands: "winnable from round 4" means something; "winnable within 100,000 nodes" does not.
• A node budget is a secondary cut that aborts with a stated reason, so a wide table cannot hang the page.
• Wording is normative. When no line is found the tool says "no winning line found in the last K rounds" — never "unwinnable". A bounded search that claims unwinnability is lying, and this is the sentence the maintainer will read.

Not chosen: determinized sampling (PIMC), ISMCTS. Both are for playing under uncertainty. Here there is one world (D1), so they would add strategy fusion to a problem that does not have it.

D4 — difficulty is the winnable fraction, not any bot's win rate

This is the decision the review forced, and it is the useful half of the pass.

A single-policy win rate cannot be a difficulty: two trivial policies span 0–100% on the same deals. Worse, improving the bot would make the game "easier" without a rule changing — a measure that moves when the measurer improves is not measuring the thing.

The solver supplies a policy-independent alternative:

Winnable fraction — over N deals at a seat count, the proportion in which the search finds any winning line within its bound.

That is a property of the deal distribution and the threshold, which is exactly what ground-game tunes. It is the number GROUND-WP-0005 is blocked on, and the bot rate never was.

Difficulty therefore ships as a small table, never one number:

column	what it is
winnable fraction	can the deal be won at all (bounded, K stated)
reference-policy win rate	what a stated bot achieves — named policy
skill gap	the difference: how much play has to supply

Every rate carries its policy, its N, its seed range and its K in the number's name, not in a footnote. A figure that loses them is inadmissible under GameDesign §1.2.

Bounded-below caveat, stated because it will be quoted: the winnable fraction from a K-round search is a lower bound on true winnability — a deal unwinnable in the last 2 rounds may have been winnable in round 1. The report says "winnable-from-round-(6−K)", never "winnable".

D5 — the harness becomes an instrument before any figure is quoted

C3 established that difficulty-baseline.rs has no assertions, no --self-test and no make target — nothing can turn it red. Under CB-WP-0022 T05's own role distinction it is a default artifact wearing a counterexample label, and GameDesign §1.3 makes it inadmissible.

Required before T06 reports anything:

• positive controls — a deal constructed to be unwinnable returns none; a deal constructed to be winnable returns a witness that replays;
• --self-test, wired into make self-tests like every other reporting tool;
• make difficulty (or equivalent), so the figure regenerates from one command;
• the policy panel is plural: at least greedy, random and first-legal, because the spread between them is what C4 exposed and hiding it would restore the error.

D6 — it lives in games/ground, not a new crate

The search needs validate, fold, legal_commands and project — all of games_ground. A separate crate would either re-export the aggregate or take a dependency on it and add nothing.

The tier was declared L on the assumption of a new capability port. There is no port, and that over-declaration is recorded rather than hidden — it is a data point for the tier rules, and the L weight paid for itself twice over regardless (§Consequences).

cb-play gains a mode to ask the question about a finished game; the difficulty sweep is an example/binary, as the baseline is.

D7 — the per-node cost is unsettled and T04 must benchmark it

The author measured 3.0–4.1 µs, the reviewer 15.6–20.4 µs, by different isolations. Both agree the published 112–161 µs was wrong by 1–2 orders; neither has established which is right.

T04 benchmarks it with criterion — already a dev-dependency, already used by benches/synthetic.rs — and the spec quotes that number and no other. Neither figure above may be cited, including by this ADR.

Consequences

• specs/ gains the witness contract and the difficulty table's shape (T04), plus the benchmarked node cost.
• T05 builds the K-round search, the visible/hidden marking, and the replay check.
• T06's payload changes completely. It reports a winnable fraction and a policy panel to GROUND-WP-0005 — not the withdrawn "too easy at 5–6 seats". The withdrawal itself is reported, per ADR-0012 D5.
• The register gains the withdrawn finding as inconsistent / withdrawn, so it is in the log rather than forgotten.

What was rejected

rejected	why
determinized sampling / PIMC / ISMCTS	strategy fusion, added to a question that has one world (D1)
a view-only search as a structural boundary	not implementable — a view cannot fold events
refusing to answer unless the line was findable at the time	throws away a true and useful answer; annotate instead (D2)
a single bot win rate as "difficulty"	two trivial policies span 0–100% on the same deals (C4)
"unwinnable" as output wording	a bounded search cannot know it (D3)
a new crate	no port exists; it would re-export the aggregate (D6)
quoting either measured node cost	they disagree 5× and neither is established (D7)