clay-borg/specs/RetrospectiveAnalysis.md

RetrospectiveAnalysis — was this deal winnable, and how hard is the game

v1.0 — CB-WP-0025 T04, 2026-08-05. Normative. Implements ADR-0013. Admissibility of anything this produces is governed by GameDesign.md §1.

Two capabilities, one machine. Was this deal winnable? is a search over a finished game. How hard is the game? is that search run over many deals and counted — not a bot's win rate (§4.1).

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1. The question, and its name

"Given the deal as it actually was, was there a line of play that reached the threshold?"

Never labelled "how you should have played." The distinction is the honest content of the feature: the tool answers a question about the deal, and a label promising advice about the player turns a true answer into a false lesson.

Strategy fusion does not apply and must not be invoked as an objection. Fusion (Frank, Basin & Matsubara 1998) is a defect of aggregating over determinizations to choose a move. After the game there is one world — the deal is known — so a line found in it is executable in the only world there is. This is why the affordable option is also the honest one.

2. The witness

A witness is a sequence of joint selections that, replayed from the recorded initial state, ends with group_success == true.

2.1 It must replay — hard gate, not a metric

100% of emitted witnesses replay through the existing scenario runner and end in group_success.

Not a target: a gate. A witness that does not replay asserts the opposite of the truth to a player who just lost, which is worse than emitting nothing.

2.2 Every move carries its information dependence

ADR-0013 D2. Each move in a witness is marked:

mark	meaning
visible	everything the move depended on was in the acting seat's projection at that point — the Problem face-up, the Solution in that seat's own hand
hidden	it was not

Computed from project(), which already exists and whose hiding rules are already asserted by games_ground::view.

This replaces the structural boundary the survey wanted. Searching a GroundView is not implementable — a view cannot fold events — so the guarantee moved from the search cannot see it to the answer says which moves needed it. A witness reads:

"This deal was winnable. Two of these six moves needed a card you had no way to know was coming."

Falsifier: a witness whose moves are all visible but which no seat could have chosen means the marking is wrong. A test constructs that case.

2.3 Wording when nothing is found

"No winning line found in the last K rounds."

Never "unwinnable". A bounded search cannot establish unwinnability, and this sentence is what the player reads.

3. The bound

Exhaustive over the last K rounds, table treated as one co-operative agent choosing joint selections.

K = 1 for an exhaustive answer; K may be larger when a witness is all that is wanted. ADR-0013 said K = 2 by default; §3.1's measurement overrides it, and the difference is which question is being asked:

answer	needs	affordable K today
"here is a winning line"	one success	2+ — DFS finds one in tens of nodes
"there is no winning line"	exhaustion	1 — K=2 exceeded 2×10⁶ nodes at two seats

A K that cannot be exhausted may still emit a witness; it may not report NoneFound { exhausted: true }, and the type keeps those apart.

Bounded in rounds, not nodes: "winnable from round 4" means something to a player; "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.

3.1 Measured cost, and what it permits

cargo bench -p games-ground --bench search — the single source for these numbers (ADR-0013 D7). Mid-game states at real decision points:

seats	branch width	legal_commands	clone	validate+fold
2	5	4.06 µs	378 ns	696 ns
3	8	4.13 µs	432 ns	508 ns
4	11	4.76 µs	639 ns	3.76 µs

Per-child cost is not uniform — validate+fold ranges 0.5–3.8 µs depending on which command is taken, because some resolve cascades and some do not. Budgets use the upper end, so ~5 µs per child (clone + validate + fold).

Joint branching over the last two rounds, from the measured per-seat widths:

seats	joint / 2 rounds	at ~5 µs/child
2	~5×10²	negligible
3	~1.6×10⁵	~0.8 s
4	~5.7×10⁵	~2.9 s

The projection above was wrong, and the real search falsified it

Measured 2026-08-05 with the search built in T05, rewinding real games to the start of their last K rounds:

case	result
2p, K=1	exhausted in 8,103 nodes, ~29 ms — a real negative
2p, K=2	budget cut at 2,000,000 nodes, ~5 s — not exhausted
3p, K=2	win found in 41 nodes, ~157 µs

§6's falsifier said "§3 fails if K=2 proves unaffordable in practice at four seats". It failed at two.

The projection assumed a joint product per round. The search explores sequential per-seat decisions, and the post-Reveal phase branches over every seat's options at every level, so orderings multiply the tree far beyond width^seats.

And the asymmetry is the operative fact: finding a win is cheap — depth-first stumbles onto one in tens of nodes — while proving none exists is expensive, because it must exhaust the space. So:

• the witness feature (§2) is affordable now, at any K a player would ask about;
• the winnable fraction (§4.2) is not, because its "not winnable" half requires exhaustion on every deal it counts.

K = 1 is the honest default for exhaustive answers today. Making K = 2 exhaustible needs transposition or move-ordering, neither of which this pass built.

The published 112–161 µs/node figure is withdrawn (CB-RES-0008 §1.2, challenge C1) and must not be quoted from anywhere.

4. Difficulty

4.1 A bot's win rate is not a difficulty

Normative prohibition, because this project already made the error and nearly exported it:

A win rate from a single policy may not be reported as a difficulty.

Measured, on identical deals: GreedyPolicy wins 100% at five and six seats where a FirstLegal policy — take legal[0], no heuristic — wins 0%; at two seats FirstLegal (77.5%) beats greedy (66.0%). Two unsophisticated agents span the entire range.

And a measure that improves when the measurer improves is not measuring the subject: a better bot would make the game "easier" with no rule changing.

4.2 What is reported instead

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

A property of the deal distribution and the threshold, which is what ground-game tunes. Ships as a 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 named policy achieves
skill gap	the difference — how much play has to supply

It is a lower bound and must be labelled one. A K-round search cannot see a line that required round 1, so the figure is "winnable-from-round-(6−K)", never "winnable".

Every rate carries its policy, N, seed range and K in the number's name, not in a footnote — GameDesign §1.2, and the reason the withdrawn finding was inadmissible.

4.3 Resolution — the number that makes it usable

The smallest threshold change the measurement can distinguish, with its N.

"We can tell a threshold of 5 from 7 but not 7 from 8" is more useful to ground-game than any rate with no error bar, and it is what makes the figure a tuning instrument rather than a statistic.

5. The instruments must be able to fail

ADR-0013 D5, and GameDesign §1.3. Before any figure from these tools is quoted anywhere:

• 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;
• one command regenerates the figure (make difficulty);
• the policy panel is plural — at least greedy, random and first-legal. The spread between them is the finding §4.1 rests on, and reporting one policy would restore the error.

games/ground/examples/difficulty-baseline.rs currently satisfies none of the first three and is inadmissible until it does. It has no assertions, no self-test, and no make target — nothing can turn it red, which under CB-WP-0022 T05's role distinction makes it a default artifact wearing a counterexample label.

6. Falsifiers for this spec

• §2.2 fails if a witness is emitted whose moves are all visible but which no seat could have chosen. Then the marking must be derived from the search rather than checked after it.
• §4.2 fails if the winnable fraction turns out to be ~100% or ~0% at every seat count and threshold — it would then have no resolution (§4.3) and be as useless as the bot rate it replaced.
• §3 fails if K = 2 proves unaffordable in practice at four seats; the measured 2.9 s is a projection from branch widths, not a timing of the real search.