affordability projection
games/ground/src/search.rs, five tests. It finds real winning lines and
replays them through validate/fold to group_success.
Two bugs in my own work, found and fixed here.
THE TRAVERSAL WAS WRONG. 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 but still had a legal move. 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. That is why the first run reported 3 nodes and looked like a
working search.
Measured with the real search, rewinding real games to the start of their
last K rounds:
2p K=1 exhausted, 8,103 nodes, ~29 ms
2p K=2 budget cut at 2,000,000 nodes, ~5 s
3p K=2 win found, 41 nodes, ~157 us
The spec's own falsifier said "§3 fails if K=2 proves unaffordable at four
seats". IT FAILED AT TWO. The projection assumed a joint product per
round; the search explores sequential per-seat decisions, so orderings
multiply the tree far beyond width^seats. That is the second projection
this pass published in place of a measurement -- C1's timer was the first.
THE ASYMMETRY IS THE OPERATIVE FINDING. Finding a win is cheap: DFS
stumbles onto one in tens of nodes. Proving none exists needs exhaustion.
So the witness feature is affordable now at any K a player would ask
about, and the winnable fraction (ADR-0013 D4) is NOT, because its
negative half must exhaust 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. specs §3 and §3.1
corrected accordingly, and the K=2 default withdrawn.
The negative control that makes "winnable" falsifiable: 2p seed 7 over its
last round returns NoneFound with exhausted=true in ~8k nodes -- a real
negative, not a budget cut wearing a verdict's clothes. And the visible/
hidden marking is tested both ways, since a marking that can only say YES
is decoration.
make all: exit 0. loop-lint clean.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
tegwick
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