FA-86066 / Game economy crafting balance / Open access
Crafted quality tier: Novices can critically craft · case 01
Crafters below skill 25 still get critical upgrades.
ROOT CAUSE
The critical upgrade ignores the minimum skill requirement.
VERIFIED REPAIR
Restore `skill >= 25 and crit_roll < 5` at the critical skill gate step.
Unsuccessful approach: A strict skill comparison excludes crafters at exactly 25.
Case contract
materials = [[quality, weight], ...]. If total weight <= 0 the craft fails (score 0, tier "failed"). score = floor(sum(q*w)/sum(w)) + skill//10, capped at 100. Tier index = number of cutoffs [40, 65, 85] with score >= cutoff over [common, fine, superior, masterwork]. A critical craft (skill >= 25 and crit_roll < 5) raises the tier by one, never above masterwork.
Why this case matters
Game economies leak or destroy currency when one crafting or pricing rule is off by one boundary, rounding stage or state update; the defect is observable in exact integer outcomes.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(materials, skill, crit_roll):
tiers = ['common', 'fine', 'superior', 'masterwork']
cuts = [40, 65, 85]
total_w = sum(w for q, w in materials)
if total_w <= 0:
return {'score': 0, 'tier': 'failed'}
score = sum(q * w for q, w in materials) // total_w + skill // 10
score = min(100, score)
t = sum(1 for c in cuts if score >= c)
if crit_roll < 5:
t = min(t + 1, len(tiers) - 1)
return {'score': score, 'tier': tiers[t]}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('fault site critical skill gate #1', [[[58, 0], [40, 0], [58, 1]], 9, 0], {'score': 58, 'tier': 'fine'}),
('fault site critical skill gate #2', [[[0, 0], [64, 3]], 0, 0], {'score': 64, 'tier': 'fine'}),
('partial repair boundary #1', [[[0, 1], [0, 3], [40, 0]], 25, 0], {'score': 2, 'tier': 'fine'}),
('partial repair boundary #2', [[[65, 3], [39, 0]], 25, 4], {'score': 67, 'tier': 'masterwork'}),
('heavy rare material #1', [[[90, 3], [30, 1]], 0, 50], {'score': 75, 'tier': 'superior'}),
('score exactly fine cutoff #1', [[[40, 1]], 0, 99], {'score': 40, 'tier': 'fine'}),
('masterwork crit #1', [[[100, 2]], 50, 0], {'score': 100, 'tier': 'masterwork'}),
('control #1', [[[39, 1]], 10, 50], {'score': 40, 'tier': 'fine'})],
[('fault site critical skill gate #1', [[[30, 1], [0, 1], [84, 1]], 10, 4], {'score': 39, 'tier': 'common'}),
('fault site critical skill gate #2',
[[[64, 2], [69, 2], [65, 2], [89, 1]], 9, 4],
{'score': 69, 'tier': 'superior'}),
('partial repair boundary #1', [[[85, 0], [84, 2], [39, 1]], 25, 0], {'score': 71, 'tier': 'masterwork'}),
('partial repair boundary #2', [[[0, 3], [39, 1]], 25, 0], {'score': 11, 'tier': 'fine'}),
('masterwork crit #1', [[[100, 2]], 50, 0], {'score': 100, 'tier': 'masterwork'}),
('heavy rare material #1', [[[90, 3], [30, 1]], 0, 50], {'score': 75, 'tier': 'superior'}),
('control #1', [[[39, 1]], 10, 50], {'score': 40, 'tier': 'fine'}),
('control #2', [[[39, 1], [100, 3], [85, 1]], 26, 5], {'score': 86, 'tier': 'masterwork'})],
[('fault site critical skill gate #1',
[[[91, 0], [100, 1], [85, 1], [39, 3]], 10, 0],
{'score': 61, 'tier': 'fine'}),
('fault site critical skill gate #2', [[[40, 2], [84, 1]], 24, 0], {'score': 56, 'tier': 'fine'}),
('partial repair boundary #1', [[[64, 1], [100, 0], [79, 1]], 25, 0], {'score': 73, 'tier': 'masterwork'}),
('partial repair boundary #2', [[[84, 1], [65, 2]], 25, 0], {'score': 73, 'tier': 'masterwork'}),
('score exactly fine cutoff #1', [[[40, 1]], 0, 99], {'score': 40, 'tier': 'fine'}),
('masterwork crit #1', [[[100, 2]], 50, 0], {'score': 100, 'tier': 'masterwork'}),
('control #1', [[[39, 1], [100, 3], [85, 1]], 26, 5], {'score': 86, 'tier': 'masterwork'}),
('control #2', [[[39, 3], [85, 0]], 52, 0], {'score': 44, 'tier': 'superior'})],
[('fault site critical skill gate #1', [[[64, 3]], 24, 4], {'score': 66, 'tier': 'superior'}),
('fault site critical skill gate #2', [[[85, 0], [39, 2], [39, 3]], 0, 4], {'score': 39, 'tier': 'common'}),
('partial repair boundary #1', [[[100, 1], [85, 0], [65, 3]], 25, 4], {'score': 75, 'tier': 'masterwork'}),
('partial repair boundary #2', [[[0, 2]], 25, 0], {'score': 2, 'tier': 'fine'}),
('heavy rare material #1', [[[90, 3], [30, 1]], 0, 50], {'score': 75, 'tier': 'superior'}),
('score exactly fine cutoff #1', [[[40, 1]], 0, 99], {'score': 40, 'tier': 'fine'}),
('control #1', [[[39, 1]], 25, 5], {'score': 41, 'tier': 'fine'}),
('control #2', [[[39, 0]], 24, 28], {'score': 0, 'tier': 'failed'})],
[('fault site critical skill gate #1',
[[[39, 3], [40, 1], [84, 1], [85, 1]], 24, 0],
{'score': 56, 'tier': 'fine'}),
('fault site critical skill gate #2', [[[65, 1]], 0, 0], {'score': 65, 'tier': 'superior'}),
('partial repair boundary #1',
[[[64, 1], [84, 0], [100, 1], [65, 1]], 25, 0],
{'score': 78, 'tier': 'masterwork'}),
('partial repair boundary #2', [[[64, 1], [65, 0], [0, 3], [64, 0]], 25, 0], {'score': 18, 'tier': 'fine'}),
('masterwork crit #1', [[[100, 2]], 50, 0], {'score': 100, 'tier': 'masterwork'}),
('heavy rare material #1', [[[90, 3], [30, 1]], 0, 50], {'score': 75, 'tier': 'superior'}),
('control #1', [[[0, 3]], 25, 5], {'score': 2, 'tier': 'common'}),
('control #2', [[[100, 1], [65, 3], [40, 1], [39, 1]], 99, 4], {'score': 71, 'tier': 'masterwork'})]]
for label, args, expected in cases[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fault site critical skill gate #1 | {'score': 58, 'tier': 'superior'} | {'score': 58, 'tier': 'fine'} | Failed |
| fault site critical skill gate #2 | {'score': 64, 'tier': 'superior'} | {'score': 64, 'tier': 'fine'} | Failed |
| partial repair boundary #1 | {'score': 2, 'tier': 'fine'} | {'score': 2, 'tier': 'fine'} | Passed |
| partial repair boundary #2 | {'score': 67, 'tier': 'masterwork'} | {'score': 67, 'tier': 'masterwork'} | Passed |
| heavy rare material #1 | {'score': 75, 'tier': 'superior'} | {'score': 75, 'tier': 'superior'} | Passed |
| score exactly fine cutoff #1 | {'score': 40, 'tier': 'fine'} | {'score': 40, 'tier': 'fine'} | Passed |
| masterwork crit #1 | {'score': 100, 'tier': 'masterwork'} | {'score': 100, 'tier': 'masterwork'} | Passed |
| control #1 | {'score': 40, 'tier': 'fine'} | {'score': 40, 'tier': 'fine'} | Passed |
SHA-256 / d0ac2e5698adad1171ba3cf0a5d712f8f04ac962ece72205719271723b82eb40
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(materials, skill, crit_roll):
tiers = ['common', 'fine', 'superior', 'masterwork']
cuts = [40, 65, 85]
total_w = sum(w for q, w in materials)
if total_w <= 0:
return {'score': 0, 'tier': 'failed'}
score = sum(q * w for q, w in materials) // total_w + skill // 10
score = min(100, score)
t = sum(1 for c in cuts if score >= c)
if skill > 25 and crit_roll < 5:
t = min(t + 1, len(tiers) - 1)
return {'score': score, 'tier': tiers[t]}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('fault site critical skill gate #1', [[[58, 0], [40, 0], [58, 1]], 9, 0], {'score': 58, 'tier': 'fine'}),
('fault site critical skill gate #2', [[[0, 0], [64, 3]], 0, 0], {'score': 64, 'tier': 'fine'}),
('partial repair boundary #1', [[[0, 1], [0, 3], [40, 0]], 25, 0], {'score': 2, 'tier': 'fine'}),
('partial repair boundary #2', [[[65, 3], [39, 0]], 25, 4], {'score': 67, 'tier': 'masterwork'}),
('heavy rare material #1', [[[90, 3], [30, 1]], 0, 50], {'score': 75, 'tier': 'superior'}),
('score exactly fine cutoff #1', [[[40, 1]], 0, 99], {'score': 40, 'tier': 'fine'}),
('masterwork crit #1', [[[100, 2]], 50, 0], {'score': 100, 'tier': 'masterwork'}),
('control #1', [[[39, 1]], 10, 50], {'score': 40, 'tier': 'fine'})],
[('fault site critical skill gate #1', [[[30, 1], [0, 1], [84, 1]], 10, 4], {'score': 39, 'tier': 'common'}),
('fault site critical skill gate #2',
[[[64, 2], [69, 2], [65, 2], [89, 1]], 9, 4],
{'score': 69, 'tier': 'superior'}),
('partial repair boundary #1', [[[85, 0], [84, 2], [39, 1]], 25, 0], {'score': 71, 'tier': 'masterwork'}),
('partial repair boundary #2', [[[0, 3], [39, 1]], 25, 0], {'score': 11, 'tier': 'fine'}),
('masterwork crit #1', [[[100, 2]], 50, 0], {'score': 100, 'tier': 'masterwork'}),
('heavy rare material #1', [[[90, 3], [30, 1]], 0, 50], {'score': 75, 'tier': 'superior'}),
('control #1', [[[39, 1]], 10, 50], {'score': 40, 'tier': 'fine'}),
('control #2', [[[39, 1], [100, 3], [85, 1]], 26, 5], {'score': 86, 'tier': 'masterwork'})],
[('fault site critical skill gate #1',
[[[91, 0], [100, 1], [85, 1], [39, 3]], 10, 0],
{'score': 61, 'tier': 'fine'}),
('fault site critical skill gate #2', [[[40, 2], [84, 1]], 24, 0], {'score': 56, 'tier': 'fine'}),
('partial repair boundary #1', [[[64, 1], [100, 0], [79, 1]], 25, 0], {'score': 73, 'tier': 'masterwork'}),
('partial repair boundary #2', [[[84, 1], [65, 2]], 25, 0], {'score': 73, 'tier': 'masterwork'}),
('score exactly fine cutoff #1', [[[40, 1]], 0, 99], {'score': 40, 'tier': 'fine'}),
('masterwork crit #1', [[[100, 2]], 50, 0], {'score': 100, 'tier': 'masterwork'}),
('control #1', [[[39, 1], [100, 3], [85, 1]], 26, 5], {'score': 86, 'tier': 'masterwork'}),
('control #2', [[[39, 3], [85, 0]], 52, 0], {'score': 44, 'tier': 'superior'})],
[('fault site critical skill gate #1', [[[64, 3]], 24, 4], {'score': 66, 'tier': 'superior'}),
('fault site critical skill gate #2', [[[85, 0], [39, 2], [39, 3]], 0, 4], {'score': 39, 'tier': 'common'}),
('partial repair boundary #1', [[[100, 1], [85, 0], [65, 3]], 25, 4], {'score': 75, 'tier': 'masterwork'}),
('partial repair boundary #2', [[[0, 2]], 25, 0], {'score': 2, 'tier': 'fine'}),
('heavy rare material #1', [[[90, 3], [30, 1]], 0, 50], {'score': 75, 'tier': 'superior'}),
('score exactly fine cutoff #1', [[[40, 1]], 0, 99], {'score': 40, 'tier': 'fine'}),
('control #1', [[[39, 1]], 25, 5], {'score': 41, 'tier': 'fine'}),
('control #2', [[[39, 0]], 24, 28], {'score': 0, 'tier': 'failed'})],
[('fault site critical skill gate #1',
[[[39, 3], [40, 1], [84, 1], [85, 1]], 24, 0],
{'score': 56, 'tier': 'fine'}),
('fault site critical skill gate #2', [[[65, 1]], 0, 0], {'score': 65, 'tier': 'superior'}),
('partial repair boundary #1',
[[[64, 1], [84, 0], [100, 1], [65, 1]], 25, 0],
{'score': 78, 'tier': 'masterwork'}),
('partial repair boundary #2', [[[64, 1], [65, 0], [0, 3], [64, 0]], 25, 0], {'score': 18, 'tier': 'fine'}),
('masterwork crit #1', [[[100, 2]], 50, 0], {'score': 100, 'tier': 'masterwork'}),
('heavy rare material #1', [[[90, 3], [30, 1]], 0, 50], {'score': 75, 'tier': 'superior'}),
('control #1', [[[0, 3]], 25, 5], {'score': 2, 'tier': 'common'}),
('control #2', [[[100, 1], [65, 3], [40, 1], [39, 1]], 99, 4], {'score': 71, 'tier': 'masterwork'})]]
for label, args, expected in cases[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fault site critical skill gate #1 | {'score': 58, 'tier': 'fine'} | {'score': 58, 'tier': 'fine'} | Passed |
| fault site critical skill gate #2 | {'score': 64, 'tier': 'fine'} | {'score': 64, 'tier': 'fine'} | Passed |
| partial repair boundary #1 | {'score': 2, 'tier': 'common'} | {'score': 2, 'tier': 'fine'} | Failed |
| partial repair boundary #2 | {'score': 67, 'tier': 'superior'} | {'score': 67, 'tier': 'masterwork'} | Failed |
| heavy rare material #1 | {'score': 75, 'tier': 'superior'} | {'score': 75, 'tier': 'superior'} | Passed |
| score exactly fine cutoff #1 | {'score': 40, 'tier': 'fine'} | {'score': 40, 'tier': 'fine'} | Passed |
| masterwork crit #1 | {'score': 100, 'tier': 'masterwork'} | {'score': 100, 'tier': 'masterwork'} | Passed |
| control #1 | {'score': 40, 'tier': 'fine'} | {'score': 40, 'tier': 'fine'} | Passed |
SHA-256 / fcd938310c18cdccafd3aab04359c87e92b8d373fcb19c443cf0294d07823624
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(materials, skill, crit_roll):
tiers = ['common', 'fine', 'superior', 'masterwork']
cuts = [40, 65, 85]
total_w = sum(w for q, w in materials)
if total_w <= 0:
return {'score': 0, 'tier': 'failed'}
score = sum(q * w for q, w in materials) // total_w + skill // 10
score = min(100, score)
t = sum(1 for c in cuts if score >= c)
if skill >= 25 and crit_roll < 5:
t = min(t + 1, len(tiers) - 1)
return {'score': score, 'tier': tiers[t]}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('fault site critical skill gate #1', [[[58, 0], [40, 0], [58, 1]], 9, 0], {'score': 58, 'tier': 'fine'}),
('fault site critical skill gate #2', [[[0, 0], [64, 3]], 0, 0], {'score': 64, 'tier': 'fine'}),
('partial repair boundary #1', [[[0, 1], [0, 3], [40, 0]], 25, 0], {'score': 2, 'tier': 'fine'}),
('partial repair boundary #2', [[[65, 3], [39, 0]], 25, 4], {'score': 67, 'tier': 'masterwork'}),
('heavy rare material #1', [[[90, 3], [30, 1]], 0, 50], {'score': 75, 'tier': 'superior'}),
('score exactly fine cutoff #1', [[[40, 1]], 0, 99], {'score': 40, 'tier': 'fine'}),
('masterwork crit #1', [[[100, 2]], 50, 0], {'score': 100, 'tier': 'masterwork'}),
('control #1', [[[39, 1]], 10, 50], {'score': 40, 'tier': 'fine'})],
[('fault site critical skill gate #1', [[[30, 1], [0, 1], [84, 1]], 10, 4], {'score': 39, 'tier': 'common'}),
('fault site critical skill gate #2',
[[[64, 2], [69, 2], [65, 2], [89, 1]], 9, 4],
{'score': 69, 'tier': 'superior'}),
('partial repair boundary #1', [[[85, 0], [84, 2], [39, 1]], 25, 0], {'score': 71, 'tier': 'masterwork'}),
('partial repair boundary #2', [[[0, 3], [39, 1]], 25, 0], {'score': 11, 'tier': 'fine'}),
('masterwork crit #1', [[[100, 2]], 50, 0], {'score': 100, 'tier': 'masterwork'}),
('heavy rare material #1', [[[90, 3], [30, 1]], 0, 50], {'score': 75, 'tier': 'superior'}),
('control #1', [[[39, 1]], 10, 50], {'score': 40, 'tier': 'fine'}),
('control #2', [[[39, 1], [100, 3], [85, 1]], 26, 5], {'score': 86, 'tier': 'masterwork'})],
[('fault site critical skill gate #1',
[[[91, 0], [100, 1], [85, 1], [39, 3]], 10, 0],
{'score': 61, 'tier': 'fine'}),
('fault site critical skill gate #2', [[[40, 2], [84, 1]], 24, 0], {'score': 56, 'tier': 'fine'}),
('partial repair boundary #1', [[[64, 1], [100, 0], [79, 1]], 25, 0], {'score': 73, 'tier': 'masterwork'}),
('partial repair boundary #2', [[[84, 1], [65, 2]], 25, 0], {'score': 73, 'tier': 'masterwork'}),
('score exactly fine cutoff #1', [[[40, 1]], 0, 99], {'score': 40, 'tier': 'fine'}),
('masterwork crit #1', [[[100, 2]], 50, 0], {'score': 100, 'tier': 'masterwork'}),
('control #1', [[[39, 1], [100, 3], [85, 1]], 26, 5], {'score': 86, 'tier': 'masterwork'}),
('control #2', [[[39, 3], [85, 0]], 52, 0], {'score': 44, 'tier': 'superior'})],
[('fault site critical skill gate #1', [[[64, 3]], 24, 4], {'score': 66, 'tier': 'superior'}),
('fault site critical skill gate #2', [[[85, 0], [39, 2], [39, 3]], 0, 4], {'score': 39, 'tier': 'common'}),
('partial repair boundary #1', [[[100, 1], [85, 0], [65, 3]], 25, 4], {'score': 75, 'tier': 'masterwork'}),
('partial repair boundary #2', [[[0, 2]], 25, 0], {'score': 2, 'tier': 'fine'}),
('heavy rare material #1', [[[90, 3], [30, 1]], 0, 50], {'score': 75, 'tier': 'superior'}),
('score exactly fine cutoff #1', [[[40, 1]], 0, 99], {'score': 40, 'tier': 'fine'}),
('control #1', [[[39, 1]], 25, 5], {'score': 41, 'tier': 'fine'}),
('control #2', [[[39, 0]], 24, 28], {'score': 0, 'tier': 'failed'})],
[('fault site critical skill gate #1',
[[[39, 3], [40, 1], [84, 1], [85, 1]], 24, 0],
{'score': 56, 'tier': 'fine'}),
('fault site critical skill gate #2', [[[65, 1]], 0, 0], {'score': 65, 'tier': 'superior'}),
('partial repair boundary #1',
[[[64, 1], [84, 0], [100, 1], [65, 1]], 25, 0],
{'score': 78, 'tier': 'masterwork'}),
('partial repair boundary #2', [[[64, 1], [65, 0], [0, 3], [64, 0]], 25, 0], {'score': 18, 'tier': 'fine'}),
('masterwork crit #1', [[[100, 2]], 50, 0], {'score': 100, 'tier': 'masterwork'}),
('heavy rare material #1', [[[90, 3], [30, 1]], 0, 50], {'score': 75, 'tier': 'superior'}),
('control #1', [[[0, 3]], 25, 5], {'score': 2, 'tier': 'common'}),
('control #2', [[[100, 1], [65, 3], [40, 1], [39, 1]], 99, 4], {'score': 71, 'tier': 'masterwork'})]]
for label, args, expected in cases[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fault site critical skill gate #1 | {'score': 58, 'tier': 'fine'} | {'score': 58, 'tier': 'fine'} | Passed |
| fault site critical skill gate #2 | {'score': 64, 'tier': 'fine'} | {'score': 64, 'tier': 'fine'} | Passed |
| partial repair boundary #1 | {'score': 2, 'tier': 'fine'} | {'score': 2, 'tier': 'fine'} | Passed |
| partial repair boundary #2 | {'score': 67, 'tier': 'masterwork'} | {'score': 67, 'tier': 'masterwork'} | Passed |
| heavy rare material #1 | {'score': 75, 'tier': 'superior'} | {'score': 75, 'tier': 'superior'} | Passed |
| score exactly fine cutoff #1 | {'score': 40, 'tier': 'fine'} | {'score': 40, 'tier': 'fine'} | Passed |
| masterwork crit #1 | {'score': 100, 'tier': 'masterwork'} | {'score': 100, 'tier': 'masterwork'} | Passed |
| control #1 | {'score': 40, 'tier': 'fine'} | {'score': 40, 'tier': 'fine'} | Passed |
SHA-256 / 737443f71acee11150233f26a54fe1af4dacc301724c899afda7b8b8ef050da2
Verification & scope
Deterministic toy contract stipulated for this model; integer or exact arithmetic only, not a reproduction of any specific game engine. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:50:46.127026+00:00.
Case digest / 1176406c1875141a7e5f37fed28d0dfe7b21a2bd6be5dff8ff3fd4c8e1b1771d