FA-86241 / Game economy crafting balance / Open access

Profession skill-up colors: Yellow threshold stays orange · case 01

Crafting at the yellow threshold still guarantees a skill-up.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The orange test includes the yellow threshold.

VERIFIED REPAIR

Restore `if skill < yellow:` at the orange boundary step.

Unsuccessful approach: Moving the boundary down turns the last orange point yellow.

Case contract

recipe_levels = [learn, yellow, green, gray]. Skill below learn cannot craft (error "too low"). Per roll (0..99), while skill < 300: chance 100 below yellow (orange), 75 below green, 25 below gray, else 0; the skill goes up when roll < chance and the color is re-evaluated each craft.

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(skill, recipe_levels, rolls):
    learn, yellow, green, gray = recipe_levels
    if skill < learn:
        return {'skill': skill, 'ups': 0, 'error': 'too low'}
    ups = 0
    for r in rolls:
        if skill >= 300:
            break
        if skill <= yellow:
            chance = 100
        elif skill < green:
            chance = 75
        elif skill < gray:
            chance = 25
        else:
            chance = 0
        if r < chance:
            skill += 1
            ups += 1
    return {'skill': skill, 'ups': ups}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('fault site orange boundary #1',
   [118, [118, 118, 123, 131], [75, 0, 66, 99, 25]],
   {'skill': 121, 'ups': 3}),
  ('fault site orange boundary #2', [239, [232, 239, 246, 246], [75]], {'skill': 239, 'ups': 0}),
  ('partial repair boundary #1', [60, [55, 61, 68, 78], [99, 0]], {'skill': 62, 'ups': 2}),
  ('partial repair boundary #2', [104, [98, 105, 115, 129], [99, 25, 99, 99]], {'skill': 106, 'ups': 2}),
  ('exactly at learn level #1', [50, [50, 60, 70, 80], [0]], {'skill': 51, 'ups': 1}),
  ('at cap #1', [299, [200, 250, 275, 320], [0, 0]], {'skill': 300, 'ups': 1}),
  ('gray recipe roll zero #1', [90, [50, 60, 70, 80], [0, 0]], {'skill': 90, 'ups': 0}),
  ('control #1', [23, [8, 14, 23, 38], [75]], {'skill': 23, 'ups': 0})],
 [('fault site orange boundary #1',
   [90, [90, 94, 100, 110], [24, 74, 24, 24, 75, 75, 74]],
   {'skill': 95, 'ups': 5}),
  ('fault site orange boundary #2', [85, [79, 85, 99, 110], [75, 0, 69, 23]], {'skill': 88, 'ups': 3}),
  ('partial repair boundary #1', [44, [39, 45, 51, 58], [75, 0]], {'skill': 46, 'ups': 2}),
  ('partial repair boundary #2', [218, [218, 220, 224, 239], [74, 99]], {'skill': 220, 'ups': 2}),
  ('gray recipe roll zero #1', [90, [50, 60, 70, 80], [0, 0]], {'skill': 90, 'ups': 0}),
  ('exactly at learn level #1', [50, [50, 60, 70, 80], [0]], {'skill': 51, 'ups': 1}),
  ('control #1', [23, [8, 14, 23, 38], [75]], {'skill': 23, 'ups': 0}),
  ('control #2', [84, [64, 70, 80, 85], [0, 99, 75, 25, 25, 99, 75, 0]], {'skill': 85, 'ups': 1})],
 [('fault site orange boundary #1', [265, [265, 266, 266, 277], [0, 75, 0, 0, 24]], {'skill': 269, 'ups': 4}),
  ('fault site orange boundary #2',
   [228, [227, 234, 240, 240], [0, 99, 75, 0, 75, 7, 75]],
   {'skill': 234, 'ups': 6}),
  ('partial repair boundary #1',
   [122, [122, 128, 142, 150], [24, 74, 0, 75, 99, 99]],
   {'skill': 128, 'ups': 6}),
  ('partial repair boundary #2', [80, [79, 81, 96, 100], [75, 53]], {'skill': 82, 'ups': 2}),
  ('at cap #1', [299, [200, 250, 275, 320], [0, 0]], {'skill': 300, 'ups': 1}),
  ('gray recipe roll zero #1', [90, [50, 60, 70, 80], [0, 0]], {'skill': 90, 'ups': 0}),
  ('control #1', [84, [64, 70, 80, 85], [0, 99, 75, 25, 25, 99, 75, 0]], {'skill': 85, 'ups': 1}),
  ('control #2', [289, [288, 314, 330, 340], [50, 0, 50, 0, 0]], {'skill': 294, 'ups': 5})],
 [('fault site orange boundary #1', [182, [167, 182, 188, 193], [76, 0]], {'skill': 183, 'ups': 1}),
  ('fault site orange boundary #2',
   [148, [139, 148, 148, 161], [74, 25, 24, 0, 74, 25, 75, 25]],
   {'skill': 150, 'ups': 2}),
  ('partial repair boundary #1', [181, [180, 182, 184, 187], [99, 16]], {'skill': 183, 'ups': 2}),
  ('partial repair boundary #2', [199, [190, 200, 202, 208], [75, 25, 0, 99]], {'skill': 202, 'ups': 3}),
  ('exactly at learn level #1', [50, [50, 60, 70, 80], [0]], {'skill': 51, 'ups': 1}),
  ('at cap #1', [299, [200, 250, 275, 320], [0, 0]], {'skill': 300, 'ups': 1}),
  ('control #1', [142, [114, 127, 141, 154], [0, 25, 0, 52, 99, 0, 24, 75]], {'skill': 146, 'ups': 4}),
  ('control #2', [36, [33, 37, 40, 42], [24, 25, 24]], {'skill': 39, 'ups': 3})],
 [('fault site orange boundary #1',
   [22, [18, 23, 29, 43], [25, 99, 25, 24, 24, 99, 25, 74]],
   {'skill': 28, 'ups': 6}),
  ('fault site orange boundary #2',
   [91, [76, 91, 95, 102], [75, 34, 24, 25, 75, 99, 75]],
   {'skill': 94, 'ups': 3}),
  ('partial repair boundary #1', [21, [8, 22, 25, 32], [75, 25, 74]], {'skill': 24, 'ups': 3}),
  ('partial repair boundary #2', [196, [194, 200, 202, 202], [75, 24, 75, 94]], {'skill': 200, 'ups': 4}),
  ('gray recipe roll zero #1', [90, [50, 60, 70, 80], [0, 0]], {'skill': 90, 'ups': 0}),
  ('exactly at learn level #1', [50, [50, 60, 70, 80], [0]], {'skill': 51, 'ups': 1}),
  ('control #1', [299, [277, 291, 302, 311], [74, 74, 74, 75, 14, 25, 25, 99]], {'skill': 300, 'ups': 1}),
  ('control #2', [100, [90, 100, 102, 105], [25, 25, 75]], {'skill': 102, 'ups': 2})]]
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 orange boundary #1	`{'skill': 122, 'ups': 4}`	`{'skill': 121, 'ups': 3}`	Failed
fault site orange boundary #2	`{'skill': 240, 'ups': 1}`	`{'skill': 239, 'ups': 0}`	Failed
partial repair boundary #1	`{'skill': 62, 'ups': 2}`	`{'skill': 62, 'ups': 2}`	Passed
partial repair boundary #2	`{'skill': 106, 'ups': 2}`	`{'skill': 106, 'ups': 2}`	Passed
exactly at learn level #1	`{'skill': 51, 'ups': 1}`	`{'skill': 51, 'ups': 1}`	Passed
at cap #1	`{'skill': 300, 'ups': 1}`	`{'skill': 300, 'ups': 1}`	Passed
gray recipe roll zero #1	`{'skill': 90, 'ups': 0}`	`{'skill': 90, 'ups': 0}`	Passed
control #1	`{'skill': 23, 'ups': 0}`	`{'skill': 23, 'ups': 0}`	Passed

SHA-256 / 09139a3a07164626f2bcac409ce44011fe77ef5b2788ef49c8e23ae7581f370f

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(skill, recipe_levels, rolls):
    learn, yellow, green, gray = recipe_levels
    if skill < learn:
        return {'skill': skill, 'ups': 0, 'error': 'too low'}
    ups = 0
    for r in rolls:
        if skill >= 300:
            break
        if skill < yellow - 1:
            chance = 100
        elif skill < green:
            chance = 75
        elif skill < gray:
            chance = 25
        else:
            chance = 0
        if r < chance:
            skill += 1
            ups += 1
    return {'skill': skill, 'ups': ups}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('fault site orange boundary #1',
   [118, [118, 118, 123, 131], [75, 0, 66, 99, 25]],
   {'skill': 121, 'ups': 3}),
  ('fault site orange boundary #2', [239, [232, 239, 246, 246], [75]], {'skill': 239, 'ups': 0}),
  ('partial repair boundary #1', [60, [55, 61, 68, 78], [99, 0]], {'skill': 62, 'ups': 2}),
  ('partial repair boundary #2', [104, [98, 105, 115, 129], [99, 25, 99, 99]], {'skill': 106, 'ups': 2}),
  ('exactly at learn level #1', [50, [50, 60, 70, 80], [0]], {'skill': 51, 'ups': 1}),
  ('at cap #1', [299, [200, 250, 275, 320], [0, 0]], {'skill': 300, 'ups': 1}),
  ('gray recipe roll zero #1', [90, [50, 60, 70, 80], [0, 0]], {'skill': 90, 'ups': 0}),
  ('control #1', [23, [8, 14, 23, 38], [75]], {'skill': 23, 'ups': 0})],
 [('fault site orange boundary #1',
   [90, [90, 94, 100, 110], [24, 74, 24, 24, 75, 75, 74]],
   {'skill': 95, 'ups': 5}),
  ('fault site orange boundary #2', [85, [79, 85, 99, 110], [75, 0, 69, 23]], {'skill': 88, 'ups': 3}),
  ('partial repair boundary #1', [44, [39, 45, 51, 58], [75, 0]], {'skill': 46, 'ups': 2}),
  ('partial repair boundary #2', [218, [218, 220, 224, 239], [74, 99]], {'skill': 220, 'ups': 2}),
  ('gray recipe roll zero #1', [90, [50, 60, 70, 80], [0, 0]], {'skill': 90, 'ups': 0}),
  ('exactly at learn level #1', [50, [50, 60, 70, 80], [0]], {'skill': 51, 'ups': 1}),
  ('control #1', [23, [8, 14, 23, 38], [75]], {'skill': 23, 'ups': 0}),
  ('control #2', [84, [64, 70, 80, 85], [0, 99, 75, 25, 25, 99, 75, 0]], {'skill': 85, 'ups': 1})],
 [('fault site orange boundary #1', [265, [265, 266, 266, 277], [0, 75, 0, 0, 24]], {'skill': 269, 'ups': 4}),
  ('fault site orange boundary #2',
   [228, [227, 234, 240, 240], [0, 99, 75, 0, 75, 7, 75]],
   {'skill': 234, 'ups': 6}),
  ('partial repair boundary #1',
   [122, [122, 128, 142, 150], [24, 74, 0, 75, 99, 99]],
   {'skill': 128, 'ups': 6}),
  ('partial repair boundary #2', [80, [79, 81, 96, 100], [75, 53]], {'skill': 82, 'ups': 2}),
  ('at cap #1', [299, [200, 250, 275, 320], [0, 0]], {'skill': 300, 'ups': 1}),
  ('gray recipe roll zero #1', [90, [50, 60, 70, 80], [0, 0]], {'skill': 90, 'ups': 0}),
  ('control #1', [84, [64, 70, 80, 85], [0, 99, 75, 25, 25, 99, 75, 0]], {'skill': 85, 'ups': 1}),
  ('control #2', [289, [288, 314, 330, 340], [50, 0, 50, 0, 0]], {'skill': 294, 'ups': 5})],
 [('fault site orange boundary #1', [182, [167, 182, 188, 193], [76, 0]], {'skill': 183, 'ups': 1}),
  ('fault site orange boundary #2',
   [148, [139, 148, 148, 161], [74, 25, 24, 0, 74, 25, 75, 25]],
   {'skill': 150, 'ups': 2}),
  ('partial repair boundary #1', [181, [180, 182, 184, 187], [99, 16]], {'skill': 183, 'ups': 2}),
  ('partial repair boundary #2', [199, [190, 200, 202, 208], [75, 25, 0, 99]], {'skill': 202, 'ups': 3}),
  ('exactly at learn level #1', [50, [50, 60, 70, 80], [0]], {'skill': 51, 'ups': 1}),
  ('at cap #1', [299, [200, 250, 275, 320], [0, 0]], {'skill': 300, 'ups': 1}),
  ('control #1', [142, [114, 127, 141, 154], [0, 25, 0, 52, 99, 0, 24, 75]], {'skill': 146, 'ups': 4}),
  ('control #2', [36, [33, 37, 40, 42], [24, 25, 24]], {'skill': 39, 'ups': 3})],
 [('fault site orange boundary #1',
   [22, [18, 23, 29, 43], [25, 99, 25, 24, 24, 99, 25, 74]],
   {'skill': 28, 'ups': 6}),
  ('fault site orange boundary #2',
   [91, [76, 91, 95, 102], [75, 34, 24, 25, 75, 99, 75]],
   {'skill': 94, 'ups': 3}),
  ('partial repair boundary #1', [21, [8, 22, 25, 32], [75, 25, 74]], {'skill': 24, 'ups': 3}),
  ('partial repair boundary #2', [196, [194, 200, 202, 202], [75, 24, 75, 94]], {'skill': 200, 'ups': 4}),
  ('gray recipe roll zero #1', [90, [50, 60, 70, 80], [0, 0]], {'skill': 90, 'ups': 0}),
  ('exactly at learn level #1', [50, [50, 60, 70, 80], [0]], {'skill': 51, 'ups': 1}),
  ('control #1', [299, [277, 291, 302, 311], [74, 74, 74, 75, 14, 25, 25, 99]], {'skill': 300, 'ups': 1}),
  ('control #2', [100, [90, 100, 102, 105], [25, 25, 75]], {'skill': 102, 'ups': 2})]]
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 orange boundary #1	`{'skill': 121, 'ups': 3}`	`{'skill': 121, 'ups': 3}`	Passed
fault site orange boundary #2	`{'skill': 239, 'ups': 0}`	`{'skill': 239, 'ups': 0}`	Passed
partial repair boundary #1	`{'skill': 61, 'ups': 1}`	`{'skill': 62, 'ups': 2}`	Failed
partial repair boundary #2	`{'skill': 105, 'ups': 1}`	`{'skill': 106, 'ups': 2}`	Failed
exactly at learn level #1	`{'skill': 51, 'ups': 1}`	`{'skill': 51, 'ups': 1}`	Passed
at cap #1	`{'skill': 300, 'ups': 1}`	`{'skill': 300, 'ups': 1}`	Passed
gray recipe roll zero #1	`{'skill': 90, 'ups': 0}`	`{'skill': 90, 'ups': 0}`	Passed
control #1	`{'skill': 23, 'ups': 0}`	`{'skill': 23, 'ups': 0}`	Passed

SHA-256 / bfa1633080cc0f42aa649fd0891e97dad6cfff09df7c46b7e63c10ae23309656

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(skill, recipe_levels, rolls):
    learn, yellow, green, gray = recipe_levels
    if skill < learn:
        return {'skill': skill, 'ups': 0, 'error': 'too low'}
    ups = 0
    for r in rolls:
        if skill >= 300:
            break
        if skill < yellow:
            chance = 100
        elif skill < green:
            chance = 75
        elif skill < gray:
            chance = 25
        else:
            chance = 0
        if r < chance:
            skill += 1
            ups += 1
    return {'skill': skill, 'ups': ups}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('fault site orange boundary #1',
   [118, [118, 118, 123, 131], [75, 0, 66, 99, 25]],
   {'skill': 121, 'ups': 3}),
  ('fault site orange boundary #2', [239, [232, 239, 246, 246], [75]], {'skill': 239, 'ups': 0}),
  ('partial repair boundary #1', [60, [55, 61, 68, 78], [99, 0]], {'skill': 62, 'ups': 2}),
  ('partial repair boundary #2', [104, [98, 105, 115, 129], [99, 25, 99, 99]], {'skill': 106, 'ups': 2}),
  ('exactly at learn level #1', [50, [50, 60, 70, 80], [0]], {'skill': 51, 'ups': 1}),
  ('at cap #1', [299, [200, 250, 275, 320], [0, 0]], {'skill': 300, 'ups': 1}),
  ('gray recipe roll zero #1', [90, [50, 60, 70, 80], [0, 0]], {'skill': 90, 'ups': 0}),
  ('control #1', [23, [8, 14, 23, 38], [75]], {'skill': 23, 'ups': 0})],
 [('fault site orange boundary #1',
   [90, [90, 94, 100, 110], [24, 74, 24, 24, 75, 75, 74]],
   {'skill': 95, 'ups': 5}),
  ('fault site orange boundary #2', [85, [79, 85, 99, 110], [75, 0, 69, 23]], {'skill': 88, 'ups': 3}),
  ('partial repair boundary #1', [44, [39, 45, 51, 58], [75, 0]], {'skill': 46, 'ups': 2}),
  ('partial repair boundary #2', [218, [218, 220, 224, 239], [74, 99]], {'skill': 220, 'ups': 2}),
  ('gray recipe roll zero #1', [90, [50, 60, 70, 80], [0, 0]], {'skill': 90, 'ups': 0}),
  ('exactly at learn level #1', [50, [50, 60, 70, 80], [0]], {'skill': 51, 'ups': 1}),
  ('control #1', [23, [8, 14, 23, 38], [75]], {'skill': 23, 'ups': 0}),
  ('control #2', [84, [64, 70, 80, 85], [0, 99, 75, 25, 25, 99, 75, 0]], {'skill': 85, 'ups': 1})],
 [('fault site orange boundary #1', [265, [265, 266, 266, 277], [0, 75, 0, 0, 24]], {'skill': 269, 'ups': 4}),
  ('fault site orange boundary #2',
   [228, [227, 234, 240, 240], [0, 99, 75, 0, 75, 7, 75]],
   {'skill': 234, 'ups': 6}),
  ('partial repair boundary #1',
   [122, [122, 128, 142, 150], [24, 74, 0, 75, 99, 99]],
   {'skill': 128, 'ups': 6}),
  ('partial repair boundary #2', [80, [79, 81, 96, 100], [75, 53]], {'skill': 82, 'ups': 2}),
  ('at cap #1', [299, [200, 250, 275, 320], [0, 0]], {'skill': 300, 'ups': 1}),
  ('gray recipe roll zero #1', [90, [50, 60, 70, 80], [0, 0]], {'skill': 90, 'ups': 0}),
  ('control #1', [84, [64, 70, 80, 85], [0, 99, 75, 25, 25, 99, 75, 0]], {'skill': 85, 'ups': 1}),
  ('control #2', [289, [288, 314, 330, 340], [50, 0, 50, 0, 0]], {'skill': 294, 'ups': 5})],
 [('fault site orange boundary #1', [182, [167, 182, 188, 193], [76, 0]], {'skill': 183, 'ups': 1}),
  ('fault site orange boundary #2',
   [148, [139, 148, 148, 161], [74, 25, 24, 0, 74, 25, 75, 25]],
   {'skill': 150, 'ups': 2}),
  ('partial repair boundary #1', [181, [180, 182, 184, 187], [99, 16]], {'skill': 183, 'ups': 2}),
  ('partial repair boundary #2', [199, [190, 200, 202, 208], [75, 25, 0, 99]], {'skill': 202, 'ups': 3}),
  ('exactly at learn level #1', [50, [50, 60, 70, 80], [0]], {'skill': 51, 'ups': 1}),
  ('at cap #1', [299, [200, 250, 275, 320], [0, 0]], {'skill': 300, 'ups': 1}),
  ('control #1', [142, [114, 127, 141, 154], [0, 25, 0, 52, 99, 0, 24, 75]], {'skill': 146, 'ups': 4}),
  ('control #2', [36, [33, 37, 40, 42], [24, 25, 24]], {'skill': 39, 'ups': 3})],
 [('fault site orange boundary #1',
   [22, [18, 23, 29, 43], [25, 99, 25, 24, 24, 99, 25, 74]],
   {'skill': 28, 'ups': 6}),
  ('fault site orange boundary #2',
   [91, [76, 91, 95, 102], [75, 34, 24, 25, 75, 99, 75]],
   {'skill': 94, 'ups': 3}),
  ('partial repair boundary #1', [21, [8, 22, 25, 32], [75, 25, 74]], {'skill': 24, 'ups': 3}),
  ('partial repair boundary #2', [196, [194, 200, 202, 202], [75, 24, 75, 94]], {'skill': 200, 'ups': 4}),
  ('gray recipe roll zero #1', [90, [50, 60, 70, 80], [0, 0]], {'skill': 90, 'ups': 0}),
  ('exactly at learn level #1', [50, [50, 60, 70, 80], [0]], {'skill': 51, 'ups': 1}),
  ('control #1', [299, [277, 291, 302, 311], [74, 74, 74, 75, 14, 25, 25, 99]], {'skill': 300, 'ups': 1}),
  ('control #2', [100, [90, 100, 102, 105], [25, 25, 75]], {'skill': 102, 'ups': 2})]]
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 orange boundary #1	`{'skill': 121, 'ups': 3}`	`{'skill': 121, 'ups': 3}`	Passed
fault site orange boundary #2	`{'skill': 239, 'ups': 0}`	`{'skill': 239, 'ups': 0}`	Passed
partial repair boundary #1	`{'skill': 62, 'ups': 2}`	`{'skill': 62, 'ups': 2}`	Passed
partial repair boundary #2	`{'skill': 106, 'ups': 2}`	`{'skill': 106, 'ups': 2}`	Passed
exactly at learn level #1	`{'skill': 51, 'ups': 1}`	`{'skill': 51, 'ups': 1}`	Passed
at cap #1	`{'skill': 300, 'ups': 1}`	`{'skill': 300, 'ups': 1}`	Passed
gray recipe roll zero #1	`{'skill': 90, 'ups': 0}`	`{'skill': 90, 'ups': 0}`	Passed
control #1	`{'skill': 23, 'ups': 0}`	`{'skill': 23, 'ups': 0}`	Passed

SHA-256 / 9342df0644784d6df37e2fccf94f925604886b77c065db306b6ad371321ddca0

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 2026-09-29T14:50:47.678751+00:00.

Case digest / bff2cab33d0043cd3e6640bf593f05a7573a4a76c5448dc604e8cbd3b34d9ab0