FA-85956 / Game economy crafting balance / Open access
Vendor sell saturation: Saturation is uncapped · case 01
Late sales collapse to the one-coin minimum instead of 40% value.
ROOT CAUSE
The saturation percentage is not capped at 60.
VERIFIED REPAIR
Restore `min(60, 5 * done)` at the saturation ceiling step.
Unsuccessful approach: A 50% cap overpays heavily saturated items.
Case contract
Selling qty units after `sales` units already sold today. Daily cap 20 units total; excess is returned. Per unit, with done = units sold today before it: saturation = min(60, 5*done) percent; unit = floor(base*(100-sat)/100), then floor(unit*(100+bonus)/100) with bonus neutral 0, friendly 5, honored 10; each unit pays at least 1.
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(base_price, sales, qty, reputation):
bonus = {'neutral': 0, 'friendly': 5, 'honored': 10}[reputation]
gold = 0
sold = 0
for i in range(qty):
done = sales + sold
if done >= 20:
break
sat = 5 * done
unit = base_price * (100 - sat) // 100
unit = unit * (100 + bonus) // 100
gold += max(1, unit)
sold += 1
return {'gold': gold, 'sold': sold, 'returned': qty - sold}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
('regression saturation ceiling #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('regression saturation ceiling #3', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
('regression saturation ceiling #4', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('regression saturation ceiling #2', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
('regression saturation ceiling #3', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
('regression saturation ceiling #4', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
('regression saturation ceiling #2', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
('regression saturation ceiling #3', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
('regression saturation ceiling #4', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
('regression saturation ceiling #2', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
('regression saturation ceiling #3', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
('regression saturation ceiling #4', [99, 15, 5, 'honored'], {'gold': 210, 'sold': 5, 'returned': 0}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
('regression saturation ceiling #2', [99, 15, 5, 'honored'], {'gold': 210, 'sold': 5, 'returned': 0}),
('regression saturation ceiling #3', [70, 11, 3, 'friendly'], {'gold': 90, 'sold': 3, 'returned': 0}),
('regression saturation ceiling #4', [160, 15, 12, 'friendly'], {'gold': 335, 'sold': 5, 'returned': 7}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0})]]
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 |
|---|---|---|---|
| cap reached mid batch #1 | {'gold': 6, 'returned': 3, 'sold': 2} | {'gold': 34, 'returned': 3, 'sold': 2} | Failed |
| regression saturation ceiling #1 | {'gold': 331, 'returned': 0, 'sold': 7} | {'gold': 532, 'returned': 0, 'sold': 7} | Failed |
| regression saturation ceiling #2 | {'gold': 50, 'returned': 0, 'sold': 10} | {'gold': 52, 'returned': 0, 'sold': 10} | Failed |
| regression saturation ceiling #3 | {'gold': 9, 'returned': 0, 'sold': 6} | {'gold': 12, 'returned': 0, 'sold': 6} | Failed |
| regression saturation ceiling #4 | {'gold': 42, 'returned': 4, 'sold': 8} | {'gold': 80, 'returned': 4, 'sold': 8} | Failed |
| fresh day single sale #1 | {'gold': 9, 'returned': 0, 'sold': 1} | {'gold': 9, 'returned': 0, 'sold': 1} | Passed |
| cheap junk at saturation #1 | {'gold': 3, 'returned': 0, 'sold': 3} | {'gold': 3, 'returned': 0, 'sold': 3} | Passed |
| control #1 | {'gold': 207, 'returned': 0, 'sold': 3} | {'gold': 207, 'returned': 0, 'sold': 3} | Passed |
SHA-256 / 25bc98ee1a1ed1a56f59598a732bd23a64e5cfbdc08d177937f58f596ba4d5ff
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(base_price, sales, qty, reputation):
bonus = {'neutral': 0, 'friendly': 5, 'honored': 10}[reputation]
gold = 0
sold = 0
for i in range(qty):
done = sales + sold
if done >= 20:
break
sat = min(50, 5 * done)
unit = base_price * (100 - sat) // 100
unit = unit * (100 + bonus) // 100
gold += max(1, unit)
sold += 1
return {'gold': gold, 'sold': sold, 'returned': qty - sold}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
('regression saturation ceiling #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('regression saturation ceiling #3', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
('regression saturation ceiling #4', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('regression saturation ceiling #2', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
('regression saturation ceiling #3', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
('regression saturation ceiling #4', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
('regression saturation ceiling #2', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
('regression saturation ceiling #3', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
('regression saturation ceiling #4', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
('regression saturation ceiling #2', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
('regression saturation ceiling #3', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
('regression saturation ceiling #4', [99, 15, 5, 'honored'], {'gold': 210, 'sold': 5, 'returned': 0}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
('regression saturation ceiling #2', [99, 15, 5, 'honored'], {'gold': 210, 'sold': 5, 'returned': 0}),
('regression saturation ceiling #3', [70, 11, 3, 'friendly'], {'gold': 90, 'sold': 3, 'returned': 0}),
('regression saturation ceiling #4', [160, 15, 12, 'friendly'], {'gold': 335, 'sold': 5, 'returned': 7}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0})]]
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 |
|---|---|---|---|
| cap reached mid batch #1 | {'gold': 44, 'returned': 3, 'sold': 2} | {'gold': 34, 'returned': 3, 'sold': 2} | Failed |
| regression saturation ceiling #1 | {'gold': 665, 'returned': 0, 'sold': 7} | {'gold': 532, 'returned': 0, 'sold': 7} | Failed |
| regression saturation ceiling #2 | {'gold': 56, 'returned': 0, 'sold': 10} | {'gold': 52, 'returned': 0, 'sold': 10} | Failed |
| regression saturation ceiling #3 | {'gold': 18, 'returned': 0, 'sold': 6} | {'gold': 12, 'returned': 0, 'sold': 6} | Failed |
| regression saturation ceiling #4 | {'gold': 96, 'returned': 4, 'sold': 8} | {'gold': 80, 'returned': 4, 'sold': 8} | Failed |
| fresh day single sale #1 | {'gold': 9, 'returned': 0, 'sold': 1} | {'gold': 9, 'returned': 0, 'sold': 1} | Passed |
| cheap junk at saturation #1 | {'gold': 3, 'returned': 0, 'sold': 3} | {'gold': 3, 'returned': 0, 'sold': 3} | Passed |
| control #1 | {'gold': 207, 'returned': 0, 'sold': 3} | {'gold': 207, 'returned': 0, 'sold': 3} | Passed |
SHA-256 / 25cbd4af7214c54926478958c3d111717c2a1e426abd4c895f9c98764cc76233
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(base_price, sales, qty, reputation):
bonus = {'neutral': 0, 'friendly': 5, 'honored': 10}[reputation]
gold = 0
sold = 0
for i in range(qty):
done = sales + sold
if done >= 20:
break
sat = min(60, 5 * done)
unit = base_price * (100 - sat) // 100
unit = unit * (100 + bonus) // 100
gold += max(1, unit)
sold += 1
return {'gold': gold, 'sold': sold, 'returned': qty - sold}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
('regression saturation ceiling #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('regression saturation ceiling #3', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
('regression saturation ceiling #4', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('regression saturation ceiling #2', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
('regression saturation ceiling #3', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
('regression saturation ceiling #4', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
('regression saturation ceiling #2', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
('regression saturation ceiling #3', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
('regression saturation ceiling #4', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
('regression saturation ceiling #2', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
('regression saturation ceiling #3', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
('regression saturation ceiling #4', [99, 15, 5, 'honored'], {'gold': 210, 'sold': 5, 'returned': 0}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression saturation ceiling #1', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
('regression saturation ceiling #2', [99, 15, 5, 'honored'], {'gold': 210, 'sold': 5, 'returned': 0}),
('regression saturation ceiling #3', [70, 11, 3, 'friendly'], {'gold': 90, 'sold': 3, 'returned': 0}),
('regression saturation ceiling #4', [160, 15, 12, 'friendly'], {'gold': 335, 'sold': 5, 'returned': 7}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('control #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0})]]
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 |
|---|---|---|---|
| cap reached mid batch #1 | {'gold': 34, 'returned': 3, 'sold': 2} | {'gold': 34, 'returned': 3, 'sold': 2} | Passed |
| regression saturation ceiling #1 | {'gold': 532, 'returned': 0, 'sold': 7} | {'gold': 532, 'returned': 0, 'sold': 7} | Passed |
| regression saturation ceiling #2 | {'gold': 52, 'returned': 0, 'sold': 10} | {'gold': 52, 'returned': 0, 'sold': 10} | Passed |
| regression saturation ceiling #3 | {'gold': 12, 'returned': 0, 'sold': 6} | {'gold': 12, 'returned': 0, 'sold': 6} | Passed |
| regression saturation ceiling #4 | {'gold': 80, 'returned': 4, 'sold': 8} | {'gold': 80, 'returned': 4, 'sold': 8} | Passed |
| fresh day single sale #1 | {'gold': 9, 'returned': 0, 'sold': 1} | {'gold': 9, 'returned': 0, 'sold': 1} | Passed |
| cheap junk at saturation #1 | {'gold': 3, 'returned': 0, 'sold': 3} | {'gold': 3, 'returned': 0, 'sold': 3} | Passed |
| control #1 | {'gold': 207, 'returned': 0, 'sold': 3} | {'gold': 207, 'returned': 0, 'sold': 3} | Passed |
SHA-256 / 3de6f2650b2ed52739957ed3c10c157a373fd25ac18f2b031b17a8f6145d751c
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 2026-09-29T14:50:45.077409+00:00.
Case digest / 6b4a59b93da85e02d7cac691cbcdff68e130178d12d6204bb71450aedece5ec4