FA-85961 / Game economy crafting balance / Open access
Vendor sell saturation: Saturated price rounds in the player favor · case 01
Vendors pay fractional coins upward, leaking currency.
ROOT CAUSE
The saturated price is rounded up rather than floored.
VERIFIED REPAIR
Restore `unit = base_price * (100 - sat) // 100` at the saturation rounding step.
Unsuccessful approach: Round-to-nearest still pays up whenever the fraction is one half or more.
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 = 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 = [[('fault site saturation rounding #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0}),
('regression saturation rounding #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0}),
('regression saturation rounding #2', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
('regression saturation rounding #3', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('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', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2})],
[('regression saturation rounding #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
('regression saturation rounding #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('regression saturation rounding #3', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, 'returned': 0}),
('regression saturation rounding #4', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('control #1', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2}),
('control #2', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0})],
[('regression saturation rounding #1', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, 'returned': 0}),
('fault site saturation rounding #1', [3, 12, 4, 'honored'], {'gold': 4, 'sold': 4, 'returned': 0}),
('regression saturation rounding #2', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('regression saturation rounding #3', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, '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', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
('control #2', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5})],
[('regression saturation rounding #1', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('fault site saturation rounding #1', [7, 11, 1, 'honored'], {'gold': 3, 'sold': 1, 'returned': 0}),
('regression saturation rounding #2', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
('regression saturation rounding #3', [2, 1, 5, 'honored'], {'gold': 5, 'sold': 5, 'returned': 0}),
('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('control #1', [3, 20, 3, 'honored'], {'gold': 0, 'sold': 0, 'returned': 3}),
('control #2', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4})],
[('regression saturation rounding #1', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
('regression saturation rounding #2', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
('regression saturation rounding #3', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
('regression saturation rounding #4', [3, 1, 12, 'honored'], {'gold': 18, 'sold': 12, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('control #1', [10, 22, 10, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 10}),
('control #2', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4})]]
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 saturation rounding #1 | {'gold': 210, 'returned': 0, 'sold': 3} | {'gold': 207, 'returned': 0, 'sold': 3} | Failed |
| regression saturation rounding #1 | {'gold': 28, 'returned': 0, 'sold': 11} | {'gold': 17, 'returned': 0, 'sold': 11} | Failed |
| regression saturation rounding #2 | {'gold': 61, 'returned': 0, 'sold': 7} | {'gold': 58, 'returned': 0, 'sold': 7} | Failed |
| regression saturation rounding #3 | {'gold': 56, 'returned': 0, 'sold': 10} | {'gold': 52, 'returned': 0, 'sold': 10} | Failed |
| cap reached mid batch #1 | {'gold': 34, 'returned': 3, 'sold': 2} | {'gold': 34, 'returned': 3, 'sold': 2} | 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': 0, 'returned': 2, 'sold': 0} | {'gold': 0, 'returned': 2, 'sold': 0} | Passed |
SHA-256 / 4cdbaba2d282311fa23aa2dbc7a9018b5d030cb7fdd9a740a630bdc7ee974053
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(60, 5 * done)
unit = round(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 = [[('fault site saturation rounding #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0}),
('regression saturation rounding #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0}),
('regression saturation rounding #2', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
('regression saturation rounding #3', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('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', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2})],
[('regression saturation rounding #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
('regression saturation rounding #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('regression saturation rounding #3', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, 'returned': 0}),
('regression saturation rounding #4', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('control #1', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2}),
('control #2', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0})],
[('regression saturation rounding #1', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, 'returned': 0}),
('fault site saturation rounding #1', [3, 12, 4, 'honored'], {'gold': 4, 'sold': 4, 'returned': 0}),
('regression saturation rounding #2', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('regression saturation rounding #3', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, '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', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
('control #2', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5})],
[('regression saturation rounding #1', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('fault site saturation rounding #1', [7, 11, 1, 'honored'], {'gold': 3, 'sold': 1, 'returned': 0}),
('regression saturation rounding #2', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
('regression saturation rounding #3', [2, 1, 5, 'honored'], {'gold': 5, 'sold': 5, 'returned': 0}),
('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('control #1', [3, 20, 3, 'honored'], {'gold': 0, 'sold': 0, 'returned': 3}),
('control #2', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4})],
[('regression saturation rounding #1', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
('regression saturation rounding #2', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
('regression saturation rounding #3', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
('regression saturation rounding #4', [3, 1, 12, 'honored'], {'gold': 18, 'sold': 12, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('control #1', [10, 22, 10, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 10}),
('control #2', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4})]]
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 saturation rounding #1 | {'gold': 207, 'returned': 0, 'sold': 3} | {'gold': 207, 'returned': 0, 'sold': 3} | Passed |
| regression saturation rounding #1 | {'gold': 24, 'returned': 0, 'sold': 11} | {'gold': 17, 'returned': 0, 'sold': 11} | Failed |
| regression saturation rounding #2 | {'gold': 60, 'returned': 0, 'sold': 7} | {'gold': 58, 'returned': 0, 'sold': 7} | Failed |
| regression saturation rounding #3 | {'gold': 54, 'returned': 0, 'sold': 10} | {'gold': 52, 'returned': 0, 'sold': 10} | Failed |
| cap reached mid batch #1 | {'gold': 34, 'returned': 3, 'sold': 2} | {'gold': 34, 'returned': 3, 'sold': 2} | 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': 0, 'returned': 2, 'sold': 0} | {'gold': 0, 'returned': 2, 'sold': 0} | Passed |
SHA-256 / 4ad779cbc1a5751e119a4bcedddd24205861e7fe7eb1ac4fb30c4ed87908e235
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 = [[('fault site saturation rounding #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0}),
('regression saturation rounding #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0}),
('regression saturation rounding #2', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
('regression saturation rounding #3', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('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', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2})],
[('regression saturation rounding #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
('regression saturation rounding #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('regression saturation rounding #3', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, 'returned': 0}),
('regression saturation rounding #4', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('control #1', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2}),
('control #2', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0})],
[('regression saturation rounding #1', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, 'returned': 0}),
('fault site saturation rounding #1', [3, 12, 4, 'honored'], {'gold': 4, 'sold': 4, 'returned': 0}),
('regression saturation rounding #2', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('regression saturation rounding #3', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, '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', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
('control #2', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5})],
[('regression saturation rounding #1', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('fault site saturation rounding #1', [7, 11, 1, 'honored'], {'gold': 3, 'sold': 1, 'returned': 0}),
('regression saturation rounding #2', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
('regression saturation rounding #3', [2, 1, 5, 'honored'], {'gold': 5, 'sold': 5, 'returned': 0}),
('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
('control #1', [3, 20, 3, 'honored'], {'gold': 0, 'sold': 0, 'returned': 3}),
('control #2', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4})],
[('regression saturation rounding #1', [7, 12, 6, 'neutral'], {'gold': 12, 'sold': 6, 'returned': 0}),
('regression saturation rounding #2', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, 'returned': 0}),
('regression saturation rounding #3', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
('regression saturation rounding #4', [3, 1, 12, 'honored'], {'gold': 18, 'sold': 12, 'returned': 0}),
('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('control #1', [10, 22, 10, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 10}),
('control #2', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4})]]
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 saturation rounding #1 | {'gold': 207, 'returned': 0, 'sold': 3} | {'gold': 207, 'returned': 0, 'sold': 3} | Passed |
| regression saturation rounding #1 | {'gold': 17, 'returned': 0, 'sold': 11} | {'gold': 17, 'returned': 0, 'sold': 11} | Passed |
| regression saturation rounding #2 | {'gold': 58, 'returned': 0, 'sold': 7} | {'gold': 58, 'returned': 0, 'sold': 7} | Passed |
| regression saturation rounding #3 | {'gold': 52, 'returned': 0, 'sold': 10} | {'gold': 52, 'returned': 0, 'sold': 10} | Passed |
| cap reached mid batch #1 | {'gold': 34, 'returned': 3, 'sold': 2} | {'gold': 34, 'returned': 3, 'sold': 2} | 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': 0, 'returned': 2, 'sold': 0} | {'gold': 0, 'returned': 2, 'sold': 0} | Passed |
SHA-256 / 59cf493395405a0bfd011a4d6381432f7e484edfd5677ed87d6db186b2f003d0
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 2026-09-29T14:50:45.122838+00:00.
Case digest / 9a0c8b7c701851ed20d1773baecbfb1970a7cc2e9586df294420f87a3e466e26