FA-85971 / Game economy crafting balance / Open access
Vendor sell saturation: Saturated junk sells for zero · case 01
Low-value items pay nothing once saturated though a unit is consumed.
ROOT CAUSE
The one-coin minimum per unit is not applied.
VERIFIED REPAIR
Restore `max(1, unit)` at the minimum payout step.
Unsuccessful approach: Dropping the minimum at full saturation still pays zero for junk sold late.
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 += 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 = [[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('regression minimum payout #1', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
('fault site minimum payout #1', [1, 0, 8, 'honored'], {'gold': 8, 'sold': 8, 'returned': 0}),
('regression minimum payout #2', [1, 15, 12, 'friendly'], {'gold': 5, 'sold': 5, 'returned': 7}),
('regression minimum payout #3', [1, 5, 8, 'neutral'], {'gold': 8, 'sold': 8, '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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('fault site minimum payout #1', [1, 0, 8, 'honored'], {'gold': 8, 'sold': 8, 'returned': 0}),
('regression minimum payout #1', [1, 15, 12, 'friendly'], {'gold': 5, 'sold': 5, 'returned': 7}),
('regression minimum payout #2', [1, 5, 8, 'neutral'], {'gold': 8, 'sold': 8, 'returned': 0}),
('regression minimum payout #3', [1, 11, 7, 'neutral'], {'gold': 7, 'sold': 7, '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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('regression minimum payout #1', [1, 5, 8, 'neutral'], {'gold': 8, 'sold': 8, 'returned': 0}),
('regression minimum payout #2', [1, 11, 7, 'neutral'], {'gold': 7, 'sold': 7, 'returned': 0}),
('regression minimum payout #3', [2, 5, 10, 'honored'], {'gold': 10, 'sold': 10, 'returned': 0}),
('regression minimum payout #4', [2, 19, 9, 'friendly'], {'gold': 1, 'sold': 1, 'returned': 8}),
('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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('regression minimum payout #1', [2, 5, 10, 'honored'], {'gold': 10, 'sold': 10, 'returned': 0}),
('regression minimum payout #2', [2, 19, 9, 'friendly'], {'gold': 1, 'sold': 1, 'returned': 8}),
('regression minimum payout #3', [2, 19, 3, 'neutral'], {'gold': 1, 'sold': 1, 'returned': 2}),
('regression minimum payout #4', [2, 18, 4, 'neutral'], {'gold': 2, 'sold': 2, 'returned': 2}),
('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, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0})],
[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('fault site minimum payout #1', [2, 1, 11, 'neutral'], {'gold': 11, 'sold': 11, 'returned': 0}),
('fault site minimum payout #2', [1, 5, 6, 'honored'], {'gold': 6, 'sold': 6, 'returned': 0}),
('regression minimum payout #1', [2, 18, 4, 'neutral'], {'gold': 2, 'sold': 2, 'returned': 2}),
('regression minimum payout #2', [1, 15, 2, 'neutral'], {'gold': 2, 'sold': 2, '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', [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 |
|---|---|---|---|
| cheap junk at saturation #1 | {'gold': 0, 'returned': 0, 'sold': 3} | {'gold': 3, 'returned': 0, 'sold': 3} | Failed |
| regression minimum payout #1 | {'gold': 0, 'returned': 5, 'sold': 5} | {'gold': 5, 'returned': 5, 'sold': 5} | Failed |
| fault site minimum payout #1 | {'gold': 1, 'returned': 0, 'sold': 8} | {'gold': 8, 'returned': 0, 'sold': 8} | Failed |
| regression minimum payout #2 | {'gold': 0, 'returned': 7, 'sold': 5} | {'gold': 5, 'returned': 7, 'sold': 5} | Failed |
| regression minimum payout #3 | {'gold': 0, 'returned': 0, 'sold': 8} | {'gold': 8, 'returned': 0, 'sold': 8} | 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 |
| control #1 | {'gold': 207, 'returned': 0, 'sold': 3} | {'gold': 207, 'returned': 0, 'sold': 3} | Passed |
SHA-256 / 7e174b637ab72cb3f5658cc89e66623f95469ec4103fa8e466406bd33ab8c615
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 = base_price * (100 - sat) // 100
unit = unit * (100 + bonus) // 100
gold += max(1, unit) if sat < 60 else 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 = [[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('regression minimum payout #1', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
('fault site minimum payout #1', [1, 0, 8, 'honored'], {'gold': 8, 'sold': 8, 'returned': 0}),
('regression minimum payout #2', [1, 15, 12, 'friendly'], {'gold': 5, 'sold': 5, 'returned': 7}),
('regression minimum payout #3', [1, 5, 8, 'neutral'], {'gold': 8, 'sold': 8, '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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('fault site minimum payout #1', [1, 0, 8, 'honored'], {'gold': 8, 'sold': 8, 'returned': 0}),
('regression minimum payout #1', [1, 15, 12, 'friendly'], {'gold': 5, 'sold': 5, 'returned': 7}),
('regression minimum payout #2', [1, 5, 8, 'neutral'], {'gold': 8, 'sold': 8, 'returned': 0}),
('regression minimum payout #3', [1, 11, 7, 'neutral'], {'gold': 7, 'sold': 7, '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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('regression minimum payout #1', [1, 5, 8, 'neutral'], {'gold': 8, 'sold': 8, 'returned': 0}),
('regression minimum payout #2', [1, 11, 7, 'neutral'], {'gold': 7, 'sold': 7, 'returned': 0}),
('regression minimum payout #3', [2, 5, 10, 'honored'], {'gold': 10, 'sold': 10, 'returned': 0}),
('regression minimum payout #4', [2, 19, 9, 'friendly'], {'gold': 1, 'sold': 1, 'returned': 8}),
('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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('regression minimum payout #1', [2, 5, 10, 'honored'], {'gold': 10, 'sold': 10, 'returned': 0}),
('regression minimum payout #2', [2, 19, 9, 'friendly'], {'gold': 1, 'sold': 1, 'returned': 8}),
('regression minimum payout #3', [2, 19, 3, 'neutral'], {'gold': 1, 'sold': 1, 'returned': 2}),
('regression minimum payout #4', [2, 18, 4, 'neutral'], {'gold': 2, 'sold': 2, 'returned': 2}),
('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, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0})],
[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('fault site minimum payout #1', [2, 1, 11, 'neutral'], {'gold': 11, 'sold': 11, 'returned': 0}),
('fault site minimum payout #2', [1, 5, 6, 'honored'], {'gold': 6, 'sold': 6, 'returned': 0}),
('regression minimum payout #1', [2, 18, 4, 'neutral'], {'gold': 2, 'sold': 2, 'returned': 2}),
('regression minimum payout #2', [1, 15, 2, 'neutral'], {'gold': 2, 'sold': 2, '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', [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 |
|---|---|---|---|
| cheap junk at saturation #1 | {'gold': 0, 'returned': 0, 'sold': 3} | {'gold': 3, 'returned': 0, 'sold': 3} | Failed |
| regression minimum payout #1 | {'gold': 0, 'returned': 5, 'sold': 5} | {'gold': 5, 'returned': 5, 'sold': 5} | Failed |
| fault site minimum payout #1 | {'gold': 8, 'returned': 0, 'sold': 8} | {'gold': 8, 'returned': 0, 'sold': 8} | Passed |
| regression minimum payout #2 | {'gold': 0, 'returned': 7, 'sold': 5} | {'gold': 5, 'returned': 7, 'sold': 5} | Failed |
| regression minimum payout #3 | {'gold': 7, 'returned': 0, 'sold': 8} | {'gold': 8, 'returned': 0, 'sold': 8} | 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 |
| control #1 | {'gold': 207, 'returned': 0, 'sold': 3} | {'gold': 207, 'returned': 0, 'sold': 3} | Passed |
SHA-256 / 63702076b330c4c3eca2cc1c4ccca9d67a3a9f5033fc31fa337fc1f6776ad35d
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 = [[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('regression minimum payout #1', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
('fault site minimum payout #1', [1, 0, 8, 'honored'], {'gold': 8, 'sold': 8, 'returned': 0}),
('regression minimum payout #2', [1, 15, 12, 'friendly'], {'gold': 5, 'sold': 5, 'returned': 7}),
('regression minimum payout #3', [1, 5, 8, 'neutral'], {'gold': 8, 'sold': 8, '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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('fault site minimum payout #1', [1, 0, 8, 'honored'], {'gold': 8, 'sold': 8, 'returned': 0}),
('regression minimum payout #1', [1, 15, 12, 'friendly'], {'gold': 5, 'sold': 5, 'returned': 7}),
('regression minimum payout #2', [1, 5, 8, 'neutral'], {'gold': 8, 'sold': 8, 'returned': 0}),
('regression minimum payout #3', [1, 11, 7, 'neutral'], {'gold': 7, 'sold': 7, '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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('regression minimum payout #1', [1, 5, 8, 'neutral'], {'gold': 8, 'sold': 8, 'returned': 0}),
('regression minimum payout #2', [1, 11, 7, 'neutral'], {'gold': 7, 'sold': 7, 'returned': 0}),
('regression minimum payout #3', [2, 5, 10, 'honored'], {'gold': 10, 'sold': 10, 'returned': 0}),
('regression minimum payout #4', [2, 19, 9, 'friendly'], {'gold': 1, 'sold': 1, 'returned': 8}),
('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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('regression minimum payout #1', [2, 5, 10, 'honored'], {'gold': 10, 'sold': 10, 'returned': 0}),
('regression minimum payout #2', [2, 19, 9, 'friendly'], {'gold': 1, 'sold': 1, 'returned': 8}),
('regression minimum payout #3', [2, 19, 3, 'neutral'], {'gold': 1, 'sold': 1, 'returned': 2}),
('regression minimum payout #4', [2, 18, 4, 'neutral'], {'gold': 2, 'sold': 2, 'returned': 2}),
('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, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0})],
[('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
('fault site minimum payout #1', [2, 1, 11, 'neutral'], {'gold': 11, 'sold': 11, 'returned': 0}),
('fault site minimum payout #2', [1, 5, 6, 'honored'], {'gold': 6, 'sold': 6, 'returned': 0}),
('regression minimum payout #1', [2, 18, 4, 'neutral'], {'gold': 2, 'sold': 2, 'returned': 2}),
('regression minimum payout #2', [1, 15, 2, 'neutral'], {'gold': 2, 'sold': 2, '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', [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 |
|---|---|---|---|
| cheap junk at saturation #1 | {'gold': 3, 'returned': 0, 'sold': 3} | {'gold': 3, 'returned': 0, 'sold': 3} | Passed |
| regression minimum payout #1 | {'gold': 5, 'returned': 5, 'sold': 5} | {'gold': 5, 'returned': 5, 'sold': 5} | Passed |
| fault site minimum payout #1 | {'gold': 8, 'returned': 0, 'sold': 8} | {'gold': 8, 'returned': 0, 'sold': 8} | Passed |
| regression minimum payout #2 | {'gold': 5, 'returned': 7, 'sold': 5} | {'gold': 5, 'returned': 7, 'sold': 5} | Passed |
| regression minimum payout #3 | {'gold': 8, 'returned': 0, 'sold': 8} | {'gold': 8, 'returned': 0, 'sold': 8} | 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 |
| control #1 | {'gold': 207, 'returned': 0, 'sold': 3} | {'gold': 207, 'returned': 0, 'sold': 3} | Passed |
SHA-256 / e89a5a8f18a6727f4afd2bdc6d8069fb220e6a876430477e4e59f32981d5d798
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 2026-09-29T14:50:45.375272+00:00.
Case digest / a5961a082c9db2e605932f3bfa9907096c75dc50edfb97aeacec0997ae722416