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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.

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

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 fixtureActualExpectedOutcome
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 fixtureActualExpectedOutcome
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 fixtureActualExpectedOutcome
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