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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.

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

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 fixtureActualExpectedOutcome
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 fixtureActualExpectedOutcome
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 fixtureActualExpectedOutcome
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