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FA-85966 / Game economy crafting balance / Open access

Vendor sell saturation: Reputation bonus adds flat coins · case 01

Cheap items gain a huge relative reputation bonus.

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

ROOT CAUSE

The reputation percentage is added as a flat coin amount.

VERIFIED REPAIR

Restore `unit = unit * (100 + bonus) // 100` at the reputation bonus form step.

Unsuccessful approach: Applying the bonus to the base price discards the saturation discount.

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 + bonus
        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}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('regression reputation bonus form #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
  ('partial repair boundary #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0}),
  ('partial repair boundary #2', [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}),
  ('control #1', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2}),
  ('control #2', [3, 20, 3, 'honored'], {'gold': 0, 'sold': 0, 'returned': 3})],
 [('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression reputation bonus form #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
  ('regression reputation bonus form #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
  ('partial repair boundary #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0}),
  ('partial repair boundary #2', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, '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})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression reputation bonus form #1', [3, 12, 4, 'honored'], {'gold': 4, 'sold': 4, 'returned': 0}),
  ('regression reputation bonus form #2', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
  ('partial repair boundary #1', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
  ('regression reputation bonus form #3', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [10, 22, 10, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 10}),
  ('control #2', [99, 20, 9, 'honored'], {'gold': 0, 'sold': 0, 'returned': 9})],
 [('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression reputation bonus form #1', [7, 11, 1, 'honored'], {'gold': 3, 'sold': 1, 'returned': 0}),
  ('regression reputation bonus form #2', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('partial repair boundary #1', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
  ('partial repair boundary #2', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression reputation bonus form #1', [2, 1, 5, 'honored'], {'gold': 5, 'sold': 5, 'returned': 0}),
  ('regression reputation bonus form #2', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
  ('regression reputation bonus form #3', [3, 12, 4, 'honored'], {'gold': 4, 'sold': 4, 'returned': 0}),
  ('regression reputation bonus form #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}),
  ('control #1', [7, 22, 10, 'honored'], {'gold': 0, 'sold': 0, 'returned': 10}),
  ('control #2', [55, 5, 0, 'neutral'], {'gold': 0, 'sold': 0, '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
cap reached mid batch #1{'gold': 52, 'returned': 3, 'sold': 2}{'gold': 34, 'returned': 3, 'sold': 2}Failed
fresh day single sale #1{'gold': 14, 'returned': 0, 'sold': 1}{'gold': 9, 'returned': 0, 'sold': 1}Failed
regression reputation bonus form #1{'gold': 93, 'returned': 0, 'sold': 7}{'gold': 58, 'returned': 0, 'sold': 7}Failed
partial repair boundary #1{'gold': 207, 'returned': 0, 'sold': 3}{'gold': 207, 'returned': 0, 'sold': 3}Passed
partial repair boundary #2{'gold': 17, 'returned': 0, 'sold': 11}{'gold': 17, 'returned': 0, 'sold': 11}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
control #2{'gold': 0, 'returned': 3, 'sold': 0}{'gold': 0, 'returned': 3, 'sold': 0}Passed

SHA-256 / 655c9e90ad0bde9da156f8a3594fb5869e66b5c7f7b52bc3871d037d887d1fad

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 = base_price * (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}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('regression reputation bonus form #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
  ('partial repair boundary #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0}),
  ('partial repair boundary #2', [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}),
  ('control #1', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2}),
  ('control #2', [3, 20, 3, 'honored'], {'gold': 0, 'sold': 0, 'returned': 3})],
 [('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression reputation bonus form #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
  ('regression reputation bonus form #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
  ('partial repair boundary #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0}),
  ('partial repair boundary #2', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, '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})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression reputation bonus form #1', [3, 12, 4, 'honored'], {'gold': 4, 'sold': 4, 'returned': 0}),
  ('regression reputation bonus form #2', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
  ('partial repair boundary #1', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
  ('regression reputation bonus form #3', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [10, 22, 10, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 10}),
  ('control #2', [99, 20, 9, 'honored'], {'gold': 0, 'sold': 0, 'returned': 9})],
 [('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression reputation bonus form #1', [7, 11, 1, 'honored'], {'gold': 3, 'sold': 1, 'returned': 0}),
  ('regression reputation bonus form #2', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('partial repair boundary #1', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
  ('partial repair boundary #2', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression reputation bonus form #1', [2, 1, 5, 'honored'], {'gold': 5, 'sold': 5, 'returned': 0}),
  ('regression reputation bonus form #2', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
  ('regression reputation bonus form #3', [3, 12, 4, 'honored'], {'gold': 4, 'sold': 4, 'returned': 0}),
  ('regression reputation bonus form #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}),
  ('control #1', [7, 22, 10, 'honored'], {'gold': 0, 'sold': 0, 'returned': 10}),
  ('control #2', [55, 5, 0, 'neutral'], {'gold': 0, 'sold': 0, '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
cap reached mid batch #1{'gold': 88, 'returned': 3, 'sold': 2}{'gold': 34, 'returned': 3, 'sold': 2}Failed
fresh day single sale #1{'gold': 9, 'returned': 0, 'sold': 1}{'gold': 9, 'returned': 0, 'sold': 1}Passed
regression reputation bonus form #1{'gold': 70, 'returned': 0, 'sold': 7}{'gold': 58, 'returned': 0, 'sold': 7}Failed
partial repair boundary #1{'gold': 297, 'returned': 0, 'sold': 3}{'gold': 207, 'returned': 0, 'sold': 3}Failed
partial repair boundary #2{'gold': 33, 'returned': 0, 'sold': 11}{'gold': 17, 'returned': 0, 'sold': 11}Failed
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
control #2{'gold': 0, 'returned': 3, 'sold': 0}{'gold': 0, 'returned': 3, 'sold': 0}Passed

SHA-256 / 031e8556ed008489d5cc4491c2753f96421a3c42ca55ff68ed8a561bea512bd4

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}),
  ('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('regression reputation bonus form #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
  ('partial repair boundary #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0}),
  ('partial repair boundary #2', [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}),
  ('control #1', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2}),
  ('control #2', [3, 20, 3, 'honored'], {'gold': 0, 'sold': 0, 'returned': 3})],
 [('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression reputation bonus form #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
  ('regression reputation bonus form #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
  ('partial repair boundary #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0}),
  ('partial repair boundary #2', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, '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})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression reputation bonus form #1', [3, 12, 4, 'honored'], {'gold': 4, 'sold': 4, 'returned': 0}),
  ('regression reputation bonus form #2', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
  ('partial repair boundary #1', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
  ('regression reputation bonus form #3', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [10, 22, 10, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 10}),
  ('control #2', [99, 20, 9, 'honored'], {'gold': 0, 'sold': 0, 'returned': 9})],
 [('fresh day single sale #1', [9, 0, 1, 'friendly'], {'gold': 9, 'sold': 1, 'returned': 0}),
  ('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression reputation bonus form #1', [7, 11, 1, 'honored'], {'gold': 3, 'sold': 1, 'returned': 0}),
  ('regression reputation bonus form #2', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('partial repair boundary #1', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
  ('partial repair boundary #2', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, 'returned': 0}),
  ('cheap junk at saturation #1', [1, 12, 3, 'neutral'], {'gold': 3, 'sold': 3, 'returned': 0}),
  ('control #1', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression reputation bonus form #1', [2, 1, 5, 'honored'], {'gold': 5, 'sold': 5, 'returned': 0}),
  ('regression reputation bonus form #2', [99, 12, 4, 'friendly'], {'gold': 160, 'sold': 4, 'returned': 0}),
  ('regression reputation bonus form #3', [3, 12, 4, 'honored'], {'gold': 4, 'sold': 4, 'returned': 0}),
  ('regression reputation bonus form #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}),
  ('control #1', [7, 22, 10, 'honored'], {'gold': 0, 'sold': 0, 'returned': 10}),
  ('control #2', [55, 5, 0, 'neutral'], {'gold': 0, 'sold': 0, '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
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
regression reputation bonus form #1{'gold': 58, 'returned': 0, 'sold': 7}{'gold': 58, 'returned': 0, 'sold': 7}Passed
partial repair boundary #1{'gold': 207, 'returned': 0, 'sold': 3}{'gold': 207, 'returned': 0, 'sold': 3}Passed
partial repair boundary #2{'gold': 17, 'returned': 0, 'sold': 11}{'gold': 17, 'returned': 0, 'sold': 11}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
control #2{'gold': 0, 'returned': 3, 'sold': 0}{'gold': 0, 'returned': 3, 'sold': 0}Passed

SHA-256 / b3aaa68013e77fa29fc4e2ba20af429768885c64c83a4b6db370c00a78a03912

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 2026-09-29T14:50:45.165572+00:00.

Case digest / 3aad9e106619e843e12bf6450c1807decf28bbc8fe84754010641c1dd3bb5e0f