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FA-85951 / Game economy crafting balance / Open access

Vendor sell saturation: Vendor buys a 21st unit · case 01

The daily cap admits one unit too many.

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

ROOT CAUSE

The cap comparison is strict so the unit at index 20 is still bought.

VERIFIED REPAIR

Restore `if done >= 20:` at the daily cap check step.

Unsuccessful approach: Checking only this batch lets repeated trips exceed the daily cap.

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 = [[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression daily cap check #1', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
  ('regression daily cap check #2', [3, 20, 3, 'honored'], {'gold': 0, 'sold': 0, 'returned': 3}),
  ('partial repair boundary #1', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2}),
  ('partial repair boundary #2', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4}),
  ('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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression daily cap check #1', [3, 20, 3, 'honored'], {'gold': 0, 'sold': 0, 'returned': 3}),
  ('regression daily cap check #2', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('regression daily cap check #3', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
  ('partial repair boundary #1', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4}),
  ('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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression daily cap check #1', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('regression daily cap check #2', [99, 20, 9, 'honored'], {'gold': 0, 'sold': 0, 'returned': 9}),
  ('partial repair boundary #1', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4}),
  ('partial repair boundary #2', [10, 22, 10, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 10}),
  ('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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression daily cap check #1', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
  ('regression daily cap check #2', [99, 20, 7, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 7}),
  ('regression daily cap check #3', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('regression daily cap check #4', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('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', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression daily cap check #1', [1, 15, 12, 'friendly'], {'gold': 5, 'sold': 5, 'returned': 7}),
  ('regression daily cap check #2', [10, 20, 7, 'honored'], {'gold': 0, 'sold': 0, 'returned': 7}),
  ('regression daily cap check #3', [99, 20, 9, 'honored'], {'gold': 0, 'sold': 0, 'returned': 9}),
  ('regression daily cap check #4', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, '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', [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
cap reached mid batch #1{'gold': 51, 'returned': 2, 'sold': 3}{'gold': 34, 'returned': 3, 'sold': 2}Failed
regression daily cap check #1{'gold': 6, 'returned': 4, 'sold': 6}{'gold': 5, 'returned': 5, 'sold': 5}Failed
regression daily cap check #2{'gold': 1, 'returned': 2, 'sold': 1}{'gold': 0, 'returned': 3, 'sold': 0}Failed
partial repair boundary #1{'gold': 0, 'returned': 2, 'sold': 0}{'gold': 0, 'returned': 2, 'sold': 0}Passed
partial repair boundary #2{'gold': 0, 'returned': 4, 'sold': 0}{'gold': 0, 'returned': 4, 'sold': 0}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': 207, 'returned': 0, 'sold': 3}{'gold': 207, 'returned': 0, 'sold': 3}Passed

SHA-256 / 8e9efd1fc8b4805fb57aa5779e305b6250ee105666db9ccf02f8d29bd202771a

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 sold >= 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}),
  ('regression daily cap check #1', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
  ('regression daily cap check #2', [3, 20, 3, 'honored'], {'gold': 0, 'sold': 0, 'returned': 3}),
  ('partial repair boundary #1', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2}),
  ('partial repair boundary #2', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4}),
  ('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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression daily cap check #1', [3, 20, 3, 'honored'], {'gold': 0, 'sold': 0, 'returned': 3}),
  ('regression daily cap check #2', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('regression daily cap check #3', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
  ('partial repair boundary #1', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4}),
  ('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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression daily cap check #1', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('regression daily cap check #2', [99, 20, 9, 'honored'], {'gold': 0, 'sold': 0, 'returned': 9}),
  ('partial repair boundary #1', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4}),
  ('partial repair boundary #2', [10, 22, 10, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 10}),
  ('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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression daily cap check #1', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
  ('regression daily cap check #2', [99, 20, 7, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 7}),
  ('regression daily cap check #3', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('regression daily cap check #4', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('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', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression daily cap check #1', [1, 15, 12, 'friendly'], {'gold': 5, 'sold': 5, 'returned': 7}),
  ('regression daily cap check #2', [10, 20, 7, 'honored'], {'gold': 0, 'sold': 0, 'returned': 7}),
  ('regression daily cap check #3', [99, 20, 9, 'honored'], {'gold': 0, 'sold': 0, 'returned': 9}),
  ('regression daily cap check #4', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, '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', [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
cap reached mid batch #1{'gold': 85, 'returned': 0, 'sold': 5}{'gold': 34, 'returned': 3, 'sold': 2}Failed
regression daily cap check #1{'gold': 10, 'returned': 0, 'sold': 10}{'gold': 5, 'returned': 5, 'sold': 5}Failed
regression daily cap check #2{'gold': 3, 'returned': 0, 'sold': 3}{'gold': 0, 'returned': 3, 'sold': 0}Failed
partial repair boundary #1{'gold': 2, 'returned': 0, 'sold': 2}{'gold': 0, 'returned': 2, 'sold': 0}Failed
partial repair boundary #2{'gold': 4, 'returned': 0, 'sold': 4}{'gold': 0, 'returned': 4, 'sold': 0}Failed
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': 207, 'returned': 0, 'sold': 3}{'gold': 207, 'returned': 0, 'sold': 3}Passed

SHA-256 / c803faf2139b0132e1ff46885c133caa0984b92dd1d72a3ed4ad4c7832c5fc24

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}),
  ('regression daily cap check #1', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
  ('regression daily cap check #2', [3, 20, 3, 'honored'], {'gold': 0, 'sold': 0, 'returned': 3}),
  ('partial repair boundary #1', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2}),
  ('partial repair boundary #2', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4}),
  ('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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression daily cap check #1', [3, 20, 3, 'honored'], {'gold': 0, 'sold': 0, 'returned': 3}),
  ('regression daily cap check #2', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('regression daily cap check #3', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
  ('partial repair boundary #1', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4}),
  ('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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression daily cap check #1', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('regression daily cap check #2', [99, 20, 9, 'honored'], {'gold': 0, 'sold': 0, 'returned': 9}),
  ('partial repair boundary #1', [3, 22, 4, 'honored'], {'gold': 0, 'sold': 0, 'returned': 4}),
  ('partial repair boundary #2', [10, 22, 10, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 10}),
  ('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', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression daily cap check #1', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, 'returned': 3}),
  ('regression daily cap check #2', [99, 20, 7, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 7}),
  ('regression daily cap check #3', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
  ('regression daily cap check #4', [15, 15, 7, 'friendly'], {'gold': 30, 'sold': 5, 'returned': 2}),
  ('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', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0})],
 [('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
  ('regression daily cap check #1', [1, 15, 12, 'friendly'], {'gold': 5, 'sold': 5, 'returned': 7}),
  ('regression daily cap check #2', [10, 20, 7, 'honored'], {'gold': 0, 'sold': 0, 'returned': 7}),
  ('regression daily cap check #3', [99, 20, 9, 'honored'], {'gold': 0, 'sold': 0, 'returned': 9}),
  ('regression daily cap check #4', [99, 19, 4, 'friendly'], {'gold': 40, 'sold': 1, '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', [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
cap reached mid batch #1{'gold': 34, 'returned': 3, 'sold': 2}{'gold': 34, 'returned': 3, 'sold': 2}Passed
regression daily cap check #1{'gold': 5, 'returned': 5, 'sold': 5}{'gold': 5, 'returned': 5, 'sold': 5}Passed
regression daily cap check #2{'gold': 0, 'returned': 3, 'sold': 0}{'gold': 0, 'returned': 3, 'sold': 0}Passed
partial repair boundary #1{'gold': 0, 'returned': 2, 'sold': 0}{'gold': 0, 'returned': 2, 'sold': 0}Passed
partial repair boundary #2{'gold': 0, 'returned': 4, 'sold': 0}{'gold': 0, 'returned': 4, 'sold': 0}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': 207, 'returned': 0, 'sold': 3}{'gold': 207, 'returned': 0, 'sold': 3}Passed

SHA-256 / 9ef5204ca700ddbb835eed75a75f463fb2dad46988b6ffef26986fb61816a95d

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 2026-09-29T14:50:45.033556+00:00.

Case digest / 57fb89ef7814cd9c148ff0c493e82c0564bce5580dba2e8240480cce4980a94e