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.
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| 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