FA-85946 / Game economy crafting balance / Open access
Vendor sell saturation: Saturation ignores earlier sales today · case 01
Splitting sales into many small trips resets vendor saturation.
ROOT CAUSE
Saturation counts only units in the current transaction.
VERIFIED REPAIR
Restore `done = sales + sold` at the prior sales carry step.
Unsuccessful approach: Counting only prior sales never raises saturation within one batch.
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 = 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 prior sales carry #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0}),
('regression prior sales carry #2', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0}),
('partial repair boundary #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
('regression prior sales carry #3', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, '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', [1, 22, 0, 'honored'], {'gold': 0, 'sold': 0, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression prior sales carry #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0}),
('fault site prior sales carry #1', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2}),
('partial repair boundary #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
('regression prior sales carry #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, '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', [1, 22, 0, 'honored'], {'gold': 0, 'sold': 0, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('fault site prior sales carry #1', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
('regression prior sales carry #1', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('regression prior sales carry #2', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
('regression prior sales carry #3', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, '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', [1, 22, 0, 'honored'], {'gold': 0, 'sold': 0, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression prior sales carry #1', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
('regression prior sales carry #2', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, 'returned': 0}),
('regression prior sales carry #3', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('regression prior sales carry #4', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, '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', [55, 5, 0, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('fault site prior sales carry #1', [3, 12, 4, 'honored'], {'gold': 4, 'sold': 4, 'returned': 0}),
('regression prior sales carry #1', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('regression prior sales carry #2', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
('regression prior sales carry #3', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, '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', [1, 0, 8, 'honored'], {'gold': 8, 'sold': 8, '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': 196, 'returned': 0, 'sold': 5} | {'gold': 34, 'returned': 3, 'sold': 2} | Failed |
| regression prior sales carry #1 | {'gold': 282, 'returned': 0, 'sold': 3} | {'gold': 207, 'returned': 0, 'sold': 3} | Failed |
| regression prior sales carry #2 | {'gold': 19, 'returned': 0, 'sold': 11} | {'gold': 17, 'returned': 0, 'sold': 11} | Failed |
| partial repair boundary #1 | {'gold': 58, 'returned': 0, 'sold': 7} | {'gold': 58, 'returned': 0, 'sold': 7} | Passed |
| regression prior sales carry #3 | {'gold': 75, 'returned': 0, 'sold': 10} | {'gold': 52, 'returned': 0, 'sold': 10} | 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': 0, 'returned': 0, 'sold': 0} | {'gold': 0, 'returned': 0, 'sold': 0} | Passed |
SHA-256 / 072aebc3e3eaacf1f5593ff5c0c65fe5cd161542949e7ff037b6a99bdd5e4966
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
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 prior sales carry #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0}),
('regression prior sales carry #2', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0}),
('partial repair boundary #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
('regression prior sales carry #3', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, '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', [1, 22, 0, 'honored'], {'gold': 0, 'sold': 0, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression prior sales carry #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0}),
('fault site prior sales carry #1', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2}),
('partial repair boundary #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
('regression prior sales carry #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, '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', [1, 22, 0, 'honored'], {'gold': 0, 'sold': 0, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('fault site prior sales carry #1', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
('regression prior sales carry #1', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('regression prior sales carry #2', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
('regression prior sales carry #3', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, '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', [1, 22, 0, 'honored'], {'gold': 0, 'sold': 0, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression prior sales carry #1', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
('regression prior sales carry #2', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, 'returned': 0}),
('regression prior sales carry #3', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('regression prior sales carry #4', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, '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', [55, 5, 0, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('fault site prior sales carry #1', [3, 12, 4, 'honored'], {'gold': 4, 'sold': 4, 'returned': 0}),
('regression prior sales carry #1', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('regression prior sales carry #2', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
('regression prior sales carry #3', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, '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', [1, 0, 8, 'honored'], {'gold': 8, 'sold': 8, '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 prior sales carry #1 | {'gold': 222, 'returned': 0, 'sold': 3} | {'gold': 207, 'returned': 0, 'sold': 3} | Failed |
| regression prior sales carry #2 | {'gold': 22, 'returned': 0, 'sold': 11} | {'gold': 17, 'returned': 0, 'sold': 11} | Failed |
| partial repair boundary #1 | {'gold': 70, 'returned': 0, 'sold': 7} | {'gold': 58, 'returned': 0, 'sold': 7} | Failed |
| regression prior sales carry #3 | {'gold': 70, 'returned': 0, 'sold': 10} | {'gold': 52, 'returned': 0, 'sold': 10} | 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': 0, 'returned': 0, 'sold': 0} | {'gold': 0, 'returned': 0, 'sold': 0} | Passed |
SHA-256 / e5eaa9c9a9f9b2c2b00add1c20e8768fdff4d04be51b2a8901767196d42f1d68
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 prior sales carry #1', [99, 5, 3, 'neutral'], {'gold': 207, 'sold': 3, 'returned': 0}),
('regression prior sales carry #2', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0}),
('partial repair boundary #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
('regression prior sales carry #3', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, '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', [1, 22, 0, 'honored'], {'gold': 0, 'sold': 0, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression prior sales carry #1', [3, 1, 11, 'neutral'], {'gold': 17, 'sold': 11, 'returned': 0}),
('fault site prior sales carry #1', [2, 22, 2, 'friendly'], {'gold': 0, 'sold': 0, 'returned': 2}),
('partial repair boundary #1', [10, 0, 7, 'friendly'], {'gold': 58, 'sold': 7, 'returned': 0}),
('regression prior sales carry #2', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, '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', [1, 22, 0, 'honored'], {'gold': 0, 'sold': 0, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('fault site prior sales carry #1', [190, 12, 7, 'neutral'], {'gold': 532, 'sold': 7, 'returned': 0}),
('regression prior sales carry #1', [10, 5, 10, 'friendly'], {'gold': 52, 'sold': 10, 'returned': 0}),
('regression prior sales carry #2', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
('regression prior sales carry #3', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, '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', [1, 22, 0, 'honored'], {'gold': 0, 'sold': 0, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('regression prior sales carry #1', [2, 15, 10, 'neutral'], {'gold': 5, 'sold': 5, 'returned': 5}),
('regression prior sales carry #2', [25, 1, 4, 'neutral'], {'gold': 86, 'sold': 4, 'returned': 0}),
('regression prior sales carry #3', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('regression prior sales carry #4', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, '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', [55, 5, 0, 'neutral'], {'gold': 0, 'sold': 0, 'returned': 0})],
[('cap reached mid batch #1', [40, 18, 5, 'honored'], {'gold': 34, 'sold': 2, 'returned': 3}),
('fault site prior sales carry #1', [3, 12, 4, 'honored'], {'gold': 4, 'sold': 4, 'returned': 0}),
('regression prior sales carry #1', [10, 1, 9, 'friendly'], {'gold': 65, 'sold': 9, 'returned': 0}),
('regression prior sales carry #2', [25, 12, 12, 'neutral'], {'gold': 80, 'sold': 8, 'returned': 4}),
('regression prior sales carry #3', [99, 11, 5, 'neutral'], {'gold': 200, 'sold': 5, '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', [1, 0, 8, 'honored'], {'gold': 8, 'sold': 8, '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 prior sales carry #1 | {'gold': 207, 'returned': 0, 'sold': 3} | {'gold': 207, 'returned': 0, 'sold': 3} | Passed |
| regression prior sales carry #2 | {'gold': 17, 'returned': 0, 'sold': 11} | {'gold': 17, 'returned': 0, 'sold': 11} | Passed |
| partial repair boundary #1 | {'gold': 58, 'returned': 0, 'sold': 7} | {'gold': 58, 'returned': 0, 'sold': 7} | Passed |
| regression prior sales carry #3 | {'gold': 52, 'returned': 0, 'sold': 10} | {'gold': 52, 'returned': 0, 'sold': 10} | 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': 0, 'sold': 0} | {'gold': 0, 'returned': 0, 'sold': 0} | Passed |
SHA-256 / 754839eb827ff7432073126ccd2f370fe8a1298ecffc20d83573791cf75b5da8
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 2026-09-29T14:50:45.032956+00:00.
Case digest / f1bdc0943454f3bb0fa01bf5faa8e79576a8a3b0a3f536051c90089c1d55dd88