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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.

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

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 fixtureActualExpectedOutcome
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 fixtureActualExpectedOutcome
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 fixtureActualExpectedOutcome
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