FAILURE MAP
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FA-86011 / Game economy crafting balance / Open access

Repair bill: Discounts stack additively · case 01

Two discounts together are worth more than applying them in turn.

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

ROOT CAUSE

Each discount is taken from the undiscounted total, making them additive.

THE FAILURE

Each discount is taken from the undiscounted total, making them additive.

Unsuccessful approach: Floor division at each stage rounds intermediate prices down before the final ceiling.

Case contract

Per item cost = max(0, max-dur) * (ilvl//4 + 1) copper. Discount percentages stack multiplicatively on the exact total; the result is rounded up once to copper. Return [gold, silver, copper] with 100 copper per silver and 100 silver per gold.

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
import math
from fractions import Fraction
N = 1
observations = []
def solve(items, discounts):
    total = 0
    for it in items:
        missing = max(0, it['max'] - it['dur'])
        total += missing * (it['ilvl'] // 4 + 1)
    price = Fraction(total)
    for pct in discounts:
        price = price - Fraction(total) * pct / 100
    cost = math.ceil(price)
    return [cost // 10000, cost // 100 % 100, cost % 100]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression discount stacking #1',
   [[{'ilvl': 1, 'dur': 120, 'max': 120},
     {'ilvl': 4, 'dur': 84, 'max': 100},
     {'ilvl': 3, 'dur': 40, 'max': 40},
     {'ilvl': 3, 'dur': 0, 'max': 120}],
    [10, 33]],
   [0, 0, 92]),
  ('regression discount stacking #2',
   [[{'ilvl': 377, 'dur': 103, 'max': 100},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 1, 'dur': 5, 'max': 60}],
    [15, 10]],
   [0, 1, 19]),
  ('partial repair boundary #1',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('partial repair boundary #2',
   [[{'ilvl': 113, 'dur': 4, 'max': 40},
     {'ilvl': 84, 'dur': 100, 'max': 100},
     {'ilvl': 276, 'dur': 62, 'max': 100},
     {'ilvl': 4, 'dur': 0, 'max': 120}],
    [33]],
   [0, 26, 43]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression discount stacking #1',
   [[{'ilvl': 377, 'dur': 103, 'max': 100},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 1, 'dur': 5, 'max': 60}],
    [15, 10]],
   [0, 1, 19]),
  ('regression discount stacking #2',
   [[{'ilvl': 4, 'dur': 29, 'max': 100}, {'ilvl': 7, 'dur': 0, 'max': 100}], [20, 10]],
   [0, 2, 47]),
  ('partial repair boundary #1',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('partial repair boundary #2',
   [[{'ilvl': 113, 'dur': 4, 'max': 40},
     {'ilvl': 84, 'dur': 100, 'max': 100},
     {'ilvl': 276, 'dur': 62, 'max': 100},
     {'ilvl': 4, 'dur': 0, 'max': 120}],
    [33]],
   [0, 26, 43]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression discount stacking #1',
   [[{'ilvl': 8, 'dur': 43, 'max': 40},
     {'ilvl': 7, 'dur': 0, 'max': 40},
     {'ilvl': 316, 'dur': 123, 'max': 120}],
    [15, 25, 10]],
   [0, 0, 46]),
  ('regression discount stacking #2',
   [[{'ilvl': 3, 'dur': 63, 'max': 60},
     {'ilvl': 3, 'dur': 40, 'max': 40},
     {'ilvl': 7, 'dur': 13, 'max': 100},
     {'ilvl': 3, 'dur': 0, 'max': 100}],
    [10, 15]],
   [0, 2, 10]),
  ('partial repair boundary #1',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('regression discount stacking #3',
   [[{'ilvl': 377, 'dur': 103, 'max': 100},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 1, 'dur': 5, 'max': 60}],
    [15, 10]],
   [0, 1, 19]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression discount stacking #1', [[{'ilvl': 3, 'dur': 0, 'max': 120}], [15, 15, 15]], [0, 0, 74]),
  ('regression discount stacking #2',
   [[{'ilvl': 14, 'dur': 0, 'max': 40}, {'ilvl': 4, 'dur': 43, 'max': 40}], [25, 10, 15]],
   [0, 0, 92]),
  ('regression discount stacking #3',
   [[{'ilvl': 4, 'dur': 29, 'max': 100}, {'ilvl': 7, 'dur': 0, 'max': 100}], [20, 10]],
   [0, 2, 47]),
  ('partial repair boundary #1', [[{'ilvl': 1, 'dur': 89, 'max': 100}], [33]], [0, 0, 8]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1',
   [[{'ilvl': 4, 'dur': 63, 'max': 60},
     {'ilvl': 130, 'dur': 63, 'max': 60},
     {'ilvl': 3, 'dur': 60, 'max': 60}],
    [25, 25]],
   [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression discount stacking #1',
   [[{'ilvl': 8, 'dur': 0, 'max': 100},
     {'ilvl': 3, 'dur': 0, 'max': 100},
     {'ilvl': 8, 'dur': 100, 'max': 100}],
    [10, 10, 10]],
   [0, 2, 92]),
  ('regression discount stacking #2',
   [[{'ilvl': 8, 'dur': 0, 'max': 120}, {'ilvl': 4, 'dur': 63, 'max': 60}, {'ilvl': 7, 'dur': 60, 'max': 60}],
    [10, 33]],
   [0, 2, 18]),
  ('regression discount stacking #3',
   [[{'ilvl': 8, 'dur': 43, 'max': 40},
     {'ilvl': 7, 'dur': 0, 'max': 40},
     {'ilvl': 316, 'dur': 123, 'max': 120}],
    [15, 25, 10]],
   [0, 0, 46]),
  ('partial repair boundary #1',
   [[{'ilvl': 7, 'dur': 100, 'max': 100},
     {'ilvl': 1, 'dur': 37, 'max': 40},
     {'ilvl': 7, 'dur': 103, 'max': 100}],
    [25, 15]],
   [0, 0, 2]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 111, 'dur': 123, 'max': 120}], []], [0, 0, 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
two stacked discounts #1[0, 21, 84][0, 22, 47]Failed
regression discount stacking #1[0, 0, 87][0, 0, 92]Failed
regression discount stacking #2[0, 1, 17][0, 1, 19]Failed
partial repair boundary #1[0, 5, 96][0, 5, 96]Passed
partial repair boundary #2[0, 26, 43][0, 26, 43]Passed
over-repaired piece #1[0, 0, 60][0, 0, 60]Passed
nothing to repair #1[0, 0, 0][0, 0, 0]Passed
control #1[0, 0, 0][0, 0, 0]Passed

SHA-256 / c5c4365d3c309d629cc7e56de4a16b39fa293fc0107072e118e433a052c44af8

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(items, discounts):
    total = 0
    for it in items:
        missing = max(0, it['max'] - it['dur'])
        total += missing * (it['ilvl'] // 4 + 1)
    price = Fraction(total)
    for pct in discounts:
        price = price * (100 - pct) // 100
    cost = math.ceil(price)
    return [cost // 10000, cost // 100 % 100, cost % 100]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression discount stacking #1',
   [[{'ilvl': 1, 'dur': 120, 'max': 120},
     {'ilvl': 4, 'dur': 84, 'max': 100},
     {'ilvl': 3, 'dur': 40, 'max': 40},
     {'ilvl': 3, 'dur': 0, 'max': 120}],
    [10, 33]],
   [0, 0, 92]),
  ('regression discount stacking #2',
   [[{'ilvl': 377, 'dur': 103, 'max': 100},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 1, 'dur': 5, 'max': 60}],
    [15, 10]],
   [0, 1, 19]),
  ('partial repair boundary #1',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('partial repair boundary #2',
   [[{'ilvl': 113, 'dur': 4, 'max': 40},
     {'ilvl': 84, 'dur': 100, 'max': 100},
     {'ilvl': 276, 'dur': 62, 'max': 100},
     {'ilvl': 4, 'dur': 0, 'max': 120}],
    [33]],
   [0, 26, 43]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression discount stacking #1',
   [[{'ilvl': 377, 'dur': 103, 'max': 100},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 1, 'dur': 5, 'max': 60}],
    [15, 10]],
   [0, 1, 19]),
  ('regression discount stacking #2',
   [[{'ilvl': 4, 'dur': 29, 'max': 100}, {'ilvl': 7, 'dur': 0, 'max': 100}], [20, 10]],
   [0, 2, 47]),
  ('partial repair boundary #1',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('partial repair boundary #2',
   [[{'ilvl': 113, 'dur': 4, 'max': 40},
     {'ilvl': 84, 'dur': 100, 'max': 100},
     {'ilvl': 276, 'dur': 62, 'max': 100},
     {'ilvl': 4, 'dur': 0, 'max': 120}],
    [33]],
   [0, 26, 43]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression discount stacking #1',
   [[{'ilvl': 8, 'dur': 43, 'max': 40},
     {'ilvl': 7, 'dur': 0, 'max': 40},
     {'ilvl': 316, 'dur': 123, 'max': 120}],
    [15, 25, 10]],
   [0, 0, 46]),
  ('regression discount stacking #2',
   [[{'ilvl': 3, 'dur': 63, 'max': 60},
     {'ilvl': 3, 'dur': 40, 'max': 40},
     {'ilvl': 7, 'dur': 13, 'max': 100},
     {'ilvl': 3, 'dur': 0, 'max': 100}],
    [10, 15]],
   [0, 2, 10]),
  ('partial repair boundary #1',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('regression discount stacking #3',
   [[{'ilvl': 377, 'dur': 103, 'max': 100},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 1, 'dur': 5, 'max': 60}],
    [15, 10]],
   [0, 1, 19]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression discount stacking #1', [[{'ilvl': 3, 'dur': 0, 'max': 120}], [15, 15, 15]], [0, 0, 74]),
  ('regression discount stacking #2',
   [[{'ilvl': 14, 'dur': 0, 'max': 40}, {'ilvl': 4, 'dur': 43, 'max': 40}], [25, 10, 15]],
   [0, 0, 92]),
  ('regression discount stacking #3',
   [[{'ilvl': 4, 'dur': 29, 'max': 100}, {'ilvl': 7, 'dur': 0, 'max': 100}], [20, 10]],
   [0, 2, 47]),
  ('partial repair boundary #1', [[{'ilvl': 1, 'dur': 89, 'max': 100}], [33]], [0, 0, 8]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1',
   [[{'ilvl': 4, 'dur': 63, 'max': 60},
     {'ilvl': 130, 'dur': 63, 'max': 60},
     {'ilvl': 3, 'dur': 60, 'max': 60}],
    [25, 25]],
   [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression discount stacking #1',
   [[{'ilvl': 8, 'dur': 0, 'max': 100},
     {'ilvl': 3, 'dur': 0, 'max': 100},
     {'ilvl': 8, 'dur': 100, 'max': 100}],
    [10, 10, 10]],
   [0, 2, 92]),
  ('regression discount stacking #2',
   [[{'ilvl': 8, 'dur': 0, 'max': 120}, {'ilvl': 4, 'dur': 63, 'max': 60}, {'ilvl': 7, 'dur': 60, 'max': 60}],
    [10, 33]],
   [0, 2, 18]),
  ('regression discount stacking #3',
   [[{'ilvl': 8, 'dur': 43, 'max': 40},
     {'ilvl': 7, 'dur': 0, 'max': 40},
     {'ilvl': 316, 'dur': 123, 'max': 120}],
    [15, 25, 10]],
   [0, 0, 46]),
  ('partial repair boundary #1',
   [[{'ilvl': 7, 'dur': 100, 'max': 100},
     {'ilvl': 1, 'dur': 37, 'max': 40},
     {'ilvl': 7, 'dur': 103, 'max': 100}],
    [25, 15]],
   [0, 0, 2]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 111, 'dur': 123, 'max': 120}], []], [0, 0, 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
two stacked discounts #1[0, 22, 46][0, 22, 47]Failed
regression discount stacking #1[0, 0, 91][0, 0, 92]Failed
regression discount stacking #2[0, 1, 17][0, 1, 19]Failed
partial repair boundary #1[0, 5, 95][0, 5, 96]Failed
partial repair boundary #2[0, 26, 42][0, 26, 43]Failed
over-repaired piece #1[0, 0, 60][0, 0, 60]Passed
nothing to repair #1[0, 0, 0][0, 0, 0]Passed
control #1[0, 0, 0][0, 0, 0]Passed

SHA-256 / 84e7d1fdf5a8bb22119a7730d50b1644379cc3b2467d56ad01565cade8d379f1

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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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 2026-09-29T14:50:45.637440+00:00.

Case digest / 62167f28592ac7d1492066abd81249d610285674b302b3f39522e15ae8871fe3