FAILURE MAP
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FA-85941 / Game economy crafting balance / Open access

Banner pity counter: Featured coin correlates with the rarity roll · case 01

Low rarity rolls are almost always featured, biasing the fifty-fifty.

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

ROOT CAUSE

The featured decision reuses a low-roll threshold that is correlated with hitting at all.

THE FAILURE

The featured decision reuses a low-roll threshold that is correlated with hitting at all.

Unsuccessful approach: Inverting the parity reverses the published featured outcome for every roll.

Case contract

Each roll is 0..999. Pull number n = pity+1. Top-rarity rate is 6 per mille, plus 50*(n-73) from n >= 74 (soft pity); n >= 90 always hits. On a hit pity resets to 0; the item is featured ("F") if guarantee is set or the roll is even, otherwise lost ("L") and the guarantee is set; a featured hit clears the guarantee. Misses ("-") set pity = n.

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(rolls, state):
    pity = state['pity']
    guarantee = state['guarantee']
    out = []
    for r in rolls:
        n = pity + 1
        rate = 6
        if n >= 74:
            rate += 50 * (n - 73)
        if n >= 90 or r < rate:
            pity = 0
            if guarantee or r < 500:
                out.append('F')
                guarantee = False
            else:
                out.append('L')
                guarantee = True
        else:
            pity = n
            out.append('-')
    return {'results': ''.join(out), 'pity': pity, 'guarantee': guarantee}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression featured coin #1',
   [[18, 973, 5], {'pity': 72, 'guarantee': False}],
   {'results': '--L', 'pity': 0, 'guarantee': True}),
  ('regression featured coin #2',
   [[935, 90, 29, 166, 937, 997, 903, 315, 848, 1, 893, 36, 218, 730, 858, 726, 972, 10],
    {'pity': 89, 'guarantee': True}],
   {'results': 'F--------L--------', 'pity': 8, 'guarantee': True}),
  ('partial repair boundary #1',
   [[922, 571, 11, 40, 49, 776, 996, 952, 946, 14, 108, 822, 888, 25], {'pity': 84, 'guarantee': False}],
   {'results': '-L------------', 'pity': 12, 'guarantee': True}),
  ('partial repair boundary #2',
   [[4, 155, 441, 951, 967, 353, 21], {'pity': 68, 'guarantee': False}],
   {'results': 'F------', 'pity': 6, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[15, 31, 302, 259, 332, 886, 12, 851, 55, 45, 6, 903, 946, 869, 725], {'pity': 88, 'guarantee': True}],
   {'results': 'F--------------', 'pity': 14, 'guarantee': False})],
 [('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression featured coin #1',
   [[935, 90, 29, 166, 937, 997, 903, 315, 848, 1, 893, 36, 218, 730, 858, 726, 972, 10],
    {'pity': 89, 'guarantee': True}],
   {'results': 'F--------L--------', 'pity': 8, 'guarantee': True}),
  ('regression featured coin #2',
   [[346, 740, 973, 629, 933, 35, 831, 930, 214, 969, 923], {'pity': 73, 'guarantee': False}],
   {'results': '-----L-----', 'pity': 5, 'guarantee': True}),
  ('partial repair boundary #1',
   [[922, 571, 11, 40, 49, 776, 996, 952, 946, 14, 108, 822, 888, 25], {'pity': 84, 'guarantee': False}],
   {'results': '-L------------', 'pity': 12, 'guarantee': True}),
  ('regression featured coin #3',
   [[18, 973, 5], {'pity': 72, 'guarantee': False}],
   {'results': '--L', 'pity': 0, 'guarantee': True}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[15, 31, 302, 259, 332, 886, 12, 851, 55, 45, 6, 903, 946, 869, 725], {'pity': 88, 'guarantee': True}],
   {'results': 'F--------------', 'pity': 14, 'guarantee': False})],
 [('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression featured coin #1',
   [[860, 832, 950, 795, 21, 53, 128, 667, 5, 11, 16], {'pity': 0, 'guarantee': False}],
   {'results': '--------L--', 'pity': 2, 'guarantee': True}),
  ('regression featured coin #2',
   [[984, 954, 47, 297, 21, 192, 35, 1, 87, 521, 965, 945, 130, 990], {'pity': 72, 'guarantee': True}],
   {'results': '--F----L------', 'pity': 6, 'guarantee': True}),
  ('regression featured coin #3',
   [[935, 90, 29, 166, 937, 997, 903, 315, 848, 1, 893, 36, 218, 730, 858, 726, 972, 10],
    {'pity': 89, 'guarantee': True}],
   {'results': 'F--------L--------', 'pity': 8, 'guarantee': True}),
  ('partial repair boundary #1',
   [[4, 155, 441, 951, 967, 353, 21], {'pity': 68, 'guarantee': False}],
   {'results': 'F------', 'pity': 6, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[507, 965, 27, 525, 851], {'pity': 73, 'guarantee': True}],
   {'results': '--F--', 'pity': 2, 'guarantee': False})],
 [('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression featured coin #1',
   [[4, 981, 950, 937, 739, 13, 768, 921, 979, 2, 3, 996], {'pity': 89, 'guarantee': False}],
   {'results': 'F--------FL-', 'pity': 1, 'guarantee': True}),
  ('regression featured coin #2',
   [[711, 926, 856, 59, 840, 978, 927, 160, 919, 993, 878, 579, 989], {'pity': 73, 'guarantee': False}],
   {'results': '---L---------', 'pity': 9, 'guarantee': True}),
  ('regression featured coin #3',
   [[346, 740, 973, 629, 933, 35, 831, 930, 214, 969, 923], {'pity': 73, 'guarantee': False}],
   {'results': '-----L-----', 'pity': 5, 'guarantee': True}),
  ('partial repair boundary #1',
   [[4, 42, 253, 999, 775, 819, 42, 973, 811, 307, 835, 958, 247, 22], {'pity': 73, 'guarantee': False}],
   {'results': 'F-------------', 'pity': 13, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[480, 489, 823, 13, 936, 776, 44, 409, 26, 974, 9, 54, 911, 804, 433, 47, 942, 847],
    {'pity': 89, 'guarantee': True}],
   {'results': 'F-----------------', 'pity': 17, 'guarantee': False})],
 [('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression featured coin #1',
   [[55, 51, 37, 985, 339, 849, 34, 33, 811, 935, 6, 3], {'pity': 66, 'guarantee': False}],
   {'results': '-------L---F', 'pity': 0, 'guarantee': False}),
  ('regression featured coin #2',
   [[13, 897, 905, 973, 838, 47, 24, 42, 813, 832, 963, 957, 47, 811, 56, 994, 13, 928],
    {'pity': 89, 'guarantee': False}],
   {'results': 'L-----------------', 'pity': 17, 'guarantee': True}),
  ('regression featured coin #3',
   [[860, 832, 950, 795, 21, 53, 128, 667, 5, 11, 16], {'pity': 0, 'guarantee': False}],
   {'results': '--------L--', 'pity': 2, 'guarantee': True}),
  ('partial repair boundary #1',
   [[4], {'pity': 73, 'guarantee': False}],
   {'results': 'F', 'pity': 0, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('control #1', [[911], {'pity': 73, 'guarantee': True}], {'results': '-', 'pity': 74, 'guarantee': True})]]
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
lost fifty fifty then featured #1{'guarantee': False, 'pity': 0, 'results': 'F-F'}{'guarantee': False, 'pity': 0, 'results': 'L-F'}Failed
hard pity pull #1{'guarantee': True, 'pity': 1, 'results': 'L-'}{'guarantee': True, 'pity': 1, 'results': 'L-'}Passed
regression featured coin #1{'guarantee': False, 'pity': 0, 'results': '--F'}{'guarantee': True, 'pity': 0, 'results': '--L'}Failed
regression featured coin #2{'guarantee': False, 'pity': 8, 'results': 'F--------F--------'}{'guarantee': True, 'pity': 8, 'results': 'F--------L--------'}Failed
partial repair boundary #1{'guarantee': True, 'pity': 12, 'results': '-L------------'}{'guarantee': True, 'pity': 12, 'results': '-L------------'}Passed
partial repair boundary #2{'guarantee': False, 'pity': 6, 'results': 'F------'}{'guarantee': False, 'pity': 6, 'results': 'F------'}Passed
first soft pity pull #1{'guarantee': False, 'pity': 0, 'results': '-F'}{'guarantee': False, 'pity': 0, 'results': '-F'}Passed
control #1{'guarantee': False, 'pity': 14, 'results': 'F--------------'}{'guarantee': False, 'pity': 14, 'results': 'F--------------'}Passed

SHA-256 / 60eed2030bccac32a8eff99e525ddd43054fefba2ec890f6824929fb8d7bdf83

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(rolls, state):
    pity = state['pity']
    guarantee = state['guarantee']
    out = []
    for r in rolls:
        n = pity + 1
        rate = 6
        if n >= 74:
            rate += 50 * (n - 73)
        if n >= 90 or r < rate:
            pity = 0
            if guarantee or r % 2 == 1:
                out.append('F')
                guarantee = False
            else:
                out.append('L')
                guarantee = True
        else:
            pity = n
            out.append('-')
    return {'results': ''.join(out), 'pity': pity, 'guarantee': guarantee}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression featured coin #1',
   [[18, 973, 5], {'pity': 72, 'guarantee': False}],
   {'results': '--L', 'pity': 0, 'guarantee': True}),
  ('regression featured coin #2',
   [[935, 90, 29, 166, 937, 997, 903, 315, 848, 1, 893, 36, 218, 730, 858, 726, 972, 10],
    {'pity': 89, 'guarantee': True}],
   {'results': 'F--------L--------', 'pity': 8, 'guarantee': True}),
  ('partial repair boundary #1',
   [[922, 571, 11, 40, 49, 776, 996, 952, 946, 14, 108, 822, 888, 25], {'pity': 84, 'guarantee': False}],
   {'results': '-L------------', 'pity': 12, 'guarantee': True}),
  ('partial repair boundary #2',
   [[4, 155, 441, 951, 967, 353, 21], {'pity': 68, 'guarantee': False}],
   {'results': 'F------', 'pity': 6, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[15, 31, 302, 259, 332, 886, 12, 851, 55, 45, 6, 903, 946, 869, 725], {'pity': 88, 'guarantee': True}],
   {'results': 'F--------------', 'pity': 14, 'guarantee': False})],
 [('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression featured coin #1',
   [[935, 90, 29, 166, 937, 997, 903, 315, 848, 1, 893, 36, 218, 730, 858, 726, 972, 10],
    {'pity': 89, 'guarantee': True}],
   {'results': 'F--------L--------', 'pity': 8, 'guarantee': True}),
  ('regression featured coin #2',
   [[346, 740, 973, 629, 933, 35, 831, 930, 214, 969, 923], {'pity': 73, 'guarantee': False}],
   {'results': '-----L-----', 'pity': 5, 'guarantee': True}),
  ('partial repair boundary #1',
   [[922, 571, 11, 40, 49, 776, 996, 952, 946, 14, 108, 822, 888, 25], {'pity': 84, 'guarantee': False}],
   {'results': '-L------------', 'pity': 12, 'guarantee': True}),
  ('regression featured coin #3',
   [[18, 973, 5], {'pity': 72, 'guarantee': False}],
   {'results': '--L', 'pity': 0, 'guarantee': True}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[15, 31, 302, 259, 332, 886, 12, 851, 55, 45, 6, 903, 946, 869, 725], {'pity': 88, 'guarantee': True}],
   {'results': 'F--------------', 'pity': 14, 'guarantee': False})],
 [('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression featured coin #1',
   [[860, 832, 950, 795, 21, 53, 128, 667, 5, 11, 16], {'pity': 0, 'guarantee': False}],
   {'results': '--------L--', 'pity': 2, 'guarantee': True}),
  ('regression featured coin #2',
   [[984, 954, 47, 297, 21, 192, 35, 1, 87, 521, 965, 945, 130, 990], {'pity': 72, 'guarantee': True}],
   {'results': '--F----L------', 'pity': 6, 'guarantee': True}),
  ('regression featured coin #3',
   [[935, 90, 29, 166, 937, 997, 903, 315, 848, 1, 893, 36, 218, 730, 858, 726, 972, 10],
    {'pity': 89, 'guarantee': True}],
   {'results': 'F--------L--------', 'pity': 8, 'guarantee': True}),
  ('partial repair boundary #1',
   [[4, 155, 441, 951, 967, 353, 21], {'pity': 68, 'guarantee': False}],
   {'results': 'F------', 'pity': 6, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[507, 965, 27, 525, 851], {'pity': 73, 'guarantee': True}],
   {'results': '--F--', 'pity': 2, 'guarantee': False})],
 [('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression featured coin #1',
   [[4, 981, 950, 937, 739, 13, 768, 921, 979, 2, 3, 996], {'pity': 89, 'guarantee': False}],
   {'results': 'F--------FL-', 'pity': 1, 'guarantee': True}),
  ('regression featured coin #2',
   [[711, 926, 856, 59, 840, 978, 927, 160, 919, 993, 878, 579, 989], {'pity': 73, 'guarantee': False}],
   {'results': '---L---------', 'pity': 9, 'guarantee': True}),
  ('regression featured coin #3',
   [[346, 740, 973, 629, 933, 35, 831, 930, 214, 969, 923], {'pity': 73, 'guarantee': False}],
   {'results': '-----L-----', 'pity': 5, 'guarantee': True}),
  ('partial repair boundary #1',
   [[4, 42, 253, 999, 775, 819, 42, 973, 811, 307, 835, 958, 247, 22], {'pity': 73, 'guarantee': False}],
   {'results': 'F-------------', 'pity': 13, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[480, 489, 823, 13, 936, 776, 44, 409, 26, 974, 9, 54, 911, 804, 433, 47, 942, 847],
    {'pity': 89, 'guarantee': True}],
   {'results': 'F-----------------', 'pity': 17, 'guarantee': False})],
 [('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression featured coin #1',
   [[55, 51, 37, 985, 339, 849, 34, 33, 811, 935, 6, 3], {'pity': 66, 'guarantee': False}],
   {'results': '-------L---F', 'pity': 0, 'guarantee': False}),
  ('regression featured coin #2',
   [[13, 897, 905, 973, 838, 47, 24, 42, 813, 832, 963, 957, 47, 811, 56, 994, 13, 928],
    {'pity': 89, 'guarantee': False}],
   {'results': 'L-----------------', 'pity': 17, 'guarantee': True}),
  ('regression featured coin #3',
   [[860, 832, 950, 795, 21, 53, 128, 667, 5, 11, 16], {'pity': 0, 'guarantee': False}],
   {'results': '--------L--', 'pity': 2, 'guarantee': True}),
  ('partial repair boundary #1',
   [[4], {'pity': 73, 'guarantee': False}],
   {'results': 'F', 'pity': 0, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('control #1', [[911], {'pity': 73, 'guarantee': True}], {'results': '-', 'pity': 74, 'guarantee': True})]]
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
lost fifty fifty then featured #1{'guarantee': True, 'pity': 0, 'results': 'F-L'}{'guarantee': False, 'pity': 0, 'results': 'L-F'}Failed
hard pity pull #1{'guarantee': False, 'pity': 1, 'results': 'F-'}{'guarantee': True, 'pity': 1, 'results': 'L-'}Failed
regression featured coin #1{'guarantee': False, 'pity': 0, 'results': '--F'}{'guarantee': True, 'pity': 0, 'results': '--L'}Failed
regression featured coin #2{'guarantee': False, 'pity': 8, 'results': 'F--------F--------'}{'guarantee': True, 'pity': 8, 'results': 'F--------L--------'}Failed
partial repair boundary #1{'guarantee': False, 'pity': 12, 'results': '-F------------'}{'guarantee': True, 'pity': 12, 'results': '-L------------'}Failed
partial repair boundary #2{'guarantee': True, 'pity': 6, 'results': 'L------'}{'guarantee': False, 'pity': 6, 'results': 'F------'}Failed
first soft pity pull #1{'guarantee': False, 'pity': 0, 'results': '-F'}{'guarantee': False, 'pity': 0, 'results': '-F'}Passed
control #1{'guarantee': False, 'pity': 14, 'results': 'F--------------'}{'guarantee': False, 'pity': 14, 'results': 'F--------------'}Passed

SHA-256 / 164b07de614377c70f1c85aa55c8cfe21666ca564636709fb47b8c4259ed8323

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.

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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 2026-09-29T14:50:44.998093+00:00.

Case digest / 76e1c630b81c82bd87bb33134fa168bdf583991e135e8a2245576d3a8a63bd1e