FA-85911 / Game economy crafting balance / Open access

Banner pity counter: Soft pity starts one pull late · case 01

Players need one more pull than advertised to enter soft and hard pity.

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

ROOT CAUSE

The current pull number is taken as the stored pity count rather than pity plus one.

VERIFIED REPAIR

Restore `n = pity + 1` at the pull numbering step.

Unsuccessful approach: Clamping to at least one fixes only a fresh counter and still lags every later pull.

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
        rate = 6
        if n >= 74:
            rate += 50 * (n - 73)
        if n >= 90 or r < rate:
            pity = 0
            if guarantee or r % 2 == 0:
                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 = [[('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #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}),
  ('regression pull numbering #2',
   [[507, 965, 27, 525, 851], {'pity': 73, 'guarantee': True}],
   {'results': '--F--', 'pity': 2, 'guarantee': False}),
  ('regression pull numbering #3',
   [[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}),
  ('regression pull numbering #4',
   [[922, 571, 11, 40, 49, 776, 996, 952, 946, 14, 108, 822, 888, 25], {'pity': 84, 'guarantee': False}],
   {'results': '-L------------', 'pity': 12, 'guarantee': True}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[18, 973, 5], {'pity': 72, 'guarantee': False}],
   {'results': '--L', 'pity': 0, 'guarantee': True})],
 [('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #1',
   [[507, 965, 27, 525, 851], {'pity': 73, 'guarantee': True}],
   {'results': '--F--', 'pity': 2, 'guarantee': False}),
  ('regression pull numbering #2',
   [[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}),
  ('regression pull numbering #3',
   [[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 pull numbering #4',
   [[911], {'pity': 73, 'guarantee': True}],
   {'results': '-', 'pity': 74, 'guarantee': True}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[18, 973, 5], {'pity': 72, 'guarantee': False}],
   {'results': '--L', 'pity': 0, 'guarantee': True})],
 [('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #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 pull numbering #2',
   [[911], {'pity': 73, 'guarantee': True}],
   {'results': '-', 'pity': 74, 'guarantee': True}),
  ('regression pull numbering #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}),
  ('regression pull numbering #4',
   [[815, 889, 39, 873, 939, 933, 908, 992, 421, 939, 821, 53, 12, 40, 8, 884, 975, 551, 967, 39],
    {'pity': 63, 'guarantee': True}],
   {'results': '-----------F--------', 'pity': 8, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[18, 973, 5], {'pity': 72, 'guarantee': False}],
   {'results': '--L', 'pity': 0, 'guarantee': True})],
 [('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #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 pull numbering #2',
   [[815, 889, 39, 873, 939, 933, 908, 992, 421, 939, 821, 53, 12, 40, 8, 884, 975, 551, 967, 39],
    {'pity': 63, 'guarantee': True}],
   {'results': '-----------F--------', 'pity': 8, 'guarantee': False}),
  ('regression pull numbering #3',
   [[4, 155, 441, 951, 967, 353, 21], {'pity': 68, 'guarantee': False}],
   {'results': 'F------', 'pity': 6, 'guarantee': False}),
  ('regression pull numbering #4',
   [[685, 976, 49, 33, 16, 30, 427, 839], {'pity': 0, 'guarantee': False}],
   {'results': '--------', 'pity': 8, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[857, 5], {'pity': 24, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False})],
 [('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #1',
   [[4, 155, 441, 951, 967, 353, 21], {'pity': 68, 'guarantee': False}],
   {'results': 'F------', 'pity': 6, 'guarantee': False}),
  ('regression pull numbering #2',
   [[685, 976, 49, 33, 16, 30, 427, 839], {'pity': 0, 'guarantee': False}],
   {'results': '--------', 'pity': 8, 'guarantee': False}),
  ('regression pull numbering #3',
   [[18, 16, 60, 53, 197, 713, 972, 933], {'pity': 75, 'guarantee': True}],
   {'results': 'F-------', 'pity': 7, 'guarantee': False}),
  ('regression pull numbering #4',
   [[773, 957, 60, 353, 59, 19, 862, 820, 993, 27, 22, 893, 950], {'pity': 0, 'guarantee': True}],
   {'results': '-------------', 'pity': 13, 'guarantee': True}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1', [[4], {'pity': 73, 'guarantee': False}], {'results': 'F', 'pity': 0, 'guarantee': False})]]
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
hard pity pull #1	`{'guarantee': False, 'pity': 89, 'results': '--'}`	`{'guarantee': True, 'pity': 1, 'results': 'L-'}`	Failed
regression pull numbering #1	`{'guarantee': False, 'pity': 0, 'results': 'F--------------'}`	`{'guarantee': False, 'pity': 14, 'results': 'F--------------'}`	Failed
regression pull numbering #2	`{'guarantee': True, 'pity': 73, 'results': '-----'}`	`{'guarantee': False, 'pity': 2, 'results': '--F--'}`	Failed
regression pull numbering #3	`{'guarantee': False, 'pity': 0, 'results': 'F-----------------'}`	`{'guarantee': False, 'pity': 17, 'results': 'F-----------------'}`	Failed
regression pull numbering #4	`{'guarantee': True, 'pity': 0, 'results': '--L-----------'}`	`{'guarantee': True, 'pity': 12, 'results': '-L------------'}`	Failed
first soft pity pull #1	`{'guarantee': False, 'pity': 0, 'results': '-F'}`	`{'guarantee': False, 'pity': 0, 'results': '-F'}`	Passed
lost fifty fifty then featured #1	`{'guarantee': False, 'pity': 0, 'results': 'L-F'}`	`{'guarantee': False, 'pity': 0, 'results': 'L-F'}`	Passed
control #1	`{'guarantee': True, 'pity': 0, 'results': '--L'}`	`{'guarantee': True, 'pity': 0, 'results': '--L'}`	Passed

SHA-256 / dadd7178f7eb2d956ae9b4cf37530211b7359aa482aff5d2ee802ffbe7c4e085

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 = max(pity, 1)
        rate = 6
        if n >= 74:
            rate += 50 * (n - 73)
        if n >= 90 or r < rate:
            pity = 0
            if guarantee or r % 2 == 0:
                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 = [[('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #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}),
  ('regression pull numbering #2',
   [[507, 965, 27, 525, 851], {'pity': 73, 'guarantee': True}],
   {'results': '--F--', 'pity': 2, 'guarantee': False}),
  ('regression pull numbering #3',
   [[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}),
  ('regression pull numbering #4',
   [[922, 571, 11, 40, 49, 776, 996, 952, 946, 14, 108, 822, 888, 25], {'pity': 84, 'guarantee': False}],
   {'results': '-L------------', 'pity': 12, 'guarantee': True}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[18, 973, 5], {'pity': 72, 'guarantee': False}],
   {'results': '--L', 'pity': 0, 'guarantee': True})],
 [('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #1',
   [[507, 965, 27, 525, 851], {'pity': 73, 'guarantee': True}],
   {'results': '--F--', 'pity': 2, 'guarantee': False}),
  ('regression pull numbering #2',
   [[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}),
  ('regression pull numbering #3',
   [[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 pull numbering #4',
   [[911], {'pity': 73, 'guarantee': True}],
   {'results': '-', 'pity': 74, 'guarantee': True}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[18, 973, 5], {'pity': 72, 'guarantee': False}],
   {'results': '--L', 'pity': 0, 'guarantee': True})],
 [('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #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 pull numbering #2',
   [[911], {'pity': 73, 'guarantee': True}],
   {'results': '-', 'pity': 74, 'guarantee': True}),
  ('regression pull numbering #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}),
  ('regression pull numbering #4',
   [[815, 889, 39, 873, 939, 933, 908, 992, 421, 939, 821, 53, 12, 40, 8, 884, 975, 551, 967, 39],
    {'pity': 63, 'guarantee': True}],
   {'results': '-----------F--------', 'pity': 8, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[18, 973, 5], {'pity': 72, 'guarantee': False}],
   {'results': '--L', 'pity': 0, 'guarantee': True})],
 [('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #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 pull numbering #2',
   [[815, 889, 39, 873, 939, 933, 908, 992, 421, 939, 821, 53, 12, 40, 8, 884, 975, 551, 967, 39],
    {'pity': 63, 'guarantee': True}],
   {'results': '-----------F--------', 'pity': 8, 'guarantee': False}),
  ('regression pull numbering #3',
   [[4, 155, 441, 951, 967, 353, 21], {'pity': 68, 'guarantee': False}],
   {'results': 'F------', 'pity': 6, 'guarantee': False}),
  ('regression pull numbering #4',
   [[685, 976, 49, 33, 16, 30, 427, 839], {'pity': 0, 'guarantee': False}],
   {'results': '--------', 'pity': 8, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[857, 5], {'pity': 24, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False})],
 [('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #1',
   [[4, 155, 441, 951, 967, 353, 21], {'pity': 68, 'guarantee': False}],
   {'results': 'F------', 'pity': 6, 'guarantee': False}),
  ('regression pull numbering #2',
   [[685, 976, 49, 33, 16, 30, 427, 839], {'pity': 0, 'guarantee': False}],
   {'results': '--------', 'pity': 8, 'guarantee': False}),
  ('regression pull numbering #3',
   [[18, 16, 60, 53, 197, 713, 972, 933], {'pity': 75, 'guarantee': True}],
   {'results': 'F-------', 'pity': 7, 'guarantee': False}),
  ('regression pull numbering #4',
   [[773, 957, 60, 353, 59, 19, 862, 820, 993, 27, 22, 893, 950], {'pity': 0, 'guarantee': True}],
   {'results': '-------------', 'pity': 13, 'guarantee': True}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1', [[4], {'pity': 73, 'guarantee': False}], {'results': 'F', 'pity': 0, 'guarantee': False})]]
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
hard pity pull #1	`{'guarantee': False, 'pity': 89, 'results': '--'}`	`{'guarantee': True, 'pity': 1, 'results': 'L-'}`	Failed
regression pull numbering #1	`{'guarantee': False, 'pity': 1, 'results': 'F--------------'}`	`{'guarantee': False, 'pity': 14, 'results': 'F--------------'}`	Failed
regression pull numbering #2	`{'guarantee': True, 'pity': 73, 'results': '-----'}`	`{'guarantee': False, 'pity': 2, 'results': '--F--'}`	Failed
regression pull numbering #3	`{'guarantee': False, 'pity': 1, 'results': 'F-----------------'}`	`{'guarantee': False, 'pity': 17, 'results': 'F-----------------'}`	Failed
regression pull numbering #4	`{'guarantee': True, 'pity': 1, 'results': '--L-----------'}`	`{'guarantee': True, 'pity': 12, 'results': '-L------------'}`	Failed
first soft pity pull #1	`{'guarantee': False, 'pity': 0, 'results': '-F'}`	`{'guarantee': False, 'pity': 0, 'results': '-F'}`	Passed
lost fifty fifty then featured #1	`{'guarantee': False, 'pity': 0, 'results': 'L-F'}`	`{'guarantee': False, 'pity': 0, 'results': 'L-F'}`	Passed
control #1	`{'guarantee': True, 'pity': 0, 'results': '--L'}`	`{'guarantee': True, 'pity': 0, 'results': '--L'}`	Passed

SHA-256 / 2d9dc5fb605d0106988f7ce9576f0f37cd94c467e109a29e5401cc68a87305f4

3 / The verified repair

Exit 0

"""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 == 0:
                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 = [[('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #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}),
  ('regression pull numbering #2',
   [[507, 965, 27, 525, 851], {'pity': 73, 'guarantee': True}],
   {'results': '--F--', 'pity': 2, 'guarantee': False}),
  ('regression pull numbering #3',
   [[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}),
  ('regression pull numbering #4',
   [[922, 571, 11, 40, 49, 776, 996, 952, 946, 14, 108, 822, 888, 25], {'pity': 84, 'guarantee': False}],
   {'results': '-L------------', 'pity': 12, 'guarantee': True}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[18, 973, 5], {'pity': 72, 'guarantee': False}],
   {'results': '--L', 'pity': 0, 'guarantee': True})],
 [('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #1',
   [[507, 965, 27, 525, 851], {'pity': 73, 'guarantee': True}],
   {'results': '--F--', 'pity': 2, 'guarantee': False}),
  ('regression pull numbering #2',
   [[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}),
  ('regression pull numbering #3',
   [[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 pull numbering #4',
   [[911], {'pity': 73, 'guarantee': True}],
   {'results': '-', 'pity': 74, 'guarantee': True}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[18, 973, 5], {'pity': 72, 'guarantee': False}],
   {'results': '--L', 'pity': 0, 'guarantee': True})],
 [('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #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 pull numbering #2',
   [[911], {'pity': 73, 'guarantee': True}],
   {'results': '-', 'pity': 74, 'guarantee': True}),
  ('regression pull numbering #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}),
  ('regression pull numbering #4',
   [[815, 889, 39, 873, 939, 933, 908, 992, 421, 939, 821, 53, 12, 40, 8, 884, 975, 551, 967, 39],
    {'pity': 63, 'guarantee': True}],
   {'results': '-----------F--------', 'pity': 8, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[18, 973, 5], {'pity': 72, 'guarantee': False}],
   {'results': '--L', 'pity': 0, 'guarantee': True})],
 [('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #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 pull numbering #2',
   [[815, 889, 39, 873, 939, 933, 908, 992, 421, 939, 821, 53, 12, 40, 8, 884, 975, 551, 967, 39],
    {'pity': 63, 'guarantee': True}],
   {'results': '-----------F--------', 'pity': 8, 'guarantee': False}),
  ('regression pull numbering #3',
   [[4, 155, 441, 951, 967, 353, 21], {'pity': 68, 'guarantee': False}],
   {'results': 'F------', 'pity': 6, 'guarantee': False}),
  ('regression pull numbering #4',
   [[685, 976, 49, 33, 16, 30, 427, 839], {'pity': 0, 'guarantee': False}],
   {'results': '--------', 'pity': 8, 'guarantee': False}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1',
   [[857, 5], {'pity': 24, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False})],
 [('hard pity pull #1',
   [[999, 999], {'pity': 89, 'guarantee': False}],
   {'results': 'L-', 'pity': 1, 'guarantee': True}),
  ('regression pull numbering #1',
   [[4, 155, 441, 951, 967, 353, 21], {'pity': 68, 'guarantee': False}],
   {'results': 'F------', 'pity': 6, 'guarantee': False}),
  ('regression pull numbering #2',
   [[685, 976, 49, 33, 16, 30, 427, 839], {'pity': 0, 'guarantee': False}],
   {'results': '--------', 'pity': 8, 'guarantee': False}),
  ('regression pull numbering #3',
   [[18, 16, 60, 53, 197, 713, 972, 933], {'pity': 75, 'guarantee': True}],
   {'results': 'F-------', 'pity': 7, 'guarantee': False}),
  ('regression pull numbering #4',
   [[773, 957, 60, 353, 59, 19, 862, 820, 993, 27, 22, 893, 950], {'pity': 0, 'guarantee': True}],
   {'results': '-------------', 'pity': 13, 'guarantee': True}),
  ('first soft pity pull #1',
   [[100, 3], {'pity': 73, 'guarantee': True}],
   {'results': '-F', 'pity': 0, 'guarantee': False}),
  ('lost fifty fifty then featured #1',
   [[1, 999, 0], {'pity': 10, 'guarantee': False}],
   {'results': 'L-F', 'pity': 0, 'guarantee': False}),
  ('control #1', [[4], {'pity': 73, 'guarantee': False}], {'results': 'F', 'pity': 0, 'guarantee': False})]]
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
hard pity pull #1	`{'guarantee': True, 'pity': 1, 'results': 'L-'}`	`{'guarantee': True, 'pity': 1, 'results': 'L-'}`	Passed
regression pull numbering #1	`{'guarantee': False, 'pity': 14, 'results': 'F--------------'}`	`{'guarantee': False, 'pity': 14, 'results': 'F--------------'}`	Passed
regression pull numbering #2	`{'guarantee': False, 'pity': 2, 'results': '--F--'}`	`{'guarantee': False, 'pity': 2, 'results': '--F--'}`	Passed
regression pull numbering #3	`{'guarantee': False, 'pity': 17, 'results': 'F-----------------'}`	`{'guarantee': False, 'pity': 17, 'results': 'F-----------------'}`	Passed
regression pull numbering #4	`{'guarantee': True, 'pity': 12, 'results': '-L------------'}`	`{'guarantee': True, 'pity': 12, 'results': '-L------------'}`	Passed
first soft pity pull #1	`{'guarantee': False, 'pity': 0, 'results': '-F'}`	`{'guarantee': False, 'pity': 0, 'results': '-F'}`	Passed
lost fifty fifty then featured #1	`{'guarantee': False, 'pity': 0, 'results': 'L-F'}`	`{'guarantee': False, 'pity': 0, 'results': 'L-F'}`	Passed
control #1	`{'guarantee': True, 'pity': 0, 'results': '--L'}`	`{'guarantee': True, 'pity': 0, 'results': '--L'}`	Passed

SHA-256 / 84043eaa549c4c7202c2f2b7328926425eb123c31d02210456f5b3dbd64b695d

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 2026-09-29T14:50:44.820028+00:00.

Case digest / 8e502355c620c9fcd9f1eed6c5f4105551f3bd1ad70f44f794d124aac2d3a006