FAILURE MAP
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FA-86146 / Game economy crafting balance / Open access

Repeatable quest rewards: Half tier spans ten completions · case 01

Players farm five extra half-reward completions.

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

ROOT CAUSE

The half-reward window is measured as ten completions after the full tier.

VERIFIED REPAIR

Restore `elif k < 10:` at the half tier boundary step.

Unsuccessful approach: An inclusive bound still pays one extra half reward.

Case contract

Completion k (0-based across the day, starting at done_today) pays tier 100% for k < 5, 50% for 5 <= k < 10, 0 after. Gap = player_level - quest_level: >= 5 pays 20%, >= 3 pays 60%, otherwise 100% (higher level quests are never penalized). Each reward = floor(base*tier*gap/10000). Returns the list of the next count rewards.

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(done_today, count, base, player_level, quest_level):
    if player_level - quest_level >= 5:
        gap = 20
    elif player_level - quest_level >= 3:
        gap = 60
    else:
        gap = 100
    out = []
    for k in range(done_today, done_today + count):
        if k < 5:
            tier = 100
        elif k < 15:
            tier = 50
        else:
            tier = 0
        out.append(base * tier * gap // 10000)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('regression half tier boundary #1', [6, 6, 215, 11, 12], [107, 107, 107, 107, 0, 0]),
  ('regression half tier boundary #2', [9, 4, 3, 24, 23], [1, 0, 0, 0]),
  ('regression half tier boundary #3', [8, 6, 99, 11, 18], [49, 49, 0, 0, 0, 0]),
  ('regression half tier boundary #4', [8, 4, 99, 8, 6], [49, 49, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [3, 4, 101, 31, 28], [60, 60, 30, 30])],
 [('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('regression half tier boundary #1', [9, 4, 3, 24, 23], [1, 0, 0, 0]),
  ('regression half tier boundary #2', [8, 6, 99, 11, 18], [49, 49, 0, 0, 0, 0]),
  ('regression half tier boundary #3', [8, 4, 99, 8, 6], [49, 49, 0, 0]),
  ('regression half tier boundary #4', [8, 4, 99, 29, 33], [49, 49, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [3, 4, 101, 31, 28], [60, 60, 30, 30])],
 [('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('fault site half tier boundary #1', [12, 2, 107, 5, -1], [0, 0]),
  ('regression half tier boundary #1', [8, 4, 99, 8, 6], [49, 49, 0, 0]),
  ('regression half tier boundary #2', [8, 4, 99, 29, 33], [49, 49, 0, 0]),
  ('regression half tier boundary #3', [9, 5, 101, 15, 10], [10, 0, 0, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [3, 4, 101, 31, 28], [60, 60, 30, 30])],
 [('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('regression half tier boundary #1', [8, 4, 99, 29, 33], [49, 49, 0, 0]),
  ('regression half tier boundary #2', [9, 5, 101, 15, 10], [10, 0, 0, 0, 0]),
  ('regression half tier boundary #3', [10, 2, 7, 12, 14], [0, 0]),
  ('regression half tier boundary #4', [10, 5, 467, 9, 16], [0, 0, 0, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [8, 2, 1, 33, 25], [0, 0])],
 [('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('regression half tier boundary #1', [10, 2, 7, 12, 14], [0, 0]),
  ('fault site half tier boundary #1', [12, 5, 7, 23, 22], [0, 0, 0, 0, 0]),
  ('regression half tier boundary #2', [10, 5, 467, 9, 16], [0, 0, 0, 0, 0]),
  ('regression half tier boundary #3', [9, 4, 132, 55, 59], [66, 0, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [3, 6, 99, 59, 64], [99, 99, 49, 49, 49, 49])]]
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
harder quest no penalty #1[25, 25, 25][25, 25, 0]Failed
regression half tier boundary #1[107, 107, 107, 107, 107, 107][107, 107, 107, 107, 0, 0]Failed
regression half tier boundary #2[1, 1, 1, 1][1, 0, 0, 0]Failed
regression half tier boundary #3[49, 49, 49, 49, 49, 49][49, 49, 0, 0, 0, 0]Failed
regression half tier boundary #4[49, 49, 49, 49][49, 49, 0, 0]Failed
crossing into half tier #1[101, 101, 50, 50][101, 101, 50, 50]Passed
gray quest #1[19, 19][19, 19]Passed
control #1[60, 60, 30, 30][60, 60, 30, 30]Passed

SHA-256 / bb0a73bf76211d1710c2bd65087fb28f0ab892c80cbcfc09f345e63e4e012098

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(done_today, count, base, player_level, quest_level):
    if player_level - quest_level >= 5:
        gap = 20
    elif player_level - quest_level >= 3:
        gap = 60
    else:
        gap = 100
    out = []
    for k in range(done_today, done_today + count):
        if k < 5:
            tier = 100
        elif k <= 10:
            tier = 50
        else:
            tier = 0
        out.append(base * tier * gap // 10000)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('regression half tier boundary #1', [6, 6, 215, 11, 12], [107, 107, 107, 107, 0, 0]),
  ('regression half tier boundary #2', [9, 4, 3, 24, 23], [1, 0, 0, 0]),
  ('regression half tier boundary #3', [8, 6, 99, 11, 18], [49, 49, 0, 0, 0, 0]),
  ('regression half tier boundary #4', [8, 4, 99, 8, 6], [49, 49, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [3, 4, 101, 31, 28], [60, 60, 30, 30])],
 [('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('regression half tier boundary #1', [9, 4, 3, 24, 23], [1, 0, 0, 0]),
  ('regression half tier boundary #2', [8, 6, 99, 11, 18], [49, 49, 0, 0, 0, 0]),
  ('regression half tier boundary #3', [8, 4, 99, 8, 6], [49, 49, 0, 0]),
  ('regression half tier boundary #4', [8, 4, 99, 29, 33], [49, 49, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [3, 4, 101, 31, 28], [60, 60, 30, 30])],
 [('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('fault site half tier boundary #1', [12, 2, 107, 5, -1], [0, 0]),
  ('regression half tier boundary #1', [8, 4, 99, 8, 6], [49, 49, 0, 0]),
  ('regression half tier boundary #2', [8, 4, 99, 29, 33], [49, 49, 0, 0]),
  ('regression half tier boundary #3', [9, 5, 101, 15, 10], [10, 0, 0, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [3, 4, 101, 31, 28], [60, 60, 30, 30])],
 [('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('regression half tier boundary #1', [8, 4, 99, 29, 33], [49, 49, 0, 0]),
  ('regression half tier boundary #2', [9, 5, 101, 15, 10], [10, 0, 0, 0, 0]),
  ('regression half tier boundary #3', [10, 2, 7, 12, 14], [0, 0]),
  ('regression half tier boundary #4', [10, 5, 467, 9, 16], [0, 0, 0, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [8, 2, 1, 33, 25], [0, 0])],
 [('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('regression half tier boundary #1', [10, 2, 7, 12, 14], [0, 0]),
  ('fault site half tier boundary #1', [12, 5, 7, 23, 22], [0, 0, 0, 0, 0]),
  ('regression half tier boundary #2', [10, 5, 467, 9, 16], [0, 0, 0, 0, 0]),
  ('regression half tier boundary #3', [9, 4, 132, 55, 59], [66, 0, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [3, 6, 99, 59, 64], [99, 99, 49, 49, 49, 49])]]
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
harder quest no penalty #1[25, 25, 25][25, 25, 0]Failed
regression half tier boundary #1[107, 107, 107, 107, 107, 0][107, 107, 107, 107, 0, 0]Failed
regression half tier boundary #2[1, 1, 0, 0][1, 0, 0, 0]Failed
regression half tier boundary #3[49, 49, 49, 0, 0, 0][49, 49, 0, 0, 0, 0]Failed
regression half tier boundary #4[49, 49, 49, 0][49, 49, 0, 0]Failed
crossing into half tier #1[101, 101, 50, 50][101, 101, 50, 50]Passed
gray quest #1[19, 19][19, 19]Passed
control #1[60, 60, 30, 30][60, 60, 30, 30]Passed

SHA-256 / 6350ad7667fc7eb05114c2f141f262fbe5bfed40190798dc8eb2d7b66ced54aa

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(done_today, count, base, player_level, quest_level):
    if player_level - quest_level >= 5:
        gap = 20
    elif player_level - quest_level >= 3:
        gap = 60
    else:
        gap = 100
    out = []
    for k in range(done_today, done_today + count):
        if k < 5:
            tier = 100
        elif k < 10:
            tier = 50
        else:
            tier = 0
        out.append(base * tier * gap // 10000)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('regression half tier boundary #1', [6, 6, 215, 11, 12], [107, 107, 107, 107, 0, 0]),
  ('regression half tier boundary #2', [9, 4, 3, 24, 23], [1, 0, 0, 0]),
  ('regression half tier boundary #3', [8, 6, 99, 11, 18], [49, 49, 0, 0, 0, 0]),
  ('regression half tier boundary #4', [8, 4, 99, 8, 6], [49, 49, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [3, 4, 101, 31, 28], [60, 60, 30, 30])],
 [('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('regression half tier boundary #1', [9, 4, 3, 24, 23], [1, 0, 0, 0]),
  ('regression half tier boundary #2', [8, 6, 99, 11, 18], [49, 49, 0, 0, 0, 0]),
  ('regression half tier boundary #3', [8, 4, 99, 8, 6], [49, 49, 0, 0]),
  ('regression half tier boundary #4', [8, 4, 99, 29, 33], [49, 49, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [3, 4, 101, 31, 28], [60, 60, 30, 30])],
 [('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('fault site half tier boundary #1', [12, 2, 107, 5, -1], [0, 0]),
  ('regression half tier boundary #1', [8, 4, 99, 8, 6], [49, 49, 0, 0]),
  ('regression half tier boundary #2', [8, 4, 99, 29, 33], [49, 49, 0, 0]),
  ('regression half tier boundary #3', [9, 5, 101, 15, 10], [10, 0, 0, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [3, 4, 101, 31, 28], [60, 60, 30, 30])],
 [('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('regression half tier boundary #1', [8, 4, 99, 29, 33], [49, 49, 0, 0]),
  ('regression half tier boundary #2', [9, 5, 101, 15, 10], [10, 0, 0, 0, 0]),
  ('regression half tier boundary #3', [10, 2, 7, 12, 14], [0, 0]),
  ('regression half tier boundary #4', [10, 5, 467, 9, 16], [0, 0, 0, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [8, 2, 1, 33, 25], [0, 0])],
 [('harder quest no penalty #1', [8, 3, 50, 10, 18], [25, 25, 0]),
  ('regression half tier boundary #1', [10, 2, 7, 12, 14], [0, 0]),
  ('fault site half tier boundary #1', [12, 5, 7, 23, 22], [0, 0, 0, 0, 0]),
  ('regression half tier boundary #2', [10, 5, 467, 9, 16], [0, 0, 0, 0, 0]),
  ('regression half tier boundary #3', [9, 4, 132, 55, 59], [66, 0, 0, 0]),
  ('crossing into half tier #1', [3, 4, 101, 20, 20], [101, 101, 50, 50]),
  ('gray quest #1', [0, 2, 99, 30, 25], [19, 19]),
  ('control #1', [3, 6, 99, 59, 64], [99, 99, 49, 49, 49, 49])]]
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
harder quest no penalty #1[25, 25, 0][25, 25, 0]Passed
regression half tier boundary #1[107, 107, 107, 107, 0, 0][107, 107, 107, 107, 0, 0]Passed
regression half tier boundary #2[1, 0, 0, 0][1, 0, 0, 0]Passed
regression half tier boundary #3[49, 49, 0, 0, 0, 0][49, 49, 0, 0, 0, 0]Passed
regression half tier boundary #4[49, 49, 0, 0][49, 49, 0, 0]Passed
crossing into half tier #1[101, 101, 50, 50][101, 101, 50, 50]Passed
gray quest #1[19, 19][19, 19]Passed
control #1[60, 60, 30, 30][60, 60, 30, 30]Passed

SHA-256 / 2e4008557bb422847aa263367fc49d9902070a9d0ffcccbe41c49d3cc66964e4

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 2026-09-29T14:50:46.950202+00:00.

Case digest / 94831df9a5afd45788a6a9f3cd9d86aa893034550854e6c59e3f06135a7ef7bf