FAILURE MAP
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FA-86331 / Game economy crafting balance / Open access

Crafting XP with rested pool: Capped characters keep leftover xp · case 01

The xp bar shows progress past the level cap.

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

ROOT CAUSE

Reaching the cap leaves the carried xp on the bar.

VERIFIED REPAIR

Restore `if level >= 50: xp = 0` at the cap bar reset step.

Unsuccessful approach: Clamping to the requirement still shows a non-empty bar at cap.

Case contract

Level L needs 80 + 20*L xp to reach L+1; max level 50. Gains are ignored once level 50 is reached (rested untouched). For each gain g: bonus = min(g, rested) is added on top of g and removed from the rested pool; then as many levels as possible are taken, carrying remaining xp; on reaching level 50 the xp bar is set to 0. Returns [level, xp, rested].

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(level, xp, gains, rested):
    for g in gains:
        if level >= 50:
            break
        bonus = min(g, rested)
        rested -= bonus
        xp += g + bonus
        while level < 50 and xp >= 80 + 20 * level:
            xp -= 80 + 20 * level
            level += 1
        if level >= 50:
            pass
    return [level, xp, rested]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression cap bar reset #1', [49, 56, [516, 2000], 100], [50, 0, 0]),
  ('regression cap bar reset #2', [49, 57, [300, 2000, 274], 0], [50, 0, 0]),
  ('regression cap bar reset #3', [49, 101, [300, 300, 100, 99, 100], 1000], [50, 0, 400]),
  ('regression cap bar reset #4', [49, 62, [99, 10, 2000, 99], 0], [50, 0, 0]),
  ('multi-level gain #1', [1, 0, [300], 0], [3, 80, 0]),
  ('exact threshold #1', [10, 0, [280], 0], [11, 0, 0]),
  ('gain at cap keeps rested #1', [50, 0, [100], 40], [50, 0, 40]),
  ('control #1', [48, 123, [50, 10, 420], 100], [48, 703, 0])],
 [('regression cap bar reset #1', [49, 101, [300, 300, 100, 99, 100], 1000], [50, 0, 400]),
  ('regression cap bar reset #2', [49, 62, [99, 10, 2000, 99], 0], [50, 0, 0]),
  ('regression cap bar reset #3', [49, 90, [2000, 89], 100], [50, 0, 0]),
  ('regression cap bar reset #4', [49, 126, [2000, 99], 345], [50, 0, 0]),
  ('gain at cap keeps rested #1', [50, 0, [100], 40], [50, 0, 40]),
  ('multi-level gain #1', [1, 0, [300], 0], [3, 80, 0]),
  ('control #1', [48, 123, [50, 10, 420], 100], [48, 703, 0]),
  ('control #2', [50, 56, [99], 100], [50, 56, 100])],
 [('regression cap bar reset #1', [49, 90, [2000, 89], 100], [50, 0, 0]),
  ('regression cap bar reset #2', [49, 126, [2000, 99], 345], [50, 0, 0]),
  ('regression cap bar reset #3', [49, 62, [300, 393, 300, 300], 0], [50, 0, 0]),
  ('regression cap bar reset #4', [49, 50, [2000, 50], 1000], [50, 0, 0]),
  ('exact threshold #1', [10, 0, [280], 0], [11, 0, 0]),
  ('gain at cap keeps rested #1', [50, 0, [100], 40], [50, 0, 40]),
  ('control #1', [50, 56, [99], 100], [50, 56, 100]),
  ('control #2', [5, 79, [300], 0], [6, 199, 0])],
 [('regression cap bar reset #1', [49, 62, [300, 393, 300, 300], 0], [50, 0, 0]),
  ('regression cap bar reset #2', [49, 50, [2000, 50], 1000], [50, 0, 0]),
  ('regression cap bar reset #3', [49, 47, [100, 10, 2000, 99], 100], [50, 0, 0]),
  ('regression cap bar reset #4', [49, 132, [300, 50, 99, 99], 1000], [50, 0, 452]),
  ('multi-level gain #1', [1, 0, [300], 0], [3, 80, 0]),
  ('exact threshold #1', [10, 0, [280], 0], [11, 0, 0]),
  ('control #1', [10, 7, [300, 50, 99, 100], 0], [11, 276, 0]),
  ('control #2', [48, 108, [300, 300, 99, 86, 300], 30], [49, 183, 0])],
 [('regression cap bar reset #1', [49, 47, [100, 10, 2000, 99], 100], [50, 0, 0]),
  ('regression cap bar reset #2', [49, 132, [300, 50, 99, 99], 1000], [50, 0, 452]),
  ('regression cap bar reset #3', [49, 30, [2000, 2000, 99, 10], 16], [50, 0, 0]),
  ('regression cap bar reset #4', [49, 105, [300, 300, 10, 390, 100], 0], [50, 0, 0]),
  ('gain at cap keeps rested #1', [50, 0, [100], 40], [50, 0, 40]),
  ('multi-level gain #1', [1, 0, [300], 0], [3, 80, 0]),
  ('control #1', [5, 79, [100, 10, 2000], 0], [13, 189, 0]),
  ('control #2', [29, 125, [2000], 0], [32, 85, 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
regression cap bar reset #1[50, 1612, 0][50, 0, 0]Failed
regression cap bar reset #2[50, 1297, 0][50, 0, 0]Failed
regression cap bar reset #3[50, 241, 400][50, 0, 400]Failed
regression cap bar reset #4[50, 1111, 0][50, 0, 0]Failed
multi-level gain #1[3, 80, 0][3, 80, 0]Passed
exact threshold #1[11, 0, 0][11, 0, 0]Passed
gain at cap keeps rested #1[50, 0, 40][50, 0, 40]Passed
control #1[48, 703, 0][48, 703, 0]Passed

SHA-256 / 5dbaaeddf2eb052b9426af796ec3cea61c00eddf822c653784511e5e75fcbdc5

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(level, xp, gains, rested):
    for g in gains:
        if level >= 50:
            break
        bonus = min(g, rested)
        rested -= bonus
        xp += g + bonus
        while level < 50 and xp >= 80 + 20 * level:
            xp -= 80 + 20 * level
            level += 1
        if level >= 50:
            xp = min(xp, 80 + 20 * level)
    return [level, xp, rested]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression cap bar reset #1', [49, 56, [516, 2000], 100], [50, 0, 0]),
  ('regression cap bar reset #2', [49, 57, [300, 2000, 274], 0], [50, 0, 0]),
  ('regression cap bar reset #3', [49, 101, [300, 300, 100, 99, 100], 1000], [50, 0, 400]),
  ('regression cap bar reset #4', [49, 62, [99, 10, 2000, 99], 0], [50, 0, 0]),
  ('multi-level gain #1', [1, 0, [300], 0], [3, 80, 0]),
  ('exact threshold #1', [10, 0, [280], 0], [11, 0, 0]),
  ('gain at cap keeps rested #1', [50, 0, [100], 40], [50, 0, 40]),
  ('control #1', [48, 123, [50, 10, 420], 100], [48, 703, 0])],
 [('regression cap bar reset #1', [49, 101, [300, 300, 100, 99, 100], 1000], [50, 0, 400]),
  ('regression cap bar reset #2', [49, 62, [99, 10, 2000, 99], 0], [50, 0, 0]),
  ('regression cap bar reset #3', [49, 90, [2000, 89], 100], [50, 0, 0]),
  ('regression cap bar reset #4', [49, 126, [2000, 99], 345], [50, 0, 0]),
  ('gain at cap keeps rested #1', [50, 0, [100], 40], [50, 0, 40]),
  ('multi-level gain #1', [1, 0, [300], 0], [3, 80, 0]),
  ('control #1', [48, 123, [50, 10, 420], 100], [48, 703, 0]),
  ('control #2', [50, 56, [99], 100], [50, 56, 100])],
 [('regression cap bar reset #1', [49, 90, [2000, 89], 100], [50, 0, 0]),
  ('regression cap bar reset #2', [49, 126, [2000, 99], 345], [50, 0, 0]),
  ('regression cap bar reset #3', [49, 62, [300, 393, 300, 300], 0], [50, 0, 0]),
  ('regression cap bar reset #4', [49, 50, [2000, 50], 1000], [50, 0, 0]),
  ('exact threshold #1', [10, 0, [280], 0], [11, 0, 0]),
  ('gain at cap keeps rested #1', [50, 0, [100], 40], [50, 0, 40]),
  ('control #1', [50, 56, [99], 100], [50, 56, 100]),
  ('control #2', [5, 79, [300], 0], [6, 199, 0])],
 [('regression cap bar reset #1', [49, 62, [300, 393, 300, 300], 0], [50, 0, 0]),
  ('regression cap bar reset #2', [49, 50, [2000, 50], 1000], [50, 0, 0]),
  ('regression cap bar reset #3', [49, 47, [100, 10, 2000, 99], 100], [50, 0, 0]),
  ('regression cap bar reset #4', [49, 132, [300, 50, 99, 99], 1000], [50, 0, 452]),
  ('multi-level gain #1', [1, 0, [300], 0], [3, 80, 0]),
  ('exact threshold #1', [10, 0, [280], 0], [11, 0, 0]),
  ('control #1', [10, 7, [300, 50, 99, 100], 0], [11, 276, 0]),
  ('control #2', [48, 108, [300, 300, 99, 86, 300], 30], [49, 183, 0])],
 [('regression cap bar reset #1', [49, 47, [100, 10, 2000, 99], 100], [50, 0, 0]),
  ('regression cap bar reset #2', [49, 132, [300, 50, 99, 99], 1000], [50, 0, 452]),
  ('regression cap bar reset #3', [49, 30, [2000, 2000, 99, 10], 16], [50, 0, 0]),
  ('regression cap bar reset #4', [49, 105, [300, 300, 10, 390, 100], 0], [50, 0, 0]),
  ('gain at cap keeps rested #1', [50, 0, [100], 40], [50, 0, 40]),
  ('multi-level gain #1', [1, 0, [300], 0], [3, 80, 0]),
  ('control #1', [5, 79, [100, 10, 2000], 0], [13, 189, 0]),
  ('control #2', [29, 125, [2000], 0], [32, 85, 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
regression cap bar reset #1[50, 1080, 0][50, 0, 0]Failed
regression cap bar reset #2[50, 1080, 0][50, 0, 0]Failed
regression cap bar reset #3[50, 241, 400][50, 0, 400]Failed
regression cap bar reset #4[50, 1080, 0][50, 0, 0]Failed
multi-level gain #1[3, 80, 0][3, 80, 0]Passed
exact threshold #1[11, 0, 0][11, 0, 0]Passed
gain at cap keeps rested #1[50, 0, 40][50, 0, 40]Passed
control #1[48, 703, 0][48, 703, 0]Passed

SHA-256 / 15786f8217c2062451cbb3247defc64e133bbe451f9212820360d095286643a0

3 / The verified repair

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

N = 1
observations = []
def solve(level, xp, gains, rested):
    for g in gains:
        if level >= 50:
            break
        bonus = min(g, rested)
        rested -= bonus
        xp += g + bonus
        while level < 50 and xp >= 80 + 20 * level:
            xp -= 80 + 20 * level
            level += 1
        if level >= 50:
            xp = 0
    return [level, xp, rested]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression cap bar reset #1', [49, 56, [516, 2000], 100], [50, 0, 0]),
  ('regression cap bar reset #2', [49, 57, [300, 2000, 274], 0], [50, 0, 0]),
  ('regression cap bar reset #3', [49, 101, [300, 300, 100, 99, 100], 1000], [50, 0, 400]),
  ('regression cap bar reset #4', [49, 62, [99, 10, 2000, 99], 0], [50, 0, 0]),
  ('multi-level gain #1', [1, 0, [300], 0], [3, 80, 0]),
  ('exact threshold #1', [10, 0, [280], 0], [11, 0, 0]),
  ('gain at cap keeps rested #1', [50, 0, [100], 40], [50, 0, 40]),
  ('control #1', [48, 123, [50, 10, 420], 100], [48, 703, 0])],
 [('regression cap bar reset #1', [49, 101, [300, 300, 100, 99, 100], 1000], [50, 0, 400]),
  ('regression cap bar reset #2', [49, 62, [99, 10, 2000, 99], 0], [50, 0, 0]),
  ('regression cap bar reset #3', [49, 90, [2000, 89], 100], [50, 0, 0]),
  ('regression cap bar reset #4', [49, 126, [2000, 99], 345], [50, 0, 0]),
  ('gain at cap keeps rested #1', [50, 0, [100], 40], [50, 0, 40]),
  ('multi-level gain #1', [1, 0, [300], 0], [3, 80, 0]),
  ('control #1', [48, 123, [50, 10, 420], 100], [48, 703, 0]),
  ('control #2', [50, 56, [99], 100], [50, 56, 100])],
 [('regression cap bar reset #1', [49, 90, [2000, 89], 100], [50, 0, 0]),
  ('regression cap bar reset #2', [49, 126, [2000, 99], 345], [50, 0, 0]),
  ('regression cap bar reset #3', [49, 62, [300, 393, 300, 300], 0], [50, 0, 0]),
  ('regression cap bar reset #4', [49, 50, [2000, 50], 1000], [50, 0, 0]),
  ('exact threshold #1', [10, 0, [280], 0], [11, 0, 0]),
  ('gain at cap keeps rested #1', [50, 0, [100], 40], [50, 0, 40]),
  ('control #1', [50, 56, [99], 100], [50, 56, 100]),
  ('control #2', [5, 79, [300], 0], [6, 199, 0])],
 [('regression cap bar reset #1', [49, 62, [300, 393, 300, 300], 0], [50, 0, 0]),
  ('regression cap bar reset #2', [49, 50, [2000, 50], 1000], [50, 0, 0]),
  ('regression cap bar reset #3', [49, 47, [100, 10, 2000, 99], 100], [50, 0, 0]),
  ('regression cap bar reset #4', [49, 132, [300, 50, 99, 99], 1000], [50, 0, 452]),
  ('multi-level gain #1', [1, 0, [300], 0], [3, 80, 0]),
  ('exact threshold #1', [10, 0, [280], 0], [11, 0, 0]),
  ('control #1', [10, 7, [300, 50, 99, 100], 0], [11, 276, 0]),
  ('control #2', [48, 108, [300, 300, 99, 86, 300], 30], [49, 183, 0])],
 [('regression cap bar reset #1', [49, 47, [100, 10, 2000, 99], 100], [50, 0, 0]),
  ('regression cap bar reset #2', [49, 132, [300, 50, 99, 99], 1000], [50, 0, 452]),
  ('regression cap bar reset #3', [49, 30, [2000, 2000, 99, 10], 16], [50, 0, 0]),
  ('regression cap bar reset #4', [49, 105, [300, 300, 10, 390, 100], 0], [50, 0, 0]),
  ('gain at cap keeps rested #1', [50, 0, [100], 40], [50, 0, 40]),
  ('multi-level gain #1', [1, 0, [300], 0], [3, 80, 0]),
  ('control #1', [5, 79, [100, 10, 2000], 0], [13, 189, 0]),
  ('control #2', [29, 125, [2000], 0], [32, 85, 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
regression cap bar reset #1[50, 0, 0][50, 0, 0]Passed
regression cap bar reset #2[50, 0, 0][50, 0, 0]Passed
regression cap bar reset #3[50, 0, 400][50, 0, 400]Passed
regression cap bar reset #4[50, 0, 0][50, 0, 0]Passed
multi-level gain #1[3, 80, 0][3, 80, 0]Passed
exact threshold #1[11, 0, 0][11, 0, 0]Passed
gain at cap keeps rested #1[50, 0, 40][50, 0, 40]Passed
control #1[48, 703, 0][48, 703, 0]Passed

SHA-256 / f2b6015cf1742ff0fd2b0f62d0e19e679e8995feb1647bc4908bb7ad86f36274

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 2026-09-29T14:50:48.615101+00:00.

Case digest / 065a37daa0a14ecb470a5c704b7c15bbef8a52945b86d1afe7186408616bf421