FA-86076 / Game economy crafting balance / Open access
Stamina regeneration: Partial regen progress is discarded · case 01
Stamina regenerates slower whenever an event lands between ticks.
ROOT CAUSE
The anchor jumps to the event time instead of advancing by whole periods.
VERIFIED REPAIR
Restore `t += gained * 300` at the anchor advance step.
Unsuccessful approach: Aligning to the original last_tick ignores anchor moves caused by capping or spending.
Case contract
Stamina regenerates 1 per 300 s while below cap, anchored at last_tick. Events [time, amount] are applied in time order (then amount); before each event (and finally at now) regeneration catches up: if it reaches cap the value becomes cap and the anchor moves to the event time, otherwise the anchor advances by whole periods. While at or above cap the anchor follows the event time. Amounts may push stamina above cap up to 999; negative amounts are spends that are rejected if they would go below zero. Return [stamina, anchor].
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(stamina, cap, last_tick, now, refills):
events = sorted(refills) + [[now, 0]]
t = last_tick
s = stamina
for at, amount in events:
if s < cap:
gained = (at - t) // 300
if s + gained >= cap:
s = cap
t = at
else:
s += gained
t = at
else:
t = at
if s + amount >= 0:
s = min(999, s + amount)
return [s, t]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('regression anchor advance #1', [23, 20, 972, 1572, [[1185, -20], [1315, -20], [1066, 20]]], [3, 1315]),
('fault site anchor advance #1', [16, 17, 83, 1773, [[154, -6]]], [15, 1583]),
('regression anchor advance #2', [20, 17, 920, 1520, [[1180, -17], [1013, -17], [1246, -5]]], [4, 1313]),
('regression anchor advance #3', [19, 17, 150, 2485, [[2240, -10]]], [9, 2240]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [9, 9, 266, 266, [[266, -9], [266, -10]]], [0, 266])],
[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('fault site anchor advance #1', [8, 9, 913, 1212, [[1053, -9], [963, -6], [1014, -5]]], [2, 913]),
('regression anchor advance #1', [20, 17, 920, 1520, [[1180, -17], [1013, -17], [1246, -5]]], [4, 1313]),
('regression anchor advance #2', [19, 17, 150, 2485, [[2240, -10]]], [9, 2240]),
('regression anchor advance #3', [9, 6, 0, 299, [[276, -6], [47, -6], [269, -6]]], [3, 47]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [9, 9, 266, 266, [[266, -9], [266, -10]]], [0, 266])],
[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('fault site anchor advance #1', [0, 14, 832, 1131, [[897, -4]]], [0, 832]),
('fault site anchor advance #2', [0, 10, 347, 646, [[390, -10], [479, -9]]], [0, 347]),
('regression anchor advance #1', [9, 6, 0, 299, [[276, -6], [47, -6], [269, -6]]], [3, 47]),
('regression anchor advance #2', [18, 15, 804, 1404, [[1122, -11], [838, -10], [1325, -15]]], [9, 1138]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [9, 9, 266, 266, [[266, -9], [266, -10]]], [0, 266])],
[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('fault site anchor advance #1', [0, 19, 453, 6068, [[1708, -7], [2101, -3], [2012, -19]]], [15, 5853]),
('regression anchor advance #1', [19, 17, 150, 2485, [[2240, -10]]], [9, 2240]),
('regression anchor advance #2', [18, 15, 245, 845, [[385, -15]]], [4, 685]),
('regression anchor advance #3', [21, 18, 351, 650, [[484, -18]]], [3, 484]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [12, 13, 710, 1010, [[793, 7], [721, 13]]], [32, 1010])],
[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('fault site anchor advance #1', [2, 19, 442, 741, [[703, -19]]], [2, 442]),
('regression anchor advance #1', [9, 6, 0, 299, [[276, -6], [47, -6], [269, -6]]], [3, 47]),
('regression anchor advance #2', [4, 5, 685, 984, [[969, -9], [731, -5], [931, 5]]], [0, 969]),
('regression anchor advance #3', [12, 13, 487, 4020, [[1176, -13], [3667, -7]]], [2, 3876]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [11, 12, 57, 163, [[92, 12], [139, 12]]], [35, 163])]]
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 |
|---|---|---|---|
| spend from full restarts timer #1 | [8, 1000] | [8, 1000] | Passed |
| regression anchor advance #1 | [3, 1572] | [3, 1315] | Failed |
| fault site anchor advance #1 | [15, 1773] | [15, 1583] | Failed |
| regression anchor advance #2 | [3, 1520] | [4, 1313] | Failed |
| regression anchor advance #3 | [9, 2485] | [9, 2240] | Failed |
| exact refill to cap #1 | [5, 600] | [5, 600] | Passed |
| overflow potion persists #1 | [15, 1200] | [15, 1200] | Passed |
| control #1 | [0, 266] | [0, 266] | Passed |
SHA-256 / 98043a8484b7ada76f5b97b2afc479da758d1f5eca36ac41ee3d104c650d31dd
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(stamina, cap, last_tick, now, refills):
events = sorted(refills) + [[now, 0]]
t = last_tick
s = stamina
for at, amount in events:
if s < cap:
gained = (at - t) // 300
if s + gained >= cap:
s = cap
t = at
else:
s += gained
t = at - (at - last_tick) % 300
else:
t = at
if s + amount >= 0:
s = min(999, s + amount)
return [s, t]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('regression anchor advance #1', [23, 20, 972, 1572, [[1185, -20], [1315, -20], [1066, 20]]], [3, 1315]),
('fault site anchor advance #1', [16, 17, 83, 1773, [[154, -6]]], [15, 1583]),
('regression anchor advance #2', [20, 17, 920, 1520, [[1180, -17], [1013, -17], [1246, -5]]], [4, 1313]),
('regression anchor advance #3', [19, 17, 150, 2485, [[2240, -10]]], [9, 2240]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [9, 9, 266, 266, [[266, -9], [266, -10]]], [0, 266])],
[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('fault site anchor advance #1', [8, 9, 913, 1212, [[1053, -9], [963, -6], [1014, -5]]], [2, 913]),
('regression anchor advance #1', [20, 17, 920, 1520, [[1180, -17], [1013, -17], [1246, -5]]], [4, 1313]),
('regression anchor advance #2', [19, 17, 150, 2485, [[2240, -10]]], [9, 2240]),
('regression anchor advance #3', [9, 6, 0, 299, [[276, -6], [47, -6], [269, -6]]], [3, 47]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [9, 9, 266, 266, [[266, -9], [266, -10]]], [0, 266])],
[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('fault site anchor advance #1', [0, 14, 832, 1131, [[897, -4]]], [0, 832]),
('fault site anchor advance #2', [0, 10, 347, 646, [[390, -10], [479, -9]]], [0, 347]),
('regression anchor advance #1', [9, 6, 0, 299, [[276, -6], [47, -6], [269, -6]]], [3, 47]),
('regression anchor advance #2', [18, 15, 804, 1404, [[1122, -11], [838, -10], [1325, -15]]], [9, 1138]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [9, 9, 266, 266, [[266, -9], [266, -10]]], [0, 266])],
[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('fault site anchor advance #1', [0, 19, 453, 6068, [[1708, -7], [2101, -3], [2012, -19]]], [15, 5853]),
('regression anchor advance #1', [19, 17, 150, 2485, [[2240, -10]]], [9, 2240]),
('regression anchor advance #2', [18, 15, 245, 845, [[385, -15]]], [4, 685]),
('regression anchor advance #3', [21, 18, 351, 650, [[484, -18]]], [3, 484]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [12, 13, 710, 1010, [[793, 7], [721, 13]]], [32, 1010])],
[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('fault site anchor advance #1', [2, 19, 442, 741, [[703, -19]]], [2, 442]),
('regression anchor advance #1', [9, 6, 0, 299, [[276, -6], [47, -6], [269, -6]]], [3, 47]),
('regression anchor advance #2', [4, 5, 685, 984, [[969, -9], [731, -5], [931, 5]]], [0, 969]),
('regression anchor advance #3', [12, 13, 487, 4020, [[1176, -13], [3667, -7]]], [2, 3876]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [11, 12, 57, 163, [[92, 12], [139, 12]]], [35, 163])]]
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 |
|---|---|---|---|
| spend from full restarts timer #1 | [8, 900] | [8, 1000] | Failed |
| regression anchor advance #1 | [3, 1572] | [3, 1315] | Failed |
| fault site anchor advance #1 | [15, 1583] | [15, 1583] | Passed |
| regression anchor advance #2 | [5, 1520] | [4, 1313] | Failed |
| regression anchor advance #3 | [9, 2250] | [9, 2240] | Failed |
| exact refill to cap #1 | [5, 600] | [5, 600] | Passed |
| overflow potion persists #1 | [15, 1200] | [15, 1200] | Passed |
| control #1 | [0, 266] | [0, 266] | Passed |
SHA-256 / b14e34270ad9ef9ef1ab1e91873483a9f2f0fdfe76897845fbadbc7242004fda
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(stamina, cap, last_tick, now, refills):
events = sorted(refills) + [[now, 0]]
t = last_tick
s = stamina
for at, amount in events:
if s < cap:
gained = (at - t) // 300
if s + gained >= cap:
s = cap
t = at
else:
s += gained
t += gained * 300
else:
t = at
if s + amount >= 0:
s = min(999, s + amount)
return [s, t]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('regression anchor advance #1', [23, 20, 972, 1572, [[1185, -20], [1315, -20], [1066, 20]]], [3, 1315]),
('fault site anchor advance #1', [16, 17, 83, 1773, [[154, -6]]], [15, 1583]),
('regression anchor advance #2', [20, 17, 920, 1520, [[1180, -17], [1013, -17], [1246, -5]]], [4, 1313]),
('regression anchor advance #3', [19, 17, 150, 2485, [[2240, -10]]], [9, 2240]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [9, 9, 266, 266, [[266, -9], [266, -10]]], [0, 266])],
[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('fault site anchor advance #1', [8, 9, 913, 1212, [[1053, -9], [963, -6], [1014, -5]]], [2, 913]),
('regression anchor advance #1', [20, 17, 920, 1520, [[1180, -17], [1013, -17], [1246, -5]]], [4, 1313]),
('regression anchor advance #2', [19, 17, 150, 2485, [[2240, -10]]], [9, 2240]),
('regression anchor advance #3', [9, 6, 0, 299, [[276, -6], [47, -6], [269, -6]]], [3, 47]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [9, 9, 266, 266, [[266, -9], [266, -10]]], [0, 266])],
[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('fault site anchor advance #1', [0, 14, 832, 1131, [[897, -4]]], [0, 832]),
('fault site anchor advance #2', [0, 10, 347, 646, [[390, -10], [479, -9]]], [0, 347]),
('regression anchor advance #1', [9, 6, 0, 299, [[276, -6], [47, -6], [269, -6]]], [3, 47]),
('regression anchor advance #2', [18, 15, 804, 1404, [[1122, -11], [838, -10], [1325, -15]]], [9, 1138]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [9, 9, 266, 266, [[266, -9], [266, -10]]], [0, 266])],
[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('fault site anchor advance #1', [0, 19, 453, 6068, [[1708, -7], [2101, -3], [2012, -19]]], [15, 5853]),
('regression anchor advance #1', [19, 17, 150, 2485, [[2240, -10]]], [9, 2240]),
('regression anchor advance #2', [18, 15, 245, 845, [[385, -15]]], [4, 685]),
('regression anchor advance #3', [21, 18, 351, 650, [[484, -18]]], [3, 484]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [12, 13, 710, 1010, [[793, 7], [721, 13]]], [32, 1010])],
[('spend from full restarts timer #1', [10, 10, 0, 1000, [[400, -4]]], [8, 1000]),
('fault site anchor advance #1', [2, 19, 442, 741, [[703, -19]]], [2, 442]),
('regression anchor advance #1', [9, 6, 0, 299, [[276, -6], [47, -6], [269, -6]]], [3, 47]),
('regression anchor advance #2', [4, 5, 685, 984, [[969, -9], [731, -5], [931, 5]]], [0, 969]),
('regression anchor advance #3', [12, 13, 487, 4020, [[1176, -13], [3667, -7]]], [2, 3876]),
('exact refill to cap #1', [3, 5, 0, 600, []], [5, 600]),
('overflow potion persists #1', [5, 5, 0, 1200, [[100, 10]]], [15, 1200]),
('control #1', [11, 12, 57, 163, [[92, 12], [139, 12]]], [35, 163])]]
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 |
|---|---|---|---|
| spend from full restarts timer #1 | [8, 1000] | [8, 1000] | Passed |
| regression anchor advance #1 | [3, 1315] | [3, 1315] | Passed |
| fault site anchor advance #1 | [15, 1583] | [15, 1583] | Passed |
| regression anchor advance #2 | [4, 1313] | [4, 1313] | Passed |
| regression anchor advance #3 | [9, 2240] | [9, 2240] | Passed |
| exact refill to cap #1 | [5, 600] | [5, 600] | Passed |
| overflow potion persists #1 | [15, 1200] | [15, 1200] | Passed |
| control #1 | [0, 266] | [0, 266] | Passed |
SHA-256 / 522ff41b0a9aa8687d89380903362cdb516b678f688392ab446d3332a744a4e9
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 2026-09-29T14:50:46.300778+00:00.
Case digest / 16a70af00e8639c6ae5da1bdab71950d6a2139bc8f55cf9eef1e14be0088bdf8