FAILURE MAP
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FA-83536 / Card game rule engines / Open access

Five-card fifteens are not counted · case 01

A hand whose five cards together total 15 misses 2 points.

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

ROOT CAUSE

The combination sizes stop at four cards.

VERIFIED REPAIR

Examine combinations of 2 through 5 cards.

Unsuccessful approach: Starting at three cards drops every two-card fifteen.

Case contract

Input [four_card_hand, starter, is_crib]. Fifteens (any 2-5 cards, A=1, T/J/Q/K=10) score 2; each pair 2; runs score their length for every distinct combination of the longest run length; a four-card hand flush scores 4 (+1 with the starter) but the crib scores only a five-card flush; a hand jack matching the starter suit scores 1. Return the total.

Why this case matters

Card-game engines, scoring apps and online tables apply this rule automatically on every hand.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import itertools
N = 1
observations = []
def solve(x):
    hand, starter, crib = x
    order = 'A23456789TJQK'
    cards = hand + [starter]
    def val(c):
        return min(order.index(c[0]) + 1, 10)
    score = 0
    for k in range(2, 5):
        for combo in itertools.combinations(cards, k):
            if sum(val(c) for c in combo) == 15:
                score += 2
    for a, b in itertools.combinations(cards, 2):
        if a[0] == b[0]:
            score += 2
    ranks = sorted(order.index(c[0]) for c in cards)
    for size in (5, 4, 3):
        runs = 0
        for combo in itertools.combinations(ranks, size):
            if all(combo[i + 1] == combo[i] + 1 for i in range(size - 1)):
                runs += 1
        if runs:
            score += runs * size
            break
    suits = [c[1] for c in hand]
    if len(set(suits)) == 1:
        if starter[1] == suits[0]:
            score += 5
        elif not crib:
            score += 4
    for c in hand:
        if c[0] == 'J' and c[1] == starter[1]:
            score += 1
    return score
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['AC', '9C', '4C', 'TC'], '5S', True], 6], [[['KD', 'AH', '4S', '8D'], 'QH', False], 4], [[['3C', '3S', '4S', '5H'], '2D', False], 12], [[['5H', '9S', '6S', '2S'], 'AH', False], 4], [[['3S', '3H', '5H', 'JH'], 'QS', False], 6], [[['4C', 'QC', 'AC', '6C'], '5D', True], 9], [[['6S', '8D', 'JD', '9C'], '6D', False], 7], [[['AS', '2H', '3D', '4C'], '5S', False], 7]], [[[['6S', '8D', 'JD', '9C'], '6D', False], 7], [[['4S', '5D', '9D', 'TC'], 'QH', True], 4], [[['5H', 'KC', '2H', '3S'], '6H', True], 4], [[['9H', '7H', 'QH', 'TH'], 'JH', False], 9], [[['2C', '2S', '3S', '4H'], 'KD', False], 12], [[['4S', '3S', '9S', 'TD'], '7C', False], 0], [[['KS', '5D', '3H', '8D'], 'KD', True], 6], [[['2C', '2D', '3H', '3S'], '5D', False], 6]], [[[['3H', 'QS', '3C', '6S'], '8D', False], 2], [[['JH', '9H', '9S', 'TD'], '3H', False], 9], [[['6C', '2C', '7C', 'AC'], '4H', True], 2], [[['4D', 'AS', '7H', 'QD'], '9S', False], 2], [[['6S', '5S', 'QS', '8C'], 'AC', False], 4], [[['8S', 'QS', 'TH', '9C'], 'QC', False], 5], [[['5H', '2H', 'QH', '6H'], '7S', True], 7], [[['AC', '2D', '3H', '4S'], '5D', True], 7]], [[[['9S', '3S', 'QS', 'TS'], 'QH', False], 6], [[['AS', '9S', 'TS', '2S'], '4C', False], 8], [[['TD', 'KS', 'TH', 'TS'], 'JC', False], 6], [[['KS', '5D', '3H', '8D'], 'KD', True], 6], [[['2S', '8S', 'TC', 'JS'], 'QH', False], 3], [[['9H', '7S', 'QH', '5H'], '3D', False], 4], [[['5S', 'JD', '4D', '3D'], 'TS', True], 7], [[['AH', 'AD', '2C', '5S'], '6H', True], 4]], [[[['8D', '8C', '9S', 'TH'], 'AH', True], 8], [[['2H', '5H', 'AC', '3S'], '8C', False], 5], [[['AD', '4S', '9D', '4H'], 'TH', False], 6], [[['9S', '9C', 'JH', 'KS'], '3H', False], 3], [[['KD', 'TC', 'QS', '4D'], 'TH', True], 2], [[['QD', '8S', 'JC', '5H'], '6C', False], 5], [[['QH', '5H', 'KS', '3C'], 'AS', True], 4], [[['AS', '2H', '3D', '4C'], '5S', False], 7]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("hand score case %d" % i, 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
hand score case 066Passed
hand score case 144Passed
hand score case 21212Passed
hand score case 344Passed
hand score case 466Passed
hand score case 599Passed
hand score case 677Passed
hand score case 757Failed

SHA-256 / e42ef41e128b90c68928b20a235c5493d50671a43a8eefe1c6bc7347d1a7cb90

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import itertools
N = 1
observations = []
def solve(x):
    hand, starter, crib = x
    order = 'A23456789TJQK'
    cards = hand + [starter]
    def val(c):
        return min(order.index(c[0]) + 1, 10)
    score = 0
    for k in range(3, 6):
        for combo in itertools.combinations(cards, k):
            if sum(val(c) for c in combo) == 15:
                score += 2
    for a, b in itertools.combinations(cards, 2):
        if a[0] == b[0]:
            score += 2
    ranks = sorted(order.index(c[0]) for c in cards)
    for size in (5, 4, 3):
        runs = 0
        for combo in itertools.combinations(ranks, size):
            if all(combo[i + 1] == combo[i] + 1 for i in range(size - 1)):
                runs += 1
        if runs:
            score += runs * size
            break
    suits = [c[1] for c in hand]
    if len(set(suits)) == 1:
        if starter[1] == suits[0]:
            score += 5
        elif not crib:
            score += 4
    for c in hand:
        if c[0] == 'J' and c[1] == starter[1]:
            score += 1
    return score
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['AC', '9C', '4C', 'TC'], '5S', True], 6], [[['KD', 'AH', '4S', '8D'], 'QH', False], 4], [[['3C', '3S', '4S', '5H'], '2D', False], 12], [[['5H', '9S', '6S', '2S'], 'AH', False], 4], [[['3S', '3H', '5H', 'JH'], 'QS', False], 6], [[['4C', 'QC', 'AC', '6C'], '5D', True], 9], [[['6S', '8D', 'JD', '9C'], '6D', False], 7], [[['AS', '2H', '3D', '4C'], '5S', False], 7]], [[[['6S', '8D', 'JD', '9C'], '6D', False], 7], [[['4S', '5D', '9D', 'TC'], 'QH', True], 4], [[['5H', 'KC', '2H', '3S'], '6H', True], 4], [[['9H', '7H', 'QH', 'TH'], 'JH', False], 9], [[['2C', '2S', '3S', '4H'], 'KD', False], 12], [[['4S', '3S', '9S', 'TD'], '7C', False], 0], [[['KS', '5D', '3H', '8D'], 'KD', True], 6], [[['2C', '2D', '3H', '3S'], '5D', False], 6]], [[[['3H', 'QS', '3C', '6S'], '8D', False], 2], [[['JH', '9H', '9S', 'TD'], '3H', False], 9], [[['6C', '2C', '7C', 'AC'], '4H', True], 2], [[['4D', 'AS', '7H', 'QD'], '9S', False], 2], [[['6S', '5S', 'QS', '8C'], 'AC', False], 4], [[['8S', 'QS', 'TH', '9C'], 'QC', False], 5], [[['5H', '2H', 'QH', '6H'], '7S', True], 7], [[['AC', '2D', '3H', '4S'], '5D', True], 7]], [[[['9S', '3S', 'QS', 'TS'], 'QH', False], 6], [[['AS', '9S', 'TS', '2S'], '4C', False], 8], [[['TD', 'KS', 'TH', 'TS'], 'JC', False], 6], [[['KS', '5D', '3H', '8D'], 'KD', True], 6], [[['2S', '8S', 'TC', 'JS'], 'QH', False], 3], [[['9H', '7S', 'QH', '5H'], '3D', False], 4], [[['5S', 'JD', '4D', '3D'], 'TS', True], 7], [[['AH', 'AD', '2C', '5S'], '6H', True], 4]], [[[['8D', '8C', '9S', 'TH'], 'AH', True], 8], [[['2H', '5H', 'AC', '3S'], '8C', False], 5], [[['AD', '4S', '9D', '4H'], 'TH', False], 6], [[['9S', '9C', 'JH', 'KS'], '3H', False], 3], [[['KD', 'TC', 'QS', '4D'], 'TH', True], 2], [[['QD', '8S', 'JC', '5H'], '6C', False], 5], [[['QH', '5H', 'KS', '3C'], 'AS', True], 4], [[['AS', '2H', '3D', '4C'], '5S', False], 7]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("hand score case %d" % i, 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
hand score case 046Failed
hand score case 144Passed
hand score case 21212Passed
hand score case 324Failed
hand score case 426Failed
hand score case 579Failed
hand score case 637Failed
hand score case 777Passed

SHA-256 / 5c80a8b2c873310ef6b51c3938baa566092a5eedcd3b09d55ae6e86303dadc29

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import itertools
N = 1
observations = []
def solve(x):
    hand, starter, crib = x
    order = 'A23456789TJQK'
    cards = hand + [starter]
    def val(c):
        return min(order.index(c[0]) + 1, 10)
    score = 0
    for k in range(2, 6):
        for combo in itertools.combinations(cards, k):
            if sum(val(c) for c in combo) == 15:
                score += 2
    for a, b in itertools.combinations(cards, 2):
        if a[0] == b[0]:
            score += 2
    ranks = sorted(order.index(c[0]) for c in cards)
    for size in (5, 4, 3):
        runs = 0
        for combo in itertools.combinations(ranks, size):
            if all(combo[i + 1] == combo[i] + 1 for i in range(size - 1)):
                runs += 1
        if runs:
            score += runs * size
            break
    suits = [c[1] for c in hand]
    if len(set(suits)) == 1:
        if starter[1] == suits[0]:
            score += 5
        elif not crib:
            score += 4
    for c in hand:
        if c[0] == 'J' and c[1] == starter[1]:
            score += 1
    return score
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['AC', '9C', '4C', 'TC'], '5S', True], 6], [[['KD', 'AH', '4S', '8D'], 'QH', False], 4], [[['3C', '3S', '4S', '5H'], '2D', False], 12], [[['5H', '9S', '6S', '2S'], 'AH', False], 4], [[['3S', '3H', '5H', 'JH'], 'QS', False], 6], [[['4C', 'QC', 'AC', '6C'], '5D', True], 9], [[['6S', '8D', 'JD', '9C'], '6D', False], 7], [[['AS', '2H', '3D', '4C'], '5S', False], 7]], [[[['6S', '8D', 'JD', '9C'], '6D', False], 7], [[['4S', '5D', '9D', 'TC'], 'QH', True], 4], [[['5H', 'KC', '2H', '3S'], '6H', True], 4], [[['9H', '7H', 'QH', 'TH'], 'JH', False], 9], [[['2C', '2S', '3S', '4H'], 'KD', False], 12], [[['4S', '3S', '9S', 'TD'], '7C', False], 0], [[['KS', '5D', '3H', '8D'], 'KD', True], 6], [[['2C', '2D', '3H', '3S'], '5D', False], 6]], [[[['3H', 'QS', '3C', '6S'], '8D', False], 2], [[['JH', '9H', '9S', 'TD'], '3H', False], 9], [[['6C', '2C', '7C', 'AC'], '4H', True], 2], [[['4D', 'AS', '7H', 'QD'], '9S', False], 2], [[['6S', '5S', 'QS', '8C'], 'AC', False], 4], [[['8S', 'QS', 'TH', '9C'], 'QC', False], 5], [[['5H', '2H', 'QH', '6H'], '7S', True], 7], [[['AC', '2D', '3H', '4S'], '5D', True], 7]], [[[['9S', '3S', 'QS', 'TS'], 'QH', False], 6], [[['AS', '9S', 'TS', '2S'], '4C', False], 8], [[['TD', 'KS', 'TH', 'TS'], 'JC', False], 6], [[['KS', '5D', '3H', '8D'], 'KD', True], 6], [[['2S', '8S', 'TC', 'JS'], 'QH', False], 3], [[['9H', '7S', 'QH', '5H'], '3D', False], 4], [[['5S', 'JD', '4D', '3D'], 'TS', True], 7], [[['AH', 'AD', '2C', '5S'], '6H', True], 4]], [[[['8D', '8C', '9S', 'TH'], 'AH', True], 8], [[['2H', '5H', 'AC', '3S'], '8C', False], 5], [[['AD', '4S', '9D', '4H'], 'TH', False], 6], [[['9S', '9C', 'JH', 'KS'], '3H', False], 3], [[['KD', 'TC', 'QS', '4D'], 'TH', True], 2], [[['QD', '8S', 'JC', '5H'], '6C', False], 5], [[['QH', '5H', 'KS', '3C'], 'AS', True], 4], [[['AS', '2H', '3D', '4C'], '5S', False], 7]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("hand score case %d" % i, 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
hand score case 066Passed
hand score case 144Passed
hand score case 21212Passed
hand score case 344Passed
hand score case 466Passed
hand score case 599Passed
hand score case 677Passed
hand score case 777Passed

SHA-256 / 4e51c9bbdbd0dbe2cd0c8affbedcae94906c62bd654f97252ef8c893350ee048

Verification & scope

A bounded toy rule contract stated explicitly in the contract field; cards are two-character codes (rank, suit). Not a complete implementation of any published rulebook or casino table rules. 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 2026-09-29T14:50:22.593537+00:00.

Case digest / 5b8c33cdf13cf16829a34603a903863e939aec542c5afac50a3f1d3bb5eb760b