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FA-83556 / Card game rule engines / Open access

Three of a kind scores as a single pair · case 01

A pair royal is worth 2 instead of 6.

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

ROOT CAUSE

Pairs are counted once per rank present twice or more.

VERIFIED REPAIR

Count every pair of equal-rank cards.

Unsuccessful approach: Scoring 2 per extra card gives 4 for trips and 6 for fours.

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, 6):
        for combo in itertools.combinations(cards, k):
            if sum(val(c) for c in combo) == 15:
                score += 2
    for r in set(c[0] for c in cards):
        if sum(1 for c in cards if c[0] == r) >= 2:
            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], [[['TD', 'KS', 'TH', 'TS'], 'JC', False], 6], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6]], [[[['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], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6], [[['5H', '5D', '5S', 'JC'], '5C', False], 29]], [[[['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], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6]], [[[['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], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6], [[['4H', '4D', '4S', '3C'], '8C', False], 14]], [[[['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], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6], [[['AC', 'AH', '2S', '3H'], 'AD', False], 15]]]
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 626Failed
hand score case 726Failed

SHA-256 / 1293f9591d4a5b179fbc50fa30063820d1fe2b62507c6062e93935f7de303f1c

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(2, 6):
        for combo in itertools.combinations(cards, k):
            if sum(val(c) for c in combo) == 15:
                score += 2
    for r in set(c[0] for c in cards):
        k = sum(1 for c in cards if c[0] == r)
        if k >= 2:
            score += 2 * (k - 1)
    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], [[['TD', 'KS', 'TH', 'TS'], 'JC', False], 6], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6]], [[[['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], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6], [[['5H', '5D', '5S', 'JC'], '5C', False], 29]], [[[['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], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6]], [[[['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], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6], [[['4H', '4D', '4S', '3C'], '8C', False], 14]], [[[['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], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6], [[['AC', 'AH', '2S', '3H'], 'AD', False], 15]]]
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 646Failed
hand score case 746Failed

SHA-256 / c2e3f74a43ce1e0f1555e46876ee1cc51a24329877121028120d662171b4691b

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], [[['TD', 'KS', 'TH', 'TS'], 'JC', False], 6], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6]], [[[['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], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6], [[['5H', '5D', '5S', 'JC'], '5C', False], 29]], [[[['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], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6]], [[[['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], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6], [[['4H', '4D', '4S', '3C'], '8C', False], 14]], [[[['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], [[['6H', '7H', 'TC', 'TD'], 'TS', False], 6], [[['AC', 'AH', '2S', '3H'], 'AD', False], 15]]]
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 666Passed
hand score case 766Passed

SHA-256 / 86259a684b2fe276455cd90e8ecda14d2bd018bb69ac762689aa9c2b69fe8b31

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 2026-09-29T14:50:22.631120+00:00.

Case digest / 2239bbf87d0234be70a213791b1929e9604fefe11d8c7fe46b161e965a41d250