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FA-83566 / Card game rule engines / Open access

Pegging runs score only three · case 01

Completing a four- or five-card run pegs 3.

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

ROOT CAUSE

The run search stops at the first qualifying length.

THE FAILURE

The run search stops at the first qualifying length.

Unsuccessful approach: Testing max-min = L-1 accepts trailing cards containing a repeated rank.

Case contract

Input [cards_in_current_count, new_card]. Values A=1, T/J/Q/K=10; a count above 31 is "illegal". Points: count 15 -> 2, count 31 -> 2; the new card with the immediately preceding same-rank run scores 2/6/12; the longest trailing sequence of 3+ cards whose ranks are consecutive in any order scores its length. Return [points, count].

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

N = 1
observations = []
def solve(x):
    pile, card = x
    order = 'A23456789TJQK'
    def val(c):
        return min(order.index(c[0]) + 1, 10)
    count = sum(val(c) for c in pile) + val(card)
    if count > 31:
        return 'illegal'
    seq = pile + [card]
    pts = 0
    if count == 15:
        pts += 2
    if count == 31:
        pts += 2
    same = 1
    for c in reversed(seq[:-1]):
        if c[0] == card[0]:
            same += 1
        else:
            break
    pts += {1: 0, 2: 2, 3: 6, 4: 12}[same]
    best = 0
    for L in range(3, len(seq) + 1):
        tail = sorted(order.index(c[0]) for c in seq[-L:])
        if all(tail[i + 1] == tail[i] + 1 for i in range(L - 1)):
            best = L
            break
    pts += best
    return [pts, count]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['TD'], 'JC'], [0, 20]], [[['4D', 'KS', '2C', 'TC'], 'TS'], 'illegal'], [[['JD', '8D', 'QD'], '9D'], 'illegal'], [[['8S', 'TD', '2H', 'QH'], '5S'], 'illegal'], [[['6S', '7D', '7C', 'KS'], '3C'], 'illegal'], [[['5C', '7H'], 'TS'], [0, 22]], [[['6D', '9H', '7D'], '8D'], [4, 30]], [[['3H', '4D', '6C'], '6S'], [2, 19]]], [[[[], '5D'], [0, 5]], [[['8C', '2D', '8S', '5H', 'AH'], 'AS'], [2, 25]], [[['5D', '4C', '3S', 'KS'], 'KC'], 'illegal'], [[['9C', '7D'], 'KD'], [0, 26]], [[[], '7C'], [0, 7]], [[['7H'], '7C'], [2, 14]], [[['6D', '9H', '7D'], '8D'], [4, 30]], [[['5C', '3D'], '5H'], [0, 13]]], [[[['5D', 'JD', '2S', '6H', 'AH'], '4C'], [0, 28]], [[['AD'], 'AS'], [2, 2]], [[['JC'], 'JD'], [2, 20]], [[['TS', '4H', '2H', '7S'], 'QD'], 'illegal'], [[['QS', '3C'], '3C'], [2, 16]], [[['QS', '7D', '6S'], '9S'], 'illegal'], [[['6D', '9H', '7D'], '8D'], [4, 30]], [[['7D', '7D', '6D', '3D'], '7C'], [0, 30]]], [[[['2S', '7C', '9D'], '9C'], [2, 27]], [[['2H', '4S', 'TC', '6H', '8D'], '8H'], 'illegal'], [[['9D', '2C', 'TC'], 'KD'], [2, 31]], [[['AS', '2D'], 'JH'], [0, 13]], [[[], 'AD'], [0, 1]], [[['JH'], '7C'], [0, 17]], [[['KC', '8S', 'JS'], 'JH'], 'illegal'], [[['6D', '9H', '7D'], '8D'], [4, 30]]], [[[[], '3S'], [0, 3]], [[['TD', '5S', 'AD'], 'AD'], [2, 17]], [[[], '5S'], [0, 5]], [[['6H', 'AD'], 'TD'], [0, 17]], [[['JC', 'JC', '3C'], '3C'], [2, 26]], [[['5C', '3S', '8D', '7D'], 'QC'], 'illegal'], [[['6D', '9H', '7D'], '8D'], [4, 30]], [[['TD', 'TS'], '8D'], [0, 28]]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("pegging 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
pegging case 0[0, 20][0, 20]Passed
pegging case 1illegalillegalPassed
pegging case 2illegalillegalPassed
pegging case 3illegalillegalPassed
pegging case 4illegalillegalPassed
pegging case 5[0, 22][0, 22]Passed
pegging case 6[3, 30][4, 30]Failed
pegging case 7[2, 19][2, 19]Passed

SHA-256 / 443bcb653f66e5b2839ce4aa64b6b31e7273bc0ecf7bbe70d77c362ec30da635

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    pile, card = x
    order = 'A23456789TJQK'
    def val(c):
        return min(order.index(c[0]) + 1, 10)
    count = sum(val(c) for c in pile) + val(card)
    if count > 31:
        return 'illegal'
    seq = pile + [card]
    pts = 0
    if count == 15:
        pts += 2
    if count == 31:
        pts += 2
    same = 1
    for c in reversed(seq[:-1]):
        if c[0] == card[0]:
            same += 1
        else:
            break
    pts += {1: 0, 2: 2, 3: 6, 4: 12}[same]
    best = 0
    for L in range(3, len(seq) + 1):
        tail = sorted(order.index(c[0]) for c in seq[-L:])
        if tail[-1] - tail[0] == L - 1:
            best = L
    pts += best
    return [pts, count]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['TD'], 'JC'], [0, 20]], [[['4D', 'KS', '2C', 'TC'], 'TS'], 'illegal'], [[['JD', '8D', 'QD'], '9D'], 'illegal'], [[['8S', 'TD', '2H', 'QH'], '5S'], 'illegal'], [[['6S', '7D', '7C', 'KS'], '3C'], 'illegal'], [[['5C', '7H'], 'TS'], [0, 22]], [[['6D', '9H', '7D'], '8D'], [4, 30]], [[['3H', '4D', '6C'], '6S'], [2, 19]]], [[[[], '5D'], [0, 5]], [[['8C', '2D', '8S', '5H', 'AH'], 'AS'], [2, 25]], [[['5D', '4C', '3S', 'KS'], 'KC'], 'illegal'], [[['9C', '7D'], 'KD'], [0, 26]], [[[], '7C'], [0, 7]], [[['7H'], '7C'], [2, 14]], [[['6D', '9H', '7D'], '8D'], [4, 30]], [[['5C', '3D'], '5H'], [0, 13]]], [[[['5D', 'JD', '2S', '6H', 'AH'], '4C'], [0, 28]], [[['AD'], 'AS'], [2, 2]], [[['JC'], 'JD'], [2, 20]], [[['TS', '4H', '2H', '7S'], 'QD'], 'illegal'], [[['QS', '3C'], '3C'], [2, 16]], [[['QS', '7D', '6S'], '9S'], 'illegal'], [[['6D', '9H', '7D'], '8D'], [4, 30]], [[['7D', '7D', '6D', '3D'], '7C'], [0, 30]]], [[[['2S', '7C', '9D'], '9C'], [2, 27]], [[['2H', '4S', 'TC', '6H', '8D'], '8H'], 'illegal'], [[['9D', '2C', 'TC'], 'KD'], [2, 31]], [[['AS', '2D'], 'JH'], [0, 13]], [[[], 'AD'], [0, 1]], [[['JH'], '7C'], [0, 17]], [[['KC', '8S', 'JS'], 'JH'], 'illegal'], [[['6D', '9H', '7D'], '8D'], [4, 30]]], [[[[], '3S'], [0, 3]], [[['TD', '5S', 'AD'], 'AD'], [2, 17]], [[[], '5S'], [0, 5]], [[['6H', 'AD'], 'TD'], [0, 17]], [[['JC', 'JC', '3C'], '3C'], [2, 26]], [[['5C', '3S', '8D', '7D'], 'QC'], 'illegal'], [[['6D', '9H', '7D'], '8D'], [4, 30]], [[['TD', 'TS'], '8D'], [0, 28]]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("pegging 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
pegging case 0[0, 20][0, 20]Passed
pegging case 1illegalillegalPassed
pegging case 2illegalillegalPassed
pegging case 3illegalillegalPassed
pegging case 4illegalillegalPassed
pegging case 5[0, 22][0, 22]Passed
pegging case 6[4, 30][4, 30]Passed
pegging case 7[6, 19][2, 19]Failed

SHA-256 / 252dd51c98b74895d65d30463caf667f4768088333eee92e796bd926d70577ba

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:50:22.678849+00:00.

Case digest / 59431cfe2d651e2afbe12c322480b80c8be51a0b2d07678e61126eace41f7f48