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FA-83676 / Card game rule engines / Open access

Banker 3 draws against a player third-card 8 · case 01

Banker takes a card it must refuse.

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

ROOT CAUSE

The banker-3 exception is missing.

VERIFIED REPAIR

Banker 3 stands only against an 8.

Unsuccessful approach: Making the exception a 9 moves it to the wrong card.

Case contract

Input [player_cards, banker_cards, next_shoe_cards]. Values A=1, 2-9 pip, T/J/Q/K 0; totals mod 10. A natural 8/9 on either side stops the coup. Player draws on 0-5. If player stood, banker draws on 0-5; otherwise banker draws on 0-2, on 3 unless the player third card is 8, on 4 vs 2-7, on 5 vs 4-7, on 6 vs 6-7. Return [player_total, banker_total, winner, cards_drawn].

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):
    p, b, shoe = x
    def val(c):
        r = c[0]
        if r == 'A':
            return 1
        if r in 'TJQK':
            return 0
        return int(r)
    def tot(h):
        return sum(val(c) for c in h) % 10
    p = list(p)
    b = list(b)
    k = 0
    pt, bt = tot(p), tot(b)
    if pt < 8 and bt < 8:
        third = None
        if pt <= 5:
            p.append(shoe[k])
            k += 1
            third = val(p[-1])
        if third is None:
            draw = bt <= 5
        elif bt <= 2:
            draw = True
        elif bt == 3:
            draw = True
        elif bt == 4:
            draw = 2 <= third <= 7
        elif bt == 5:
            draw = 4 <= third <= 7
        elif bt == 6:
            draw = 6 <= third <= 7
        else:
            draw = False
        if draw:
            b.append(shoe[k])
            k += 1
    pt, bt = tot(p), tot(b)
    winner = 'player' if pt > bt else 'banker' if bt > pt else 'tie'
    return [pt, bt, winner, k]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['6C', '8D'], ['3H', 'TS'], ['9D', 'QS']], [3, 3, 'tie', 2]], [[['JD', '4H'], ['QC', '8D'], ['TS', '7H']], [4, 8, 'banker', 0]], [[['2H', '8C'], ['7C', 'JS'], ['2C', '7D']], [2, 7, 'banker', 1]], [[['2C', '9D'], ['7C', 'JH'], ['2S', '8H']], [3, 7, 'banker', 1]], [[['5C', '3C'], ['TC', '5H'], ['AC', 'TH']], [8, 5, 'player', 0]], [[['7C', '2C'], ['6H', '3S'], ['AH', '5S']], [9, 9, 'tie', 0]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]], [[[['6S', 'QD'], ['6C', '7D'], ['7S', '4D']], [6, 0, 'player', 1]], [[['7H', '3D'], ['JS', 'JH'], ['6H', 'AC']], [6, 1, 'player', 2]], [[['2S', '2C'], ['AS', '7D'], ['2H', '9H']], [4, 8, 'banker', 0]], [[['KC', '6H'], ['9D', 'QS'], ['2C', 'KD']], [6, 9, 'banker', 0]], [[['5S', '6C'], ['6S', '3S'], ['KC', 'KH']], [1, 9, 'banker', 0]], [[['9C', '2H'], ['JC', 'JS'], ['TH', 'QC']], [1, 0, 'player', 2]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]], [[[['4C', '5S'], ['6S', '4H'], ['QC', '3C']], [9, 0, 'player', 0]], [[['5H', '2C'], ['TD', '6C'], ['7S', 'KC']], [7, 6, 'player', 0]], [[['2C', '4D'], ['8D', '3H'], ['KS', '6C']], [6, 1, 'player', 1]], [[['6S', 'QD'], ['8H', '9D'], ['3S', 'TD']], [6, 7, 'banker', 0]], [[['3H', 'TD'], ['QS', '5C'], ['5D', 'AD']], [8, 6, 'player', 2]], [[['6S', 'JS'], ['4D', '6D'], ['2C', 'KD']], [6, 2, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]], [[[['8D', 'TH'], ['QS', '9S'], ['3S', '9H']], [8, 9, 'banker', 0]], [[['AS', '5H'], ['5D', '9D'], ['7S', '5S']], [6, 1, 'player', 1]], [[['7C', 'JD'], ['2H', 'KC'], ['JS', 'AS']], [7, 2, 'player', 1]], [[['TH', '8C'], ['2C', '7H'], ['JH', '4D']], [8, 9, 'banker', 0]], [[['TC', '5D'], ['JC', '7S'], ['7C', '4C']], [2, 7, 'banker', 1]], [[['AS', '5H'], ['6C', '8C'], ['7D', '9S']], [6, 1, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]], [[[['5S', 'JS'], ['KH', 'TC'], ['4C', '9S']], [9, 9, 'tie', 2]], [[['9H', '9S'], ['TS', '4S'], ['TD', 'TC']], [8, 4, 'player', 0]], [[['9D', '9S'], ['2S', '6D'], ['6S', '4C']], [8, 8, 'tie', 0]], [[['2S', '9H'], ['7H', 'AS'], ['AH', '5H']], [1, 8, 'banker', 0]], [[['2C', '6H'], ['3D', 'TH'], ['QD', 'KS']], [8, 3, 'player', 0]], [[['2S', '2H'], ['3C', '9D'], ['KH', '6C']], [4, 8, 'banker', 2]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("coup 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
coup case 0[3, 3, 'tie', 2][3, 3, 'tie', 2]Passed
coup case 1[4, 8, 'banker', 0][4, 8, 'banker', 0]Passed
coup case 2[2, 7, 'banker', 1][2, 7, 'banker', 1]Passed
coup case 3[3, 7, 'banker', 1][3, 7, 'banker', 1]Passed
coup case 4[8, 5, 'player', 0][8, 5, 'player', 0]Passed
coup case 5[9, 9, 'tie', 0][9, 9, 'tie', 0]Passed
coup case 6[9, 8, 'player', 2][9, 3, 'player', 1]Failed
coup case 7[9, 8, 'player', 2][9, 3, 'player', 1]Failed

SHA-256 / 5ab8752c6310252c492032895e9a97ca79e753bef6ad6cf1e6514e67fd568409

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    p, b, shoe = x
    def val(c):
        r = c[0]
        if r == 'A':
            return 1
        if r in 'TJQK':
            return 0
        return int(r)
    def tot(h):
        return sum(val(c) for c in h) % 10
    p = list(p)
    b = list(b)
    k = 0
    pt, bt = tot(p), tot(b)
    if pt < 8 and bt < 8:
        third = None
        if pt <= 5:
            p.append(shoe[k])
            k += 1
            third = val(p[-1])
        if third is None:
            draw = bt <= 5
        elif bt <= 2:
            draw = True
        elif bt == 3:
            draw = third != 9
        elif bt == 4:
            draw = 2 <= third <= 7
        elif bt == 5:
            draw = 4 <= third <= 7
        elif bt == 6:
            draw = 6 <= third <= 7
        else:
            draw = False
        if draw:
            b.append(shoe[k])
            k += 1
    pt, bt = tot(p), tot(b)
    winner = 'player' if pt > bt else 'banker' if bt > pt else 'tie'
    return [pt, bt, winner, k]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['6C', '8D'], ['3H', 'TS'], ['9D', 'QS']], [3, 3, 'tie', 2]], [[['JD', '4H'], ['QC', '8D'], ['TS', '7H']], [4, 8, 'banker', 0]], [[['2H', '8C'], ['7C', 'JS'], ['2C', '7D']], [2, 7, 'banker', 1]], [[['2C', '9D'], ['7C', 'JH'], ['2S', '8H']], [3, 7, 'banker', 1]], [[['5C', '3C'], ['TC', '5H'], ['AC', 'TH']], [8, 5, 'player', 0]], [[['7C', '2C'], ['6H', '3S'], ['AH', '5S']], [9, 9, 'tie', 0]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]], [[[['6S', 'QD'], ['6C', '7D'], ['7S', '4D']], [6, 0, 'player', 1]], [[['7H', '3D'], ['JS', 'JH'], ['6H', 'AC']], [6, 1, 'player', 2]], [[['2S', '2C'], ['AS', '7D'], ['2H', '9H']], [4, 8, 'banker', 0]], [[['KC', '6H'], ['9D', 'QS'], ['2C', 'KD']], [6, 9, 'banker', 0]], [[['5S', '6C'], ['6S', '3S'], ['KC', 'KH']], [1, 9, 'banker', 0]], [[['9C', '2H'], ['JC', 'JS'], ['TH', 'QC']], [1, 0, 'player', 2]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]], [[[['4C', '5S'], ['6S', '4H'], ['QC', '3C']], [9, 0, 'player', 0]], [[['5H', '2C'], ['TD', '6C'], ['7S', 'KC']], [7, 6, 'player', 0]], [[['2C', '4D'], ['8D', '3H'], ['KS', '6C']], [6, 1, 'player', 1]], [[['6S', 'QD'], ['8H', '9D'], ['3S', 'TD']], [6, 7, 'banker', 0]], [[['3H', 'TD'], ['QS', '5C'], ['5D', 'AD']], [8, 6, 'player', 2]], [[['6S', 'JS'], ['4D', '6D'], ['2C', 'KD']], [6, 2, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]], [[[['8D', 'TH'], ['QS', '9S'], ['3S', '9H']], [8, 9, 'banker', 0]], [[['AS', '5H'], ['5D', '9D'], ['7S', '5S']], [6, 1, 'player', 1]], [[['7C', 'JD'], ['2H', 'KC'], ['JS', 'AS']], [7, 2, 'player', 1]], [[['TH', '8C'], ['2C', '7H'], ['JH', '4D']], [8, 9, 'banker', 0]], [[['TC', '5D'], ['JC', '7S'], ['7C', '4C']], [2, 7, 'banker', 1]], [[['AS', '5H'], ['6C', '8C'], ['7D', '9S']], [6, 1, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]], [[[['5S', 'JS'], ['KH', 'TC'], ['4C', '9S']], [9, 9, 'tie', 2]], [[['9H', '9S'], ['TS', '4S'], ['TD', 'TC']], [8, 4, 'player', 0]], [[['9D', '9S'], ['2S', '6D'], ['6S', '4C']], [8, 8, 'tie', 0]], [[['2S', '9H'], ['7H', 'AS'], ['AH', '5H']], [1, 8, 'banker', 0]], [[['2C', '6H'], ['3D', 'TH'], ['QD', 'KS']], [8, 3, 'player', 0]], [[['2S', '2H'], ['3C', '9D'], ['KH', '6C']], [4, 8, 'banker', 2]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("coup 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
coup case 0[3, 3, 'tie', 1][3, 3, 'tie', 2]Failed
coup case 1[4, 8, 'banker', 0][4, 8, 'banker', 0]Passed
coup case 2[2, 7, 'banker', 1][2, 7, 'banker', 1]Passed
coup case 3[3, 7, 'banker', 1][3, 7, 'banker', 1]Passed
coup case 4[8, 5, 'player', 0][8, 5, 'player', 0]Passed
coup case 5[9, 9, 'tie', 0][9, 9, 'tie', 0]Passed
coup case 6[9, 8, 'player', 2][9, 3, 'player', 1]Failed
coup case 7[9, 8, 'player', 2][9, 3, 'player', 1]Failed

SHA-256 / 6f19a676367d18c259140eb9435798ad356fc1cc2d43357f200548da7fd2533c

3 / The verified repair

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

N = 1
observations = []
def solve(x):
    p, b, shoe = x
    def val(c):
        r = c[0]
        if r == 'A':
            return 1
        if r in 'TJQK':
            return 0
        return int(r)
    def tot(h):
        return sum(val(c) for c in h) % 10
    p = list(p)
    b = list(b)
    k = 0
    pt, bt = tot(p), tot(b)
    if pt < 8 and bt < 8:
        third = None
        if pt <= 5:
            p.append(shoe[k])
            k += 1
            third = val(p[-1])
        if third is None:
            draw = bt <= 5
        elif bt <= 2:
            draw = True
        elif bt == 3:
            draw = third != 8
        elif bt == 4:
            draw = 2 <= third <= 7
        elif bt == 5:
            draw = 4 <= third <= 7
        elif bt == 6:
            draw = 6 <= third <= 7
        else:
            draw = False
        if draw:
            b.append(shoe[k])
            k += 1
    pt, bt = tot(p), tot(b)
    winner = 'player' if pt > bt else 'banker' if bt > pt else 'tie'
    return [pt, bt, winner, k]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[['6C', '8D'], ['3H', 'TS'], ['9D', 'QS']], [3, 3, 'tie', 2]], [[['JD', '4H'], ['QC', '8D'], ['TS', '7H']], [4, 8, 'banker', 0]], [[['2H', '8C'], ['7C', 'JS'], ['2C', '7D']], [2, 7, 'banker', 1]], [[['2C', '9D'], ['7C', 'JH'], ['2S', '8H']], [3, 7, 'banker', 1]], [[['5C', '3C'], ['TC', '5H'], ['AC', 'TH']], [8, 5, 'player', 0]], [[['7C', '2C'], ['6H', '3S'], ['AH', '5S']], [9, 9, 'tie', 0]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]], [[[['6S', 'QD'], ['6C', '7D'], ['7S', '4D']], [6, 0, 'player', 1]], [[['7H', '3D'], ['JS', 'JH'], ['6H', 'AC']], [6, 1, 'player', 2]], [[['2S', '2C'], ['AS', '7D'], ['2H', '9H']], [4, 8, 'banker', 0]], [[['KC', '6H'], ['9D', 'QS'], ['2C', 'KD']], [6, 9, 'banker', 0]], [[['5S', '6C'], ['6S', '3S'], ['KC', 'KH']], [1, 9, 'banker', 0]], [[['9C', '2H'], ['JC', 'JS'], ['TH', 'QC']], [1, 0, 'player', 2]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]], [[[['4C', '5S'], ['6S', '4H'], ['QC', '3C']], [9, 0, 'player', 0]], [[['5H', '2C'], ['TD', '6C'], ['7S', 'KC']], [7, 6, 'player', 0]], [[['2C', '4D'], ['8D', '3H'], ['KS', '6C']], [6, 1, 'player', 1]], [[['6S', 'QD'], ['8H', '9D'], ['3S', 'TD']], [6, 7, 'banker', 0]], [[['3H', 'TD'], ['QS', '5C'], ['5D', 'AD']], [8, 6, 'player', 2]], [[['6S', 'JS'], ['4D', '6D'], ['2C', 'KD']], [6, 2, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]], [[[['8D', 'TH'], ['QS', '9S'], ['3S', '9H']], [8, 9, 'banker', 0]], [[['AS', '5H'], ['5D', '9D'], ['7S', '5S']], [6, 1, 'player', 1]], [[['7C', 'JD'], ['2H', 'KC'], ['JS', 'AS']], [7, 2, 'player', 1]], [[['TH', '8C'], ['2C', '7H'], ['JH', '4D']], [8, 9, 'banker', 0]], [[['TC', '5D'], ['JC', '7S'], ['7C', '4C']], [2, 7, 'banker', 1]], [[['AS', '5H'], ['6C', '8C'], ['7D', '9S']], [6, 1, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]], [[[['5S', 'JS'], ['KH', 'TC'], ['4C', '9S']], [9, 9, 'tie', 2]], [[['9H', '9S'], ['TS', '4S'], ['TD', 'TC']], [8, 4, 'player', 0]], [[['9D', '9S'], ['2S', '6D'], ['6S', '4C']], [8, 8, 'tie', 0]], [[['2S', '9H'], ['7H', 'AS'], ['AH', '5H']], [1, 8, 'banker', 0]], [[['2C', '6H'], ['3D', 'TH'], ['QD', 'KS']], [8, 3, 'player', 0]], [[['2S', '2H'], ['3C', '9D'], ['KH', '6C']], [4, 8, 'banker', 2]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]], [[['3S', '8C'], ['3H', 'TS'], ['8S', '5C']], [9, 3, 'player', 1]]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("coup 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
coup case 0[3, 3, 'tie', 2][3, 3, 'tie', 2]Passed
coup case 1[4, 8, 'banker', 0][4, 8, 'banker', 0]Passed
coup case 2[2, 7, 'banker', 1][2, 7, 'banker', 1]Passed
coup case 3[3, 7, 'banker', 1][3, 7, 'banker', 1]Passed
coup case 4[8, 5, 'player', 0][8, 5, 'player', 0]Passed
coup case 5[9, 9, 'tie', 0][9, 9, 'tie', 0]Passed
coup case 6[9, 3, 'player', 1][9, 3, 'player', 1]Passed
coup case 7[9, 3, 'player', 1][9, 3, 'player', 1]Passed

SHA-256 / 354e6c30992c6c03801dd9d7644ca29c64c2820bff2721f6b584c16e44cecbd4

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 2026-09-29T14:50:23.928982+00:00.

Case digest / c591042aec316aae3ab84efacb739aef7a292a6cd00cdcebc331791722b154a2