FA-82166 / Poker hand evaluation / Open access

Blockers on the second rank are ignored · case 01

A dead king does not reduce "AKs" or "AKo" combos.

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

ROOT CAUSE

Only the first card of each combo is tested against the dead cards.

VERIFIED REPAIR

Discard a combo if either of its cards is dead.

Unsuccessful approach: Requiring both cards to be dead discards almost nothing.

Case contract

Input: {"hand": class such as "AKs", "AKo", "AK" or "QQ", "dead": [known cards, rank upper-case or lower-case, suit lower-case or upper-case]}. Enumerate the concrete two-card combos of the class (suits c,d,h,s) and return how many contain no dead card.

Why this case matters

Blocker math decides how many value combos an opponent can still hold.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    S='cdhs'
    h=x['hand']; dead={c[0].upper()+c[1].lower() for c in x['dead']}
    r1,r2=h[0],h[1]; suf=h[2:]
    n=0
    for i,s1 in enumerate(S):
        for j,s2 in enumerate(S):
            if r1==r2 and j<=i: continue
            if suf=='s' and s1!=s2: continue
            if suf=='o' and s1==s2: continue
            if r1+s1 in dead: continue
            n+=1
    return n
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('pair no blockers', {'dead': [], 'hand': 'QQ'}, 6),
  ('pair one blocker', {'dead': ['Qh'], 'hand': 'QQ'}, 3),
  ('suited no blockers', {'dead': [], 'hand': 'AKs'}, 4),
  ('suited blocked king', {'dead': ['Kd'], 'hand': 'AKs'}, 3),
  ('offsuit blocked king', {'dead': ['Kd'], 'hand': 'AKo'}, 9),
  ('any ace king two blockers', {'dead': ['As', 'Kc'], 'hand': 'AK'}, 9),
  ('unrelated dead', {'dead': ['2c', '7d'], 'hand': 'AKs'}, 4),
  ('offsuit no blockers', {'dead': [], 'hand': 'T9o'}, 12)],
 [('pair one blocker', {'dead': ['Qh'], 'hand': 'QQ'}, 3),
  ('suited blocked king', {'dead': ['Kd'], 'hand': 'AKs'}, 3),
  ('offsuit blocked king', {'dead': ['Kd'], 'hand': 'AKo'}, 9),
  ('any ace king two blockers', {'dead': ['As', 'Kc'], 'hand': 'AK'}, 9),
  ('lower-case dead', {'dead': ['ah', 'kS'], 'hand': 'AKo'}, 7),
  ('upper-case suit dead', {'dead': ['JH'], 'hand': 'JTs'}, 3),
  ('pair two blockers', {'dead': ['9c', '9s'], 'hand': '99'}, 1),
  ('offsuit no blockers', {'dead': [], 'hand': 'T9o'}, 12)],
 [('pair no blockers', {'dead': [], 'hand': 'QQ'}, 6),
  ('suited no blockers', {'dead': [], 'hand': 'AKs'}, 4),
  ('offsuit blocked king', {'dead': ['Kd'], 'hand': 'AKo'}, 9),
  ('any ace king two blockers', {'dead': ['As', 'Kc'], 'hand': 'AK'}, 9),
  ('lower-case dead', {'dead': ['ah', 'kS'], 'hand': 'AKo'}, 7),
  ('upper-case suit dead', {'dead': ['JH'], 'hand': 'JTs'}, 3),
  ('pair two blockers', {'dead': ['9c', '9s'], 'hand': '99'}, 1),
  ('blocked first rank only', {'dead': ['Qs', 'Qh'], 'hand': 'KQs'}, 2)],
 [('pair no blockers', {'dead': [], 'hand': 'QQ'}, 6),
  ('suited no blockers', {'dead': [], 'hand': 'AKs'}, 4),
  ('any ace king two blockers', {'dead': ['As', 'Kc'], 'hand': 'AK'}, 9),
  ('lower-case dead', {'dead': ['ah', 'kS'], 'hand': 'AKo'}, 7),
  ('upper-case suit dead', {'dead': ['JH'], 'hand': 'JTs'}, 3),
  ('unrelated dead', {'dead': ['2c', '7d'], 'hand': 'AKs'}, 4),
  ('pair two blockers', {'dead': ['9c', '9s'], 'hand': '99'}, 1),
  ('blocked first rank only', {'dead': ['Qs', 'Qh'], 'hand': 'KQs'}, 2)],
 [('pair no blockers', {'dead': [], 'hand': 'QQ'}, 6),
  ('pair one blocker', {'dead': ['Qh'], 'hand': 'QQ'}, 3),
  ('suited no blockers', {'dead': [], 'hand': 'AKs'}, 4),
  ('lower-case dead', {'dead': ['ah', 'kS'], 'hand': 'AKo'}, 7),
  ('upper-case suit dead', {'dead': ['JH'], 'hand': 'JTs'}, 3),
  ('unrelated dead', {'dead': ['2c', '7d'], 'hand': 'AKs'}, 4),
  ('pair two blockers', {'dead': ['9c', '9s'], 'hand': '99'}, 1),
  ('offsuit no blockers', {'dead': [], 'hand': 'T9o'}, 12)]]
for label, args, expected in fixtures[N-1]:
    try:
        actual = solve(args)
    except Exception as exc:
        actual = 'error:' + type(exc).__name__
    check(label, actual, 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
pair no blockers	`6`	`6`	Passed
pair one blocker	`5`	`3`	Failed
suited no blockers	`4`	`4`	Passed
suited blocked king	`4`	`3`	Failed
offsuit blocked king	`12`	`9`	Failed
any ace king two blockers	`12`	`9`	Failed
unrelated dead	`4`	`4`	Passed
offsuit no blockers	`12`	`12`	Passed

SHA-256 / eeab4279dfc67e2fa62163a83e2f762b09461bbc066ef714f12ddd1f379d0f49

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    S='cdhs'
    h=x['hand']; dead={c[0].upper()+c[1].lower() for c in x['dead']}
    r1,r2=h[0],h[1]; suf=h[2:]
    n=0
    for i,s1 in enumerate(S):
        for j,s2 in enumerate(S):
            if r1==r2 and j<=i: continue
            if suf=='s' and s1!=s2: continue
            if suf=='o' and s1==s2: continue
            if r1+s1 in dead and r2+s2 in dead: continue
            n+=1
    return n
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('pair no blockers', {'dead': [], 'hand': 'QQ'}, 6),
  ('pair one blocker', {'dead': ['Qh'], 'hand': 'QQ'}, 3),
  ('suited no blockers', {'dead': [], 'hand': 'AKs'}, 4),
  ('suited blocked king', {'dead': ['Kd'], 'hand': 'AKs'}, 3),
  ('offsuit blocked king', {'dead': ['Kd'], 'hand': 'AKo'}, 9),
  ('any ace king two blockers', {'dead': ['As', 'Kc'], 'hand': 'AK'}, 9),
  ('unrelated dead', {'dead': ['2c', '7d'], 'hand': 'AKs'}, 4),
  ('offsuit no blockers', {'dead': [], 'hand': 'T9o'}, 12)],
 [('pair one blocker', {'dead': ['Qh'], 'hand': 'QQ'}, 3),
  ('suited blocked king', {'dead': ['Kd'], 'hand': 'AKs'}, 3),
  ('offsuit blocked king', {'dead': ['Kd'], 'hand': 'AKo'}, 9),
  ('any ace king two blockers', {'dead': ['As', 'Kc'], 'hand': 'AK'}, 9),
  ('lower-case dead', {'dead': ['ah', 'kS'], 'hand': 'AKo'}, 7),
  ('upper-case suit dead', {'dead': ['JH'], 'hand': 'JTs'}, 3),
  ('pair two blockers', {'dead': ['9c', '9s'], 'hand': '99'}, 1),
  ('offsuit no blockers', {'dead': [], 'hand': 'T9o'}, 12)],
 [('pair no blockers', {'dead': [], 'hand': 'QQ'}, 6),
  ('suited no blockers', {'dead': [], 'hand': 'AKs'}, 4),
  ('offsuit blocked king', {'dead': ['Kd'], 'hand': 'AKo'}, 9),
  ('any ace king two blockers', {'dead': ['As', 'Kc'], 'hand': 'AK'}, 9),
  ('lower-case dead', {'dead': ['ah', 'kS'], 'hand': 'AKo'}, 7),
  ('upper-case suit dead', {'dead': ['JH'], 'hand': 'JTs'}, 3),
  ('pair two blockers', {'dead': ['9c', '9s'], 'hand': '99'}, 1),
  ('blocked first rank only', {'dead': ['Qs', 'Qh'], 'hand': 'KQs'}, 2)],
 [('pair no blockers', {'dead': [], 'hand': 'QQ'}, 6),
  ('suited no blockers', {'dead': [], 'hand': 'AKs'}, 4),
  ('any ace king two blockers', {'dead': ['As', 'Kc'], 'hand': 'AK'}, 9),
  ('lower-case dead', {'dead': ['ah', 'kS'], 'hand': 'AKo'}, 7),
  ('upper-case suit dead', {'dead': ['JH'], 'hand': 'JTs'}, 3),
  ('unrelated dead', {'dead': ['2c', '7d'], 'hand': 'AKs'}, 4),
  ('pair two blockers', {'dead': ['9c', '9s'], 'hand': '99'}, 1),
  ('blocked first rank only', {'dead': ['Qs', 'Qh'], 'hand': 'KQs'}, 2)],
 [('pair no blockers', {'dead': [], 'hand': 'QQ'}, 6),
  ('pair one blocker', {'dead': ['Qh'], 'hand': 'QQ'}, 3),
  ('suited no blockers', {'dead': [], 'hand': 'AKs'}, 4),
  ('lower-case dead', {'dead': ['ah', 'kS'], 'hand': 'AKo'}, 7),
  ('upper-case suit dead', {'dead': ['JH'], 'hand': 'JTs'}, 3),
  ('unrelated dead', {'dead': ['2c', '7d'], 'hand': 'AKs'}, 4),
  ('pair two blockers', {'dead': ['9c', '9s'], 'hand': '99'}, 1),
  ('offsuit no blockers', {'dead': [], 'hand': 'T9o'}, 12)]]
for label, args, expected in fixtures[N-1]:
    try:
        actual = solve(args)
    except Exception as exc:
        actual = 'error:' + type(exc).__name__
    check(label, actual, 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
pair no blockers	`6`	`6`	Passed
pair one blocker	`6`	`3`	Failed
suited no blockers	`4`	`4`	Passed
suited blocked king	`4`	`3`	Failed
offsuit blocked king	`12`	`9`	Failed
any ace king two blockers	`15`	`9`	Failed
unrelated dead	`4`	`4`	Passed
offsuit no blockers	`12`	`12`	Passed

SHA-256 / 9fe05133742120eb3e7dbfdb25eb605fcbef3738a67b1f8a5c3d00fc5e9511be

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    S='cdhs'
    h=x['hand']; dead={c[0].upper()+c[1].lower() for c in x['dead']}
    r1,r2=h[0],h[1]; suf=h[2:]
    n=0
    for i,s1 in enumerate(S):
        for j,s2 in enumerate(S):
            if r1==r2 and j<=i: continue
            if suf=='s' and s1!=s2: continue
            if suf=='o' and s1==s2: continue
            if r1+s1 in dead or r2+s2 in dead: continue
            n+=1
    return n
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('pair no blockers', {'dead': [], 'hand': 'QQ'}, 6),
  ('pair one blocker', {'dead': ['Qh'], 'hand': 'QQ'}, 3),
  ('suited no blockers', {'dead': [], 'hand': 'AKs'}, 4),
  ('suited blocked king', {'dead': ['Kd'], 'hand': 'AKs'}, 3),
  ('offsuit blocked king', {'dead': ['Kd'], 'hand': 'AKo'}, 9),
  ('any ace king two blockers', {'dead': ['As', 'Kc'], 'hand': 'AK'}, 9),
  ('unrelated dead', {'dead': ['2c', '7d'], 'hand': 'AKs'}, 4),
  ('offsuit no blockers', {'dead': [], 'hand': 'T9o'}, 12)],
 [('pair one blocker', {'dead': ['Qh'], 'hand': 'QQ'}, 3),
  ('suited blocked king', {'dead': ['Kd'], 'hand': 'AKs'}, 3),
  ('offsuit blocked king', {'dead': ['Kd'], 'hand': 'AKo'}, 9),
  ('any ace king two blockers', {'dead': ['As', 'Kc'], 'hand': 'AK'}, 9),
  ('lower-case dead', {'dead': ['ah', 'kS'], 'hand': 'AKo'}, 7),
  ('upper-case suit dead', {'dead': ['JH'], 'hand': 'JTs'}, 3),
  ('pair two blockers', {'dead': ['9c', '9s'], 'hand': '99'}, 1),
  ('offsuit no blockers', {'dead': [], 'hand': 'T9o'}, 12)],
 [('pair no blockers', {'dead': [], 'hand': 'QQ'}, 6),
  ('suited no blockers', {'dead': [], 'hand': 'AKs'}, 4),
  ('offsuit blocked king', {'dead': ['Kd'], 'hand': 'AKo'}, 9),
  ('any ace king two blockers', {'dead': ['As', 'Kc'], 'hand': 'AK'}, 9),
  ('lower-case dead', {'dead': ['ah', 'kS'], 'hand': 'AKo'}, 7),
  ('upper-case suit dead', {'dead': ['JH'], 'hand': 'JTs'}, 3),
  ('pair two blockers', {'dead': ['9c', '9s'], 'hand': '99'}, 1),
  ('blocked first rank only', {'dead': ['Qs', 'Qh'], 'hand': 'KQs'}, 2)],
 [('pair no blockers', {'dead': [], 'hand': 'QQ'}, 6),
  ('suited no blockers', {'dead': [], 'hand': 'AKs'}, 4),
  ('any ace king two blockers', {'dead': ['As', 'Kc'], 'hand': 'AK'}, 9),
  ('lower-case dead', {'dead': ['ah', 'kS'], 'hand': 'AKo'}, 7),
  ('upper-case suit dead', {'dead': ['JH'], 'hand': 'JTs'}, 3),
  ('unrelated dead', {'dead': ['2c', '7d'], 'hand': 'AKs'}, 4),
  ('pair two blockers', {'dead': ['9c', '9s'], 'hand': '99'}, 1),
  ('blocked first rank only', {'dead': ['Qs', 'Qh'], 'hand': 'KQs'}, 2)],
 [('pair no blockers', {'dead': [], 'hand': 'QQ'}, 6),
  ('pair one blocker', {'dead': ['Qh'], 'hand': 'QQ'}, 3),
  ('suited no blockers', {'dead': [], 'hand': 'AKs'}, 4),
  ('lower-case dead', {'dead': ['ah', 'kS'], 'hand': 'AKo'}, 7),
  ('upper-case suit dead', {'dead': ['JH'], 'hand': 'JTs'}, 3),
  ('unrelated dead', {'dead': ['2c', '7d'], 'hand': 'AKs'}, 4),
  ('pair two blockers', {'dead': ['9c', '9s'], 'hand': '99'}, 1),
  ('offsuit no blockers', {'dead': [], 'hand': 'T9o'}, 12)]]
for label, args, expected in fixtures[N-1]:
    try:
        actual = solve(args)
    except Exception as exc:
        actual = 'error:' + type(exc).__name__
    check(label, actual, 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
pair no blockers	`6`	`6`	Passed
pair one blocker	`3`	`3`	Passed
suited no blockers	`4`	`4`	Passed
suited blocked king	`3`	`3`	Passed
offsuit blocked king	`9`	`9`	Passed
any ace king two blockers	`9`	`9`	Passed
unrelated dead	`4`	`4`	Passed
offsuit no blockers	`12`	`12`	Passed

SHA-256 / 98517965491cc578095e737c44687f3fd3cf5cb7a5d31de4ae8d68acbd51810f

Verification & scope

A deterministic toy model with an explicitly stated contract; card strings are rank+suit (for example "As", "Td"); no claim of conformance to any casino or tournament rulebook. 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 2026-09-29T14:50:09.550902+00:00.

Case digest / b249f1363dca32ff45dad9ff4b112492536825ea2340c37a3c42b832e7fe485c