FA-82096 / Poker hand evaluation / Open access

Case variants of one card accepted as two cards · case 01

"Ah" with "aH" is notated "AA" instead of being rejected.

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

ROOT CAUSE

Duplicate detection compares raw strings although ranks and suits are case-insensitive.

VERIFIED REPAIR

Compare the case-normalized card strings.

Unsuccessful approach: Comparing only the rank tokens rejects every legitimate pocket pair.

Case contract

Input: two hole cards as strings (rank may be "10"; rank and suit case-insensitive). Return canonical hold'em notation: pairs "QQ", otherwise higher rank first with "s" for suited or "o" for offsuit (e.g. "AKs", "T9o"). Return "invalid" for duplicate cards or unknown ranks.

Why this case matters

Range tools, solvers and hand histories key statistics on this notation.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    R='23456789TJQKA'
    if len(x)!=2 or x[0]==x[1]: return 'invalid'
    def rank(c):
        t=c[:-1].upper()
        return 'T' if t=='10' else t
    a,b=rank(x[0]),rank(x[1])
    if a not in list(R) or b not in list(R): return 'invalid'
    if a==b: return a+b
    hi,lo=sorted([a,b], key=R.index, reverse=True)
    return hi+lo+('s' if x[0][-1].lower()==x[1][-1].lower() else 'o')
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('ace king suited', ['Ah', 'Kh'], 'AKs'), ('king ace offsuit order', ['Kd', 'Ah'], 'AKo'),
  ('ten nine suited with 10', ['10s', '9s'], 'T9s'), ('nine ten mixed', ['9c', '10d'], 'T9o'),
  ('pair of queens', ['Qh', 'Qs'], 'QQ'), ('duplicate card case', ['Ah', 'aH'], 'invalid'),
  ('exact duplicate', ['7c', '7c'], 'invalid'), ('queen ten', ['Tc', 'Qc'], 'QTs')],
 [('nine ten mixed', ['9c', '10d'], 'T9o'), ('pair of queens', ['Qh', 'Qs'], 'QQ'),
  ('duplicate card case', ['Ah', 'aH'], 'invalid'), ('exact duplicate', ['7c', '7c'], 'invalid'),
  ('queen ten', ['Tc', 'Qc'], 'QTs'), ('lower case ranks', ['kd', 'js'], 'KJo'),
  ('suit case differs', ['Jh', 'TH'], 'JTs'), ('empty rank', ['h', 'Kd'], 'invalid')],
 [('pair of queens', ['Qh', 'Qs'], 'QQ'), ('duplicate card case', ['Ah', 'aH'], 'invalid'),
  ('lower case ranks', ['kd', 'js'], 'KJo'), ('suit case differs', ['Jh', 'TH'], 'JTs'),
  ('empty rank', ['h', 'Kd'], 'invalid'), ('two-letter rank', ['KQh', '2d'], 'invalid'),
  ('ten first suited', ['10h', 'Jh'], 'JTs'), ('deuce seven', ['2d', '7s'], '72o')],
 [('ace king suited', ['Ah', 'Kh'], 'AKs'), ('king ace offsuit order', ['Kd', 'Ah'], 'AKo'),
  ('pair of queens', ['Qh', 'Qs'], 'QQ'), ('duplicate card case', ['Ah', 'aH'], 'invalid'),
  ('two-letter rank', ['KQh', '2d'], 'invalid'), ('ten first suited', ['10h', 'Jh'], 'JTs'),
  ('deuce seven', ['2d', '7s'], '72o'), ('pair of tens mixed tokens', ['10h', 'Td'], 'TT')],
 [('ace king suited', ['Ah', 'Kh'], 'AKs'), ('king ace offsuit order', ['Kd', 'Ah'], 'AKo'),
  ('ten nine suited with 10', ['10s', '9s'], 'T9s'), ('nine ten mixed', ['9c', '10d'], 'T9o'),
  ('pair of queens', ['Qh', 'Qs'], 'QQ'), ('duplicate card case', ['Ah', 'aH'], 'invalid'),
  ('exact duplicate', ['7c', '7c'], 'invalid'),
  ('pair of tens mixed tokens', ['10h', 'Td'], 'TT')]]
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
ace king suited	`AKs`	`AKs`	Passed
king ace offsuit order	`AKo`	`AKo`	Passed
ten nine suited with 10	`T9s`	`T9s`	Passed
nine ten mixed	`T9o`	`T9o`	Passed
pair of queens	`QQ`	`QQ`	Passed
duplicate card case	`AA`	`invalid`	Failed
exact duplicate	`invalid`	`invalid`	Passed
queen ten	`QTs`	`QTs`	Passed

SHA-256 / c923864553fe3b2d0a46c4bcb125328eee421761c6609e32fa30b957351bfca2

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    R='23456789TJQKA'
    if len(x)!=2 or x[0][:-1]==x[1][:-1]: return 'invalid'
    def rank(c):
        t=c[:-1].upper()
        return 'T' if t=='10' else t
    a,b=rank(x[0]),rank(x[1])
    if a not in list(R) or b not in list(R): return 'invalid'
    if a==b: return a+b
    hi,lo=sorted([a,b], key=R.index, reverse=True)
    return hi+lo+('s' if x[0][-1].lower()==x[1][-1].lower() else 'o')
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('ace king suited', ['Ah', 'Kh'], 'AKs'), ('king ace offsuit order', ['Kd', 'Ah'], 'AKo'),
  ('ten nine suited with 10', ['10s', '9s'], 'T9s'), ('nine ten mixed', ['9c', '10d'], 'T9o'),
  ('pair of queens', ['Qh', 'Qs'], 'QQ'), ('duplicate card case', ['Ah', 'aH'], 'invalid'),
  ('exact duplicate', ['7c', '7c'], 'invalid'), ('queen ten', ['Tc', 'Qc'], 'QTs')],
 [('nine ten mixed', ['9c', '10d'], 'T9o'), ('pair of queens', ['Qh', 'Qs'], 'QQ'),
  ('duplicate card case', ['Ah', 'aH'], 'invalid'), ('exact duplicate', ['7c', '7c'], 'invalid'),
  ('queen ten', ['Tc', 'Qc'], 'QTs'), ('lower case ranks', ['kd', 'js'], 'KJo'),
  ('suit case differs', ['Jh', 'TH'], 'JTs'), ('empty rank', ['h', 'Kd'], 'invalid')],
 [('pair of queens', ['Qh', 'Qs'], 'QQ'), ('duplicate card case', ['Ah', 'aH'], 'invalid'),
  ('lower case ranks', ['kd', 'js'], 'KJo'), ('suit case differs', ['Jh', 'TH'], 'JTs'),
  ('empty rank', ['h', 'Kd'], 'invalid'), ('two-letter rank', ['KQh', '2d'], 'invalid'),
  ('ten first suited', ['10h', 'Jh'], 'JTs'), ('deuce seven', ['2d', '7s'], '72o')],
 [('ace king suited', ['Ah', 'Kh'], 'AKs'), ('king ace offsuit order', ['Kd', 'Ah'], 'AKo'),
  ('pair of queens', ['Qh', 'Qs'], 'QQ'), ('duplicate card case', ['Ah', 'aH'], 'invalid'),
  ('two-letter rank', ['KQh', '2d'], 'invalid'), ('ten first suited', ['10h', 'Jh'], 'JTs'),
  ('deuce seven', ['2d', '7s'], '72o'), ('pair of tens mixed tokens', ['10h', 'Td'], 'TT')],
 [('ace king suited', ['Ah', 'Kh'], 'AKs'), ('king ace offsuit order', ['Kd', 'Ah'], 'AKo'),
  ('ten nine suited with 10', ['10s', '9s'], 'T9s'), ('nine ten mixed', ['9c', '10d'], 'T9o'),
  ('pair of queens', ['Qh', 'Qs'], 'QQ'), ('duplicate card case', ['Ah', 'aH'], 'invalid'),
  ('exact duplicate', ['7c', '7c'], 'invalid'),
  ('pair of tens mixed tokens', ['10h', 'Td'], 'TT')]]
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
ace king suited	`AKs`	`AKs`	Passed
king ace offsuit order	`AKo`	`AKo`	Passed
ten nine suited with 10	`T9s`	`T9s`	Passed
nine ten mixed	`T9o`	`T9o`	Passed
pair of queens	`invalid`	`QQ`	Failed
duplicate card case	`AA`	`invalid`	Failed
exact duplicate	`invalid`	`invalid`	Passed
queen ten	`QTs`	`QTs`	Passed

SHA-256 / b37a4dbd9b3a0043d6ad7a7532fc1ceba7b7a86394580fb43e22d7dd76ebc005

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    R='23456789TJQKA'
    if len(x)!=2 or x[0].upper()==x[1].upper(): return 'invalid'
    def rank(c):
        t=c[:-1].upper()
        return 'T' if t=='10' else t
    a,b=rank(x[0]),rank(x[1])
    if a not in list(R) or b not in list(R): return 'invalid'
    if a==b: return a+b
    hi,lo=sorted([a,b], key=R.index, reverse=True)
    return hi+lo+('s' if x[0][-1].lower()==x[1][-1].lower() else 'o')
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('ace king suited', ['Ah', 'Kh'], 'AKs'), ('king ace offsuit order', ['Kd', 'Ah'], 'AKo'),
  ('ten nine suited with 10', ['10s', '9s'], 'T9s'), ('nine ten mixed', ['9c', '10d'], 'T9o'),
  ('pair of queens', ['Qh', 'Qs'], 'QQ'), ('duplicate card case', ['Ah', 'aH'], 'invalid'),
  ('exact duplicate', ['7c', '7c'], 'invalid'), ('queen ten', ['Tc', 'Qc'], 'QTs')],
 [('nine ten mixed', ['9c', '10d'], 'T9o'), ('pair of queens', ['Qh', 'Qs'], 'QQ'),
  ('duplicate card case', ['Ah', 'aH'], 'invalid'), ('exact duplicate', ['7c', '7c'], 'invalid'),
  ('queen ten', ['Tc', 'Qc'], 'QTs'), ('lower case ranks', ['kd', 'js'], 'KJo'),
  ('suit case differs', ['Jh', 'TH'], 'JTs'), ('empty rank', ['h', 'Kd'], 'invalid')],
 [('pair of queens', ['Qh', 'Qs'], 'QQ'), ('duplicate card case', ['Ah', 'aH'], 'invalid'),
  ('lower case ranks', ['kd', 'js'], 'KJo'), ('suit case differs', ['Jh', 'TH'], 'JTs'),
  ('empty rank', ['h', 'Kd'], 'invalid'), ('two-letter rank', ['KQh', '2d'], 'invalid'),
  ('ten first suited', ['10h', 'Jh'], 'JTs'), ('deuce seven', ['2d', '7s'], '72o')],
 [('ace king suited', ['Ah', 'Kh'], 'AKs'), ('king ace offsuit order', ['Kd', 'Ah'], 'AKo'),
  ('pair of queens', ['Qh', 'Qs'], 'QQ'), ('duplicate card case', ['Ah', 'aH'], 'invalid'),
  ('two-letter rank', ['KQh', '2d'], 'invalid'), ('ten first suited', ['10h', 'Jh'], 'JTs'),
  ('deuce seven', ['2d', '7s'], '72o'), ('pair of tens mixed tokens', ['10h', 'Td'], 'TT')],
 [('ace king suited', ['Ah', 'Kh'], 'AKs'), ('king ace offsuit order', ['Kd', 'Ah'], 'AKo'),
  ('ten nine suited with 10', ['10s', '9s'], 'T9s'), ('nine ten mixed', ['9c', '10d'], 'T9o'),
  ('pair of queens', ['Qh', 'Qs'], 'QQ'), ('duplicate card case', ['Ah', 'aH'], 'invalid'),
  ('exact duplicate', ['7c', '7c'], 'invalid'),
  ('pair of tens mixed tokens', ['10h', 'Td'], 'TT')]]
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
ace king suited	`AKs`	`AKs`	Passed
king ace offsuit order	`AKo`	`AKo`	Passed
ten nine suited with 10	`T9s`	`T9s`	Passed
nine ten mixed	`T9o`	`T9o`	Passed
pair of queens	`QQ`	`QQ`	Passed
duplicate card case	`invalid`	`invalid`	Passed
exact duplicate	`invalid`	`invalid`	Passed
queen ten	`QTs`	`QTs`	Passed

SHA-256 / b8b0a1fe33b155bb6dd539b80ed8420f53f1c15246fb66974e546490b44f15be

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 2026-09-29T14:50:08.911769+00:00.

Case digest / a0a4a3b24afcb5c35233b8f37dad5c8415b222c607ce1ed00c16438c46601fee