FA-82186 / Poker hand evaluation / Open access

Steel wheel announced as a royal flush · case 01

A-2-3-4-5 suited is announced as "Royal Flush".

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

ROOT CAUSE

Royal is decided by the presence of an ace rather than by an ace-high straight flush.

VERIFIED REPAIR

A royal flush is a straight flush whose top card (after wheel handling) is the ace.

Unsuccessful approach: Accepting king-high as royal still misnames a king-high straight flush.

Case contract

Input: five distinct cards. Return the showdown announcement: "Royal Flush", "Straight Flush, <top> high", "Four <plural>", "Full House, <trips plural> full of <pair plural>", "Flush, <top> high", "Straight, <top> high" (wheel is Five high), "Three <plural>", "Two Pair, <higher plural> and <lower plural>", "Pair of <plural>", "High Card, <top>". Rank names Two..Ace; plurals add "s" except Deuces and Sixes.

Why this case matters

Dealer announcements and hand histories must name the same hand the evaluator paid.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import collections
N = 1
observations = []
def solve(x):
    R='23456789TJQKA'
    NAME={2:'Two',3:'Three',4:'Four',5:'Five',6:'Six',7:'Seven',8:'Eight',9:'Nine',10:'Ten',11:'Jack',12:'Queen',13:'King',14:'Ace'}
    def pl(v): return {2:'Deuces',6:'Sixes'}.get(v, NAME[v]+'s')
    vals=sorted((R.index(c[0])+2 for c in x), reverse=True)
    cnt=collections.Counter(vals)
    groups=sorted(cnt, key=lambda v:(cnt[v],v), reverse=True)
    shape=sorted(cnt.values(), reverse=True)
    flush=len({c[1] for c in x})==1
    wheel=vals==[14,5,4,3,2]
    straight=len(cnt)==5 and (vals[0]-vals[4]==4 or wheel)
    top=5 if wheel else vals[0]
    if straight and flush: return 'Royal Flush' if vals[0]==14 else 'Straight Flush, %s high' % NAME[top]
    if shape==[4,1]: return 'Four %s' % pl(groups[0])
    if shape==[3,2]: return 'Full House, %s full of %s' % (pl(groups[0]), pl(groups[1]))
    if flush: return 'Flush, %s high' % NAME[vals[0]]
    if straight: return 'Straight, %s high' % NAME[top]
    if shape==[3,1,1]: return 'Three %s' % pl(groups[0])
    if shape==[2,2,1]: return 'Two Pair, %s and %s' % (pl(groups[0]), pl(groups[1]))
    if shape==[2,1,1,1]: return 'Pair of %s' % pl(groups[0])
    return 'High Card, %s' % NAME[vals[0]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('pair of sixes', ['6h', '6d', 'Kc', '9s', '2h'], 'Pair of Sixes'),
  ('pair of deuces', ['2h', '2d', 'Kc', '9s', '5h'], 'Pair of Deuces'),
  ('wheel', ['Ah', '2d', '3c', '4s', '5h'], 'Straight, Five high'),
  ('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('royal', ['Th', 'Jh', 'Qh', 'Kh', 'Ah'], 'Royal Flush'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('threes full of kings', ['3h', '3d', '3c', 'Ks', 'Kh'], 'Full House, Threes full of Kings'),
  ('kings full of threes', ['Kh', 'Kd', 'Kc', '3s', '3h'], 'Full House, Kings full of Threes')],
 [('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('royal', ['Th', 'Jh', 'Qh', 'Kh', 'Ah'], 'Royal Flush'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('threes full of kings', ['3h', '3d', '3c', 'Ks', 'Kh'], 'Full House, Threes full of Kings'),
  ('kings full of threes', ['Kh', 'Kd', 'Kc', '3s', '3h'], 'Full House, Kings full of Threes'),
  ('two pair ace kicker', ['Ah', 'Kd', 'Kc', '7s', '7h'], 'Two Pair, Kings and Sevens'),
  ('two pair low kicker', ['Kh', 'Kd', '7c', '7s', '2h'], 'Two Pair, Kings and Sevens'),
  ('pair below high cards', ['Ah', 'Kd', '5c', '5s', '9h'], 'Pair of Fives')],
 [('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('two pair ace kicker', ['Ah', 'Kd', 'Kc', '7s', '7h'], 'Two Pair, Kings and Sevens'),
  ('two pair low kicker', ['Kh', 'Kd', '7c', '7s', '2h'], 'Two Pair, Kings and Sevens'),
  ('pair below high cards', ['Ah', 'Kd', '5c', '5s', '9h'], 'Pair of Fives'),
  ('high card', ['Ah', 'Jd', '8c', '5s', '3h'], 'High Card, Ace'),
  ('four nines', ['9h', '9d', '9c', '9s', '2h'], 'Four Nines'),
  ('flush', ['2c', '7c', '9c', 'Jc', 'Qc'], 'Flush, Queen high')],
 [('pair of sixes', ['6h', '6d', 'Kc', '9s', '2h'], 'Pair of Sixes'),
  ('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('high card', ['Ah', 'Jd', '8c', '5s', '3h'], 'High Card, Ace'),
  ('four nines', ['9h', '9d', '9c', '9s', '2h'], 'Four Nines'),
  ('flush', ['2c', '7c', '9c', 'Jc', 'Qc'], 'Flush, Queen high'),
  ('six-high straight', ['2h', '3d', '4c', '5s', '6h'], 'Straight, Six high'),
  ('three sixes', ['6h', '6d', '6c', 'Ks', '2h'], 'Three Sixes')],
 [('pair of sixes', ['6h', '6d', 'Kc', '9s', '2h'], 'Pair of Sixes'),
  ('pair of deuces', ['2h', '2d', 'Kc', '9s', '5h'], 'Pair of Deuces'),
  ('wheel', ['Ah', '2d', '3c', '4s', '5h'], 'Straight, Five high'),
  ('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('royal', ['Th', 'Jh', 'Qh', 'Kh', 'Ah'], 'Royal Flush'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('six-high straight', ['2h', '3d', '4c', '5s', '6h'], 'Straight, Six high'),
  ('three sixes', ['6h', '6d', '6c', 'Ks', '2h'], 'Three Sixes')]]
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 of sixes	`Pair of Sixes`	`Pair of Sixes`	Passed
pair of deuces	`Pair of Deuces`	`Pair of Deuces`	Passed
wheel	`Straight, Five high`	`Straight, Five high`	Passed
steel wheel	`Royal Flush`	`Straight Flush, Five high`	Failed
royal	`Royal Flush`	`Royal Flush`	Passed
king-high straight flush	`Straight Flush, King high`	`Straight Flush, King high`	Passed
threes full of kings	`Full House, Threes full of Kings`	`Full House, Threes full of Kings`	Passed
kings full of threes	`Full House, Kings full of Threes`	`Full House, Kings full of Threes`	Passed

SHA-256 / 07802bfbb10b704db8b5a90295d274a6aa2ae26ff15533f3aff33bfedcea2a90

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import collections
N = 1
observations = []
def solve(x):
    R='23456789TJQKA'
    NAME={2:'Two',3:'Three',4:'Four',5:'Five',6:'Six',7:'Seven',8:'Eight',9:'Nine',10:'Ten',11:'Jack',12:'Queen',13:'King',14:'Ace'}
    def pl(v): return {2:'Deuces',6:'Sixes'}.get(v, NAME[v]+'s')
    vals=sorted((R.index(c[0])+2 for c in x), reverse=True)
    cnt=collections.Counter(vals)
    groups=sorted(cnt, key=lambda v:(cnt[v],v), reverse=True)
    shape=sorted(cnt.values(), reverse=True)
    flush=len({c[1] for c in x})==1
    wheel=vals==[14,5,4,3,2]
    straight=len(cnt)==5 and (vals[0]-vals[4]==4 or wheel)
    top=5 if wheel else vals[0]
    if straight and flush: return 'Royal Flush' if top>=13 else 'Straight Flush, %s high' % NAME[top]
    if shape==[4,1]: return 'Four %s' % pl(groups[0])
    if shape==[3,2]: return 'Full House, %s full of %s' % (pl(groups[0]), pl(groups[1]))
    if flush: return 'Flush, %s high' % NAME[vals[0]]
    if straight: return 'Straight, %s high' % NAME[top]
    if shape==[3,1,1]: return 'Three %s' % pl(groups[0])
    if shape==[2,2,1]: return 'Two Pair, %s and %s' % (pl(groups[0]), pl(groups[1]))
    if shape==[2,1,1,1]: return 'Pair of %s' % pl(groups[0])
    return 'High Card, %s' % NAME[vals[0]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('pair of sixes', ['6h', '6d', 'Kc', '9s', '2h'], 'Pair of Sixes'),
  ('pair of deuces', ['2h', '2d', 'Kc', '9s', '5h'], 'Pair of Deuces'),
  ('wheel', ['Ah', '2d', '3c', '4s', '5h'], 'Straight, Five high'),
  ('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('royal', ['Th', 'Jh', 'Qh', 'Kh', 'Ah'], 'Royal Flush'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('threes full of kings', ['3h', '3d', '3c', 'Ks', 'Kh'], 'Full House, Threes full of Kings'),
  ('kings full of threes', ['Kh', 'Kd', 'Kc', '3s', '3h'], 'Full House, Kings full of Threes')],
 [('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('royal', ['Th', 'Jh', 'Qh', 'Kh', 'Ah'], 'Royal Flush'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('threes full of kings', ['3h', '3d', '3c', 'Ks', 'Kh'], 'Full House, Threes full of Kings'),
  ('kings full of threes', ['Kh', 'Kd', 'Kc', '3s', '3h'], 'Full House, Kings full of Threes'),
  ('two pair ace kicker', ['Ah', 'Kd', 'Kc', '7s', '7h'], 'Two Pair, Kings and Sevens'),
  ('two pair low kicker', ['Kh', 'Kd', '7c', '7s', '2h'], 'Two Pair, Kings and Sevens'),
  ('pair below high cards', ['Ah', 'Kd', '5c', '5s', '9h'], 'Pair of Fives')],
 [('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('two pair ace kicker', ['Ah', 'Kd', 'Kc', '7s', '7h'], 'Two Pair, Kings and Sevens'),
  ('two pair low kicker', ['Kh', 'Kd', '7c', '7s', '2h'], 'Two Pair, Kings and Sevens'),
  ('pair below high cards', ['Ah', 'Kd', '5c', '5s', '9h'], 'Pair of Fives'),
  ('high card', ['Ah', 'Jd', '8c', '5s', '3h'], 'High Card, Ace'),
  ('four nines', ['9h', '9d', '9c', '9s', '2h'], 'Four Nines'),
  ('flush', ['2c', '7c', '9c', 'Jc', 'Qc'], 'Flush, Queen high')],
 [('pair of sixes', ['6h', '6d', 'Kc', '9s', '2h'], 'Pair of Sixes'),
  ('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('high card', ['Ah', 'Jd', '8c', '5s', '3h'], 'High Card, Ace'),
  ('four nines', ['9h', '9d', '9c', '9s', '2h'], 'Four Nines'),
  ('flush', ['2c', '7c', '9c', 'Jc', 'Qc'], 'Flush, Queen high'),
  ('six-high straight', ['2h', '3d', '4c', '5s', '6h'], 'Straight, Six high'),
  ('three sixes', ['6h', '6d', '6c', 'Ks', '2h'], 'Three Sixes')],
 [('pair of sixes', ['6h', '6d', 'Kc', '9s', '2h'], 'Pair of Sixes'),
  ('pair of deuces', ['2h', '2d', 'Kc', '9s', '5h'], 'Pair of Deuces'),
  ('wheel', ['Ah', '2d', '3c', '4s', '5h'], 'Straight, Five high'),
  ('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('royal', ['Th', 'Jh', 'Qh', 'Kh', 'Ah'], 'Royal Flush'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('six-high straight', ['2h', '3d', '4c', '5s', '6h'], 'Straight, Six high'),
  ('three sixes', ['6h', '6d', '6c', 'Ks', '2h'], 'Three Sixes')]]
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 of sixes	`Pair of Sixes`	`Pair of Sixes`	Passed
pair of deuces	`Pair of Deuces`	`Pair of Deuces`	Passed
wheel	`Straight, Five high`	`Straight, Five high`	Passed
steel wheel	`Straight Flush, Five high`	`Straight Flush, Five high`	Passed
royal	`Royal Flush`	`Royal Flush`	Passed
king-high straight flush	`Royal Flush`	`Straight Flush, King high`	Failed
threes full of kings	`Full House, Threes full of Kings`	`Full House, Threes full of Kings`	Passed
kings full of threes	`Full House, Kings full of Threes`	`Full House, Kings full of Threes`	Passed

SHA-256 / bf5a8e43861fb94e7c89184de4a3ecf66fc47309d3195634e2c83bc074243169

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import collections
N = 1
observations = []
def solve(x):
    R='23456789TJQKA'
    NAME={2:'Two',3:'Three',4:'Four',5:'Five',6:'Six',7:'Seven',8:'Eight',9:'Nine',10:'Ten',11:'Jack',12:'Queen',13:'King',14:'Ace'}
    def pl(v): return {2:'Deuces',6:'Sixes'}.get(v, NAME[v]+'s')
    vals=sorted((R.index(c[0])+2 for c in x), reverse=True)
    cnt=collections.Counter(vals)
    groups=sorted(cnt, key=lambda v:(cnt[v],v), reverse=True)
    shape=sorted(cnt.values(), reverse=True)
    flush=len({c[1] for c in x})==1
    wheel=vals==[14,5,4,3,2]
    straight=len(cnt)==5 and (vals[0]-vals[4]==4 or wheel)
    top=5 if wheel else vals[0]
    if straight and flush: return 'Royal Flush' if top==14 else 'Straight Flush, %s high' % NAME[top]
    if shape==[4,1]: return 'Four %s' % pl(groups[0])
    if shape==[3,2]: return 'Full House, %s full of %s' % (pl(groups[0]), pl(groups[1]))
    if flush: return 'Flush, %s high' % NAME[vals[0]]
    if straight: return 'Straight, %s high' % NAME[top]
    if shape==[3,1,1]: return 'Three %s' % pl(groups[0])
    if shape==[2,2,1]: return 'Two Pair, %s and %s' % (pl(groups[0]), pl(groups[1]))
    if shape==[2,1,1,1]: return 'Pair of %s' % pl(groups[0])
    return 'High Card, %s' % NAME[vals[0]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('pair of sixes', ['6h', '6d', 'Kc', '9s', '2h'], 'Pair of Sixes'),
  ('pair of deuces', ['2h', '2d', 'Kc', '9s', '5h'], 'Pair of Deuces'),
  ('wheel', ['Ah', '2d', '3c', '4s', '5h'], 'Straight, Five high'),
  ('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('royal', ['Th', 'Jh', 'Qh', 'Kh', 'Ah'], 'Royal Flush'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('threes full of kings', ['3h', '3d', '3c', 'Ks', 'Kh'], 'Full House, Threes full of Kings'),
  ('kings full of threes', ['Kh', 'Kd', 'Kc', '3s', '3h'], 'Full House, Kings full of Threes')],
 [('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('royal', ['Th', 'Jh', 'Qh', 'Kh', 'Ah'], 'Royal Flush'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('threes full of kings', ['3h', '3d', '3c', 'Ks', 'Kh'], 'Full House, Threes full of Kings'),
  ('kings full of threes', ['Kh', 'Kd', 'Kc', '3s', '3h'], 'Full House, Kings full of Threes'),
  ('two pair ace kicker', ['Ah', 'Kd', 'Kc', '7s', '7h'], 'Two Pair, Kings and Sevens'),
  ('two pair low kicker', ['Kh', 'Kd', '7c', '7s', '2h'], 'Two Pair, Kings and Sevens'),
  ('pair below high cards', ['Ah', 'Kd', '5c', '5s', '9h'], 'Pair of Fives')],
 [('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('two pair ace kicker', ['Ah', 'Kd', 'Kc', '7s', '7h'], 'Two Pair, Kings and Sevens'),
  ('two pair low kicker', ['Kh', 'Kd', '7c', '7s', '2h'], 'Two Pair, Kings and Sevens'),
  ('pair below high cards', ['Ah', 'Kd', '5c', '5s', '9h'], 'Pair of Fives'),
  ('high card', ['Ah', 'Jd', '8c', '5s', '3h'], 'High Card, Ace'),
  ('four nines', ['9h', '9d', '9c', '9s', '2h'], 'Four Nines'),
  ('flush', ['2c', '7c', '9c', 'Jc', 'Qc'], 'Flush, Queen high')],
 [('pair of sixes', ['6h', '6d', 'Kc', '9s', '2h'], 'Pair of Sixes'),
  ('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('high card', ['Ah', 'Jd', '8c', '5s', '3h'], 'High Card, Ace'),
  ('four nines', ['9h', '9d', '9c', '9s', '2h'], 'Four Nines'),
  ('flush', ['2c', '7c', '9c', 'Jc', 'Qc'], 'Flush, Queen high'),
  ('six-high straight', ['2h', '3d', '4c', '5s', '6h'], 'Straight, Six high'),
  ('three sixes', ['6h', '6d', '6c', 'Ks', '2h'], 'Three Sixes')],
 [('pair of sixes', ['6h', '6d', 'Kc', '9s', '2h'], 'Pair of Sixes'),
  ('pair of deuces', ['2h', '2d', 'Kc', '9s', '5h'], 'Pair of Deuces'),
  ('wheel', ['Ah', '2d', '3c', '4s', '5h'], 'Straight, Five high'),
  ('steel wheel', ['As', '2s', '3s', '4s', '5s'], 'Straight Flush, Five high'),
  ('royal', ['Th', 'Jh', 'Qh', 'Kh', 'Ah'], 'Royal Flush'),
  ('king-high straight flush', ['9d', 'Td', 'Jd', 'Qd', 'Kd'], 'Straight Flush, King high'),
  ('six-high straight', ['2h', '3d', '4c', '5s', '6h'], 'Straight, Six high'),
  ('three sixes', ['6h', '6d', '6c', 'Ks', '2h'], 'Three Sixes')]]
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 of sixes	`Pair of Sixes`	`Pair of Sixes`	Passed
pair of deuces	`Pair of Deuces`	`Pair of Deuces`	Passed
wheel	`Straight, Five high`	`Straight, Five high`	Passed
steel wheel	`Straight Flush, Five high`	`Straight Flush, Five high`	Passed
royal	`Royal Flush`	`Royal Flush`	Passed
king-high straight flush	`Straight Flush, King high`	`Straight Flush, King high`	Passed
threes full of kings	`Full House, Threes full of Kings`	`Full House, Threes full of Kings`	Passed
kings full of threes	`Full House, Kings full of Threes`	`Full House, Kings full of Threes`	Passed

SHA-256 / 974a119dfddcf0d40294affd8130c023fb28d28919e9b160461a62ecac850744

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 2026-09-29T14:50:09.807810+00:00.

Case digest / 1bad5113a8c50dc0f42a1b647aec6b85bee67a7aed14147be5bd7634cf3ea7f4