FA-82086 / Poker hand evaluation / Open access
Straight flush scored as a mere straight in lowball · case 01
2-3-4-5-6 suited beats a nine-low flush.
ROOT CAUSE
The straight flush case is mapped to the straight category, underrating how bad it is for low.
THE FAILURE
The straight flush case is mapped to the straight category, underrating how bad it is for low.
Unsuccessful approach: Mapping it to flush still ranks it below full houses and quads.
Case contract
Input: [hand_a, hand_b] five distinct cards each. Deuce-to-seven lowball: aces are always high, A-2-3-4-5 is not a straight, straights and flushes count against the hand, and the standard high-hand ordering is inverted so the weaker high hand wins. Return 1 if hand_a wins, -1 if hand_b wins, 0 for a tie.
Why this case matters
Lowball variants reuse high-hand evaluators with inverted outcomes, a common source of subtle bugs.
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'
def key(h):
vals=sorted((R.index(c[0])+2 for c in h), reverse=True)
cnt=collections.Counter(vals)
order=sorted(cnt, key=lambda v:(cnt[v],v), reverse=True)
shape=sorted(cnt.values(), reverse=True)
straight=len(cnt)==5 and vals[0]-vals[4]==4
flush=len({c[1] for c in h})==1
if straight and flush: return (4,vals)
if shape==[4,1]: return (7,order)
if shape==[3,2]: return (6,order)
if flush: return (5,vals)
if straight: return (4,vals)
if shape==[3,1,1]: return (3,order)
if shape==[2,2,1]: return (2,order)
if shape==[2,1,1,1]: return (1,order)
return (0,vals)
ka,kb=key(x[0]),key(x[1])
if ka==kb: return 0
return 1 if ka<kb else -1
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('wheel is ace high', [['Ah', '2d', '3c', '4s', '5h'], ['Kh', 'Qd', 'Jc', '9s', '8h']], -1),
('seven low vs eight low', [['8h', '6d', '4c', '3s', '2h'], ['7c', '6h', '4d', '3c', '2d']], -1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('pair loses to king high', [['2h', '2d', '4c', '5s', '7h'], ['Kh', '8d', '6c', '4s', '3h']], -1),
('ace-king gap hand', [['Ah', 'Kd', '7c', '4s', '2h'], ['Qh', 'Jd', 'Tc', '8s', '6h']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']],
-1)],
[('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('pair loses to king high', [['2h', '2d', '4c', '5s', '7h'], ['Kh', '8d', '6c', '4s', '3h']], -1),
('ace-king gap hand', [['Ah', 'Kd', '7c', '4s', '2h'], ['Qh', 'Jd', 'Tc', '8s', '6h']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('tie', [['7h', '5d', '4c', '3s', '2h'], ['7c', '5h', '4d', '3c', '2d']], 0),
('ace high vs pair', [['Ah', 'Qd', '9c', '7s', '5h'], ['3h', '3d', '6c', '5s', '4h']], 1),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1)],
[('ace-king gap hand', [['Ah', 'Kd', '7c', '4s', '2h'], ['Qh', 'Jd', 'Tc', '8s', '6h']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('tie', [['7h', '5d', '4c', '3s', '2h'], ['7c', '5h', '4d', '3c', '2d']], 0),
('ace high vs pair', [['Ah', 'Qd', '9c', '7s', '5h'], ['3h', '3d', '6c', '5s', '4h']], 1),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('wheel vs pair', [['Ah', '2d', '3c', '4s', '5h'], ['3h', '3d', '6c', '8s', '9h']], 1),
('ace-deuce span vs pair', [['Ah', 'Jd', '8c', '6s', '2h'], ['4h', '4d', '6d', '8d', '9s']], 1),
('ace high vs king high', [['Ah', '9d', '7c', '4s', '2h'], ['Kh', 'Qd', 'Jc', '9s', '8c']], -1)],
[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('wheel vs pair', [['Ah', '2d', '3c', '4s', '5h'], ['3h', '3d', '6c', '8s', '9h']], 1),
('ace-deuce span vs pair', [['Ah', 'Jd', '8c', '6s', '2h'], ['4h', '4d', '6d', '8d', '9s']], 1),
('ace high vs king high', [['Ah', '9d', '7c', '4s', '2h'], ['Kh', 'Qd', 'Jc', '9s', '8c']], -1),
('second tie', [['Kh', 'Jd', '9c', '6s', '3h'], ['Kc', 'Jh', '9d', '6c', '3d']], 0),
('nine vs ten', [['9h', '7d', '5c', '3s', '2h'], ['Th', '4d', '3c', '6s', '2c']], 1)],
[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('wheel is ace high', [['Ah', '2d', '3c', '4s', '5h'], ['Kh', 'Qd', 'Jc', '9s', '8h']], -1),
('seven low vs eight low', [['8h', '6d', '4c', '3s', '2h'], ['7c', '6h', '4d', '3c', '2d']], -1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('ace high vs king high', [['Ah', '9d', '7c', '4s', '2h'], ['Kh', 'Qd', 'Jc', '9s', '8c']], -1),
('second tie', [['Kh', 'Jd', '9c', '6s', '3h'], ['Kc', 'Jh', '9d', '6c', '3d']], 0),
('nine vs ten', [['9h', '7d', '5c', '3s', '2h'], ['Th', '4d', '3c', '6s', '2c']], 1)]]
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 |
|---|---|---|---|
| number one vs wheel | 1 | 1 | Passed |
| wheel is ace high | -1 | -1 | Passed |
| seven low vs eight low | -1 | -1 | Passed |
| flush counts against | -1 | -1 | Passed |
| straight counts against | -1 | -1 | Passed |
| pair loses to king high | -1 | -1 | Passed |
| ace-king gap hand | -1 | -1 | Passed |
| straight flush vs flush | 1 | -1 | Failed |
SHA-256 / 86a30fba773d15f4b471d74fcf0c53e3095ae8204696a391d2f29c30cffd63cd
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'
def key(h):
vals=sorted((R.index(c[0])+2 for c in h), reverse=True)
cnt=collections.Counter(vals)
order=sorted(cnt, key=lambda v:(cnt[v],v), reverse=True)
shape=sorted(cnt.values(), reverse=True)
straight=len(cnt)==5 and vals[0]-vals[4]==4
flush=len({c[1] for c in h})==1
if straight and flush: return (5,vals)
if shape==[4,1]: return (7,order)
if shape==[3,2]: return (6,order)
if flush: return (5,vals)
if straight: return (4,vals)
if shape==[3,1,1]: return (3,order)
if shape==[2,2,1]: return (2,order)
if shape==[2,1,1,1]: return (1,order)
return (0,vals)
ka,kb=key(x[0]),key(x[1])
if ka==kb: return 0
return 1 if ka<kb else -1
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('wheel is ace high', [['Ah', '2d', '3c', '4s', '5h'], ['Kh', 'Qd', 'Jc', '9s', '8h']], -1),
('seven low vs eight low', [['8h', '6d', '4c', '3s', '2h'], ['7c', '6h', '4d', '3c', '2d']], -1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('pair loses to king high', [['2h', '2d', '4c', '5s', '7h'], ['Kh', '8d', '6c', '4s', '3h']], -1),
('ace-king gap hand', [['Ah', 'Kd', '7c', '4s', '2h'], ['Qh', 'Jd', 'Tc', '8s', '6h']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']],
-1)],
[('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight counts against', [['3h', '4d', '5c', '6s', '7h'], ['Kh', 'Qd', 'Jc', '9s', '7c']], -1),
('pair loses to king high', [['2h', '2d', '4c', '5s', '7h'], ['Kh', '8d', '6c', '4s', '3h']], -1),
('ace-king gap hand', [['Ah', 'Kd', '7c', '4s', '2h'], ['Qh', 'Jd', 'Tc', '8s', '6h']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('tie', [['7h', '5d', '4c', '3s', '2h'], ['7c', '5h', '4d', '3c', '2d']], 0),
('ace high vs pair', [['Ah', 'Qd', '9c', '7s', '5h'], ['3h', '3d', '6c', '5s', '4h']], 1),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1)],
[('ace-king gap hand', [['Ah', 'Kd', '7c', '4s', '2h'], ['Qh', 'Jd', 'Tc', '8s', '6h']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('tie', [['7h', '5d', '4c', '3s', '2h'], ['7c', '5h', '4d', '3c', '2d']], 0),
('ace high vs pair', [['Ah', 'Qd', '9c', '7s', '5h'], ['3h', '3d', '6c', '5s', '4h']], 1),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('wheel vs pair', [['Ah', '2d', '3c', '4s', '5h'], ['3h', '3d', '6c', '8s', '9h']], 1),
('ace-deuce span vs pair', [['Ah', 'Jd', '8c', '6s', '2h'], ['4h', '4d', '6d', '8d', '9s']], 1),
('ace high vs king high', [['Ah', '9d', '7c', '4s', '2h'], ['Kh', 'Qd', 'Jc', '9s', '8c']], -1)],
[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('both pairs lower pair wins', [['4h', '4d', 'Kc', 'Qs', 'Jh'], ['5h', '5d', '2c', '3s', '7h']],
1),
('wheel vs pair', [['Ah', '2d', '3c', '4s', '5h'], ['3h', '3d', '6c', '8s', '9h']], 1),
('ace-deuce span vs pair', [['Ah', 'Jd', '8c', '6s', '2h'], ['4h', '4d', '6d', '8d', '9s']], 1),
('ace high vs king high', [['Ah', '9d', '7c', '4s', '2h'], ['Kh', 'Qd', 'Jc', '9s', '8c']], -1),
('second tie', [['Kh', 'Jd', '9c', '6s', '3h'], ['Kc', 'Jh', '9d', '6c', '3d']], 0),
('nine vs ten', [['9h', '7d', '5c', '3s', '2h'], ['Th', '4d', '3c', '6s', '2c']], 1)],
[('number one vs wheel', [['7h', '5d', '4c', '3s', '2h'], ['Ah', '2d', '3c', '4s', '5h']], 1),
('wheel is ace high', [['Ah', '2d', '3c', '4s', '5h'], ['Kh', 'Qd', 'Jc', '9s', '8h']], -1),
('seven low vs eight low', [['8h', '6d', '4c', '3s', '2h'], ['7c', '6h', '4d', '3c', '2d']], -1),
('flush counts against', [['2h', '4h', '5h', '6h', '8h'], ['9c', '6d', '4d', '3c', '2d']], -1),
('straight flush vs flush', [['2c', '3c', '4c', '5c', '6c'], ['9d', '7d', '5d', '3d', '2d']], -1),
('ace high vs king high', [['Ah', '9d', '7c', '4s', '2h'], ['Kh', 'Qd', 'Jc', '9s', '8c']], -1),
('second tie', [['Kh', 'Jd', '9c', '6s', '3h'], ['Kc', 'Jh', '9d', '6c', '3d']], 0),
('nine vs ten', [['9h', '7d', '5c', '3s', '2h'], ['Th', '4d', '3c', '6s', '2c']], 1)]]
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 |
|---|---|---|---|
| number one vs wheel | 1 | 1 | Passed |
| wheel is ace high | -1 | -1 | Passed |
| seven low vs eight low | -1 | -1 | Passed |
| flush counts against | -1 | -1 | Passed |
| straight counts against | -1 | -1 | Passed |
| pair loses to king high | -1 | -1 | Passed |
| ace-king gap hand | -1 | -1 | Passed |
| straight flush vs flush | 1 | -1 | Failed |
SHA-256 / 1ca5a355366c3d1a4a4c6fee8da529c4086ff507889864a899d476287bb56f2d
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.
Member access is invitation-based. Sign in with your invited account to inspect the repair.
Sign in to the archive ↗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 2026-09-29T14:50:08.881901+00:00.
Case digest / 7a0f7d241279756d74b0d174ba13c15f06bd4a248d2ff310c2b9b2e2ce3bfa03