FA-81961 / Poker hand evaluation / Open access

Each rank prime divided out only once · case 01

Every paired hand is reported as high card.

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

ROOT CAUSE

The factorization divides by each prime at most once, so the multiplicity of a repeated rank is always 1.

VERIFIED REPAIR

Keep dividing while the prime still divides the product and count the divisions.

Unsuccessful approach: Dividing by p squared then p caps multiplicity at two, so trips and quads are misread.

Case contract

Input: five cards "Rs" (rank may be written "10" for ten; suits ignored, repeated ranks allowed up to four). Each rank maps to a distinct prime (2 for deuce ... 41 for ace); the product of the five primes is factored back into rank multiplicities, and the sorted multiplicity pattern names the rank shape: four of a kind, full house, three of a kind, two pair, one pair or high card.

Why this case matters

Prime-product hashing is how table-driven evaluators identify non-flush rank multisets.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    R='23456789TJQKA'
    P=[2,3,5,7,11,13,17,19,23,29,31,37,41]
    prod=1
    for c in x:
        prod*=P[R.index('T' if c[:-1]=='10' else c[:-1])]
    exps=[]
    for p in P:
        e=0
        if prod%p==0:
            prod//=p
            e+=1
        if e: exps.append(e)
    exps.sort(reverse=True)
    names={(4,1):'four of a kind',(3,2):'full house',(3,1,1):'three of a kind',(2,2,1):'two pair',(2,1,1,1):'one pair',(1,1,1,1,1):'high card'}
    return names[tuple(exps)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('ace high', ['Ah', 'Kd', '9c', '7s', '4h'], 'high card'),
  ('pair of aces', ['Ah', 'Ad', '9c', '7s', '4h'], 'one pair'),
  ('ace with three', ['Ah', '3d', '9c', '7s', '4h'], 'high card'),
  ('ace with king', ['Ah', 'Kd', 'Qc', '7s', '4h'], 'high card'),
  ('ace with seven pair', ['Ah', '7d', '7c', '2s', '4h'], 'one pair'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('deuce and ace', ['2h', 'Ad', '8c', '6s', '4h'], 'high card')],
 [('pair of aces', ['Ah', 'Ad', '9c', '7s', '4h'], 'one pair'),
  ('ace with seven pair', ['Ah', '7d', '7c', '2s', '4h'], 'one pair'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('trips deuces', ['2h', '2d', '2c', 'Ks', 'Qh'], 'three of a kind'),
  ('deuce and ace', ['2h', 'Ad', '8c', '6s', '4h'], 'high card'),
  ('high card low', ['2h', '3d', '5c', '7s', '9h'], 'high card'),
  ('ten token with ace', ['10h', 'Ad', '8c', '6s', '4h'], 'high card')],
 [('pair of aces', ['Ah', 'Ad', '9c', '7s', '4h'], 'one pair'),
  ('ace with seven pair', ['Ah', '7d', '7c', '2s', '4h'], 'one pair'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('two pair', ['Jh', 'Jd', '4c', '4s', 'Ah'], 'two pair'),
  ('trips deuces', ['2h', '2d', '2c', 'Ks', 'Qh'], 'three of a kind'),
  ('pair of deuces', ['2h', '2d', '5c', '7s', '9h'], 'one pair'),
  ('ten token full house', ['10h', '10d', 'Tc', '6s', '6h'], 'full house')],
 [('ace high', ['Ah', 'Kd', '9c', '7s', '4h'], 'high card'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('two pair', ['Jh', 'Jd', '4c', '4s', 'Ah'], 'two pair'),
  ('trips deuces', ['2h', '2d', '2c', 'Ks', 'Qh'], 'three of a kind'),
  ('pair of deuces', ['2h', '2d', '5c', '7s', '9h'], 'one pair'),
  ('ten token pair', ['10h', 'Td', '8c', '6s', '4h'], 'one pair'),
  ('ten token full house', ['10h', '10d', 'Tc', '6s', '6h'], 'full house')],
 [('ace high', ['Ah', 'Kd', '9c', '7s', '4h'], 'high card'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('two pair', ['Jh', 'Jd', '4c', '4s', 'Ah'], 'two pair'),
  ('trips deuces', ['2h', '2d', '2c', 'Ks', 'Qh'], 'three of a kind'),
  ('pair of deuces', ['2h', '2d', '5c', '7s', '9h'], 'one pair'),
  ('ten token pair', ['10h', 'Td', '8c', '6s', '4h'], 'one pair'),
  ('ten token full house', ['10h', '10d', 'Tc', '6s', '6h'], 'full house')]]
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 high	`high card`	`high card`	Passed
pair of aces	`error:KeyError`	`one pair`	Failed
ace with three	`high card`	`high card`	Passed
ace with king	`high card`	`high card`	Passed
ace with seven pair	`error:KeyError`	`one pair`	Failed
full house	`error:KeyError`	`full house`	Failed
quads	`error:KeyError`	`four of a kind`	Failed
deuce and ace	`high card`	`high card`	Passed

SHA-256 / fcb25f197ca058238122b506234888214a3e9b7f154633fc45ebbec45c9001ec

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    R='23456789TJQKA'
    P=[2,3,5,7,11,13,17,19,23,29,31,37,41]
    prod=1
    for c in x:
        prod*=P[R.index('T' if c[:-1]=='10' else c[:-1])]
    exps=[]
    for p in P:
        e=0
        while prod%(p*p)==0:
            prod//=p*p
            e+=2
        if prod%p==0:
            prod//=p
            e+=1
        e=min(e,2)
        if e: exps.append(e)
    exps.sort(reverse=True)
    names={(4,1):'four of a kind',(3,2):'full house',(3,1,1):'three of a kind',(2,2,1):'two pair',(2,1,1,1):'one pair',(1,1,1,1,1):'high card'}
    return names[tuple(exps)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('ace high', ['Ah', 'Kd', '9c', '7s', '4h'], 'high card'),
  ('pair of aces', ['Ah', 'Ad', '9c', '7s', '4h'], 'one pair'),
  ('ace with three', ['Ah', '3d', '9c', '7s', '4h'], 'high card'),
  ('ace with king', ['Ah', 'Kd', 'Qc', '7s', '4h'], 'high card'),
  ('ace with seven pair', ['Ah', '7d', '7c', '2s', '4h'], 'one pair'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('deuce and ace', ['2h', 'Ad', '8c', '6s', '4h'], 'high card')],
 [('pair of aces', ['Ah', 'Ad', '9c', '7s', '4h'], 'one pair'),
  ('ace with seven pair', ['Ah', '7d', '7c', '2s', '4h'], 'one pair'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('trips deuces', ['2h', '2d', '2c', 'Ks', 'Qh'], 'three of a kind'),
  ('deuce and ace', ['2h', 'Ad', '8c', '6s', '4h'], 'high card'),
  ('high card low', ['2h', '3d', '5c', '7s', '9h'], 'high card'),
  ('ten token with ace', ['10h', 'Ad', '8c', '6s', '4h'], 'high card')],
 [('pair of aces', ['Ah', 'Ad', '9c', '7s', '4h'], 'one pair'),
  ('ace with seven pair', ['Ah', '7d', '7c', '2s', '4h'], 'one pair'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('two pair', ['Jh', 'Jd', '4c', '4s', 'Ah'], 'two pair'),
  ('trips deuces', ['2h', '2d', '2c', 'Ks', 'Qh'], 'three of a kind'),
  ('pair of deuces', ['2h', '2d', '5c', '7s', '9h'], 'one pair'),
  ('ten token full house', ['10h', '10d', 'Tc', '6s', '6h'], 'full house')],
 [('ace high', ['Ah', 'Kd', '9c', '7s', '4h'], 'high card'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('two pair', ['Jh', 'Jd', '4c', '4s', 'Ah'], 'two pair'),
  ('trips deuces', ['2h', '2d', '2c', 'Ks', 'Qh'], 'three of a kind'),
  ('pair of deuces', ['2h', '2d', '5c', '7s', '9h'], 'one pair'),
  ('ten token pair', ['10h', 'Td', '8c', '6s', '4h'], 'one pair'),
  ('ten token full house', ['10h', '10d', 'Tc', '6s', '6h'], 'full house')],
 [('ace high', ['Ah', 'Kd', '9c', '7s', '4h'], 'high card'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('two pair', ['Jh', 'Jd', '4c', '4s', 'Ah'], 'two pair'),
  ('trips deuces', ['2h', '2d', '2c', 'Ks', 'Qh'], 'three of a kind'),
  ('pair of deuces', ['2h', '2d', '5c', '7s', '9h'], 'one pair'),
  ('ten token pair', ['10h', 'Td', '8c', '6s', '4h'], 'one pair'),
  ('ten token full house', ['10h', '10d', 'Tc', '6s', '6h'], 'full house')]]
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 high	`high card`	`high card`	Passed
pair of aces	`one pair`	`one pair`	Passed
ace with three	`high card`	`high card`	Passed
ace with king	`high card`	`high card`	Passed
ace with seven pair	`one pair`	`one pair`	Passed
full house	`error:KeyError`	`full house`	Failed
quads	`error:KeyError`	`four of a kind`	Failed
deuce and ace	`high card`	`high card`	Passed

SHA-256 / 871f8130908b6ce5755eaa92879e50e7849e77f143314a76ae2ecdc65f03dc39

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    R='23456789TJQKA'
    P=[2,3,5,7,11,13,17,19,23,29,31,37,41]
    prod=1
    for c in x:
        prod*=P[R.index('T' if c[:-1]=='10' else c[:-1])]
    exps=[]
    for p in P:
        e=0
        while prod%p==0:
            prod//=p
            e+=1
        if e: exps.append(e)
    exps.sort(reverse=True)
    names={(4,1):'four of a kind',(3,2):'full house',(3,1,1):'three of a kind',(2,2,1):'two pair',(2,1,1,1):'one pair',(1,1,1,1,1):'high card'}
    return names[tuple(exps)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('ace high', ['Ah', 'Kd', '9c', '7s', '4h'], 'high card'),
  ('pair of aces', ['Ah', 'Ad', '9c', '7s', '4h'], 'one pair'),
  ('ace with three', ['Ah', '3d', '9c', '7s', '4h'], 'high card'),
  ('ace with king', ['Ah', 'Kd', 'Qc', '7s', '4h'], 'high card'),
  ('ace with seven pair', ['Ah', '7d', '7c', '2s', '4h'], 'one pair'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('deuce and ace', ['2h', 'Ad', '8c', '6s', '4h'], 'high card')],
 [('pair of aces', ['Ah', 'Ad', '9c', '7s', '4h'], 'one pair'),
  ('ace with seven pair', ['Ah', '7d', '7c', '2s', '4h'], 'one pair'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('trips deuces', ['2h', '2d', '2c', 'Ks', 'Qh'], 'three of a kind'),
  ('deuce and ace', ['2h', 'Ad', '8c', '6s', '4h'], 'high card'),
  ('high card low', ['2h', '3d', '5c', '7s', '9h'], 'high card'),
  ('ten token with ace', ['10h', 'Ad', '8c', '6s', '4h'], 'high card')],
 [('pair of aces', ['Ah', 'Ad', '9c', '7s', '4h'], 'one pair'),
  ('ace with seven pair', ['Ah', '7d', '7c', '2s', '4h'], 'one pair'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('two pair', ['Jh', 'Jd', '4c', '4s', 'Ah'], 'two pair'),
  ('trips deuces', ['2h', '2d', '2c', 'Ks', 'Qh'], 'three of a kind'),
  ('pair of deuces', ['2h', '2d', '5c', '7s', '9h'], 'one pair'),
  ('ten token full house', ['10h', '10d', 'Tc', '6s', '6h'], 'full house')],
 [('ace high', ['Ah', 'Kd', '9c', '7s', '4h'], 'high card'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('two pair', ['Jh', 'Jd', '4c', '4s', 'Ah'], 'two pair'),
  ('trips deuces', ['2h', '2d', '2c', 'Ks', 'Qh'], 'three of a kind'),
  ('pair of deuces', ['2h', '2d', '5c', '7s', '9h'], 'one pair'),
  ('ten token pair', ['10h', 'Td', '8c', '6s', '4h'], 'one pair'),
  ('ten token full house', ['10h', '10d', 'Tc', '6s', '6h'], 'full house')],
 [('ace high', ['Ah', 'Kd', '9c', '7s', '4h'], 'high card'),
  ('full house', ['Kh', 'Kd', '2c', '2s', '2h'], 'full house'),
  ('quads', ['9h', '9d', '9c', '9s', '2h'], 'four of a kind'),
  ('two pair', ['Jh', 'Jd', '4c', '4s', 'Ah'], 'two pair'),
  ('trips deuces', ['2h', '2d', '2c', 'Ks', 'Qh'], 'three of a kind'),
  ('pair of deuces', ['2h', '2d', '5c', '7s', '9h'], 'one pair'),
  ('ten token pair', ['10h', 'Td', '8c', '6s', '4h'], 'one pair'),
  ('ten token full house', ['10h', '10d', 'Tc', '6s', '6h'], 'full house')]]
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 high	`high card`	`high card`	Passed
pair of aces	`one pair`	`one pair`	Passed
ace with three	`high card`	`high card`	Passed
ace with king	`high card`	`high card`	Passed
ace with seven pair	`one pair`	`one pair`	Passed
full house	`full house`	`full house`	Passed
quads	`four of a kind`	`four of a kind`	Passed
deuce and ace	`high card`	`high card`	Passed

SHA-256 / c319ad56b6beffe42a2c4cbc8403b557baebc1ce8e99d0b4ad11e96495fb7639

Verification & scope

A deterministic toy model with an explicitly stated contract; card strings are rank+suit (for example "As", "Td", "10h"); 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 2026-09-29T14:50:07.660318+00:00.

Case digest / 46de30f0e201eb0bc3a877966792377e654c7657ed94cfe397c45a725edbf28e