FA-84416 / Betting odds conversion / Open access

Fair prices shortened instead of lengthened · case 01

No-vig prices come out shorter than the quoted prices.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Fair prices divide by the book instead of multiplying.

VERIFIED REPAIR

Multiply each price by the book sum.

Unsuccessful approach: Adding the overround as a flat amount is the additive method, not proportional removal.

Case contract

Market book analysis for decimal prices (strings, each > 1, else "invalid"). Implied probability is 1/d; book = sum of implied probabilities. Return [overround percent (book - 1) * 100, bookmaker margin percent (1 - 1/book) * 100, fair prices d * book for proportional margin removal], every number rounded half up to two decimals (negative values are rounded toward +infinity at the half) and formatted with two decimals.

Why this case matters

Trading tools report overround and margin separately and derive no-vig fair prices.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(prices):
    def fmt(x):
        c = math.floor(x * 100 + Fraction(1, 2))
        sign = '-' if c < 0 else ''
        c = abs(c)
        return sign + '%d.%02d' % (c // 100, c % 100)
    ds = [Fraction(p) for p in prices]
    if any(d <= 1 for d in ds):
        return 'invalid'
    book = sum(1 / d for d in ds)
    over = (book - 1) * 100
    margin = (1 - 1 / book) * 100
    fair = [fmt(d / book) for d in ds]
    return [fmt(over), fmt(margin), fair]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
def run(args):
    try:
        return solve(*args)
    except Exception as exc:
        return 'raised ' + type(exc).__name__
cases = [[('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction',
   (['4.28', '3.78', '1.86'],),
   ['3.58', '3.46', ['4.43', '3.92', '1.93']]),
  ('variant scenario 1',
   (['2.38', '9.10', '1.69'],),
   ['12.18', '10.86', ['2.67', '10.21', '1.90']]),
  ('variant scenario 2', (['3.25', '2.80', '2.78'],), ['2.45', '2.40', ['3.33', '2.87', '2.85']])],
 [('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction',
   (['4.98', '3.07', '3.86', '5.09'],),
   ['-1.79', '-1.83', ['4.89', '3.01', '3.79', '5.00']]),
  ('variant scenario 1', (['2.65', '9.18', '1.83'],), ['3.27', '3.17', ['2.74', '9.48', '1.89']]),
  ('variant scenario 2', (['2.11', '4.77', '2.91'],), ['2.72', '2.65', ['2.17', '4.90', '2.99']])],
 [('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction', (['1.36', '3.90'],), ['-0.83', '-0.84', ['1.35', '3.87']]),
  ('variant scenario 1', (['1.12', '6.59'],), ['4.46', '4.27', ['1.17', '6.88']]),
  ('variant scenario 2', (['1.86', '1.65'],), ['14.37', '12.56', ['2.13', '1.89']])],
 [('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction', (['1.99', '1.97'],), ['1.01', '1.00', ['2.01', '1.99']]),
  ('variant scenario 1', (['2.21', '2.07', '7.52'],), ['6.86', '6.42', ['2.36', '2.21', '8.04']]),
  ('variant scenario 2', (['1.37', '3.08'],), ['5.46', '5.18', ['1.44', '3.25']])],
 [('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction',
   (['1.67', '6.50', '3.71'],),
   ['2.22', '2.17', ['1.71', '6.64', '3.79']]),
  ('variant scenario 1', (['5.20', '1.15'],), ['6.19', '5.83', ['5.52', '1.22']]),
  ('variant scenario 2',
   (['7.11', '3.30', '9.10', '2.32'],),
   ['-1.54', '-1.56', ['7.00', '3.25', '8.96', '2.28']])]]
for label, args, expected in cases[N - 1]:
    check(label, run(args), 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
control fair coin	`['0.00', '0.00', ['2.00', '2.00']]`	`['0.00', '0.00', ['2.00', '2.00']]`	Passed
control standard juice	`['4.71', '4.50', ['1.82', '1.82']]`	`['4.71', '4.50', ['2.00', '2.00']]`	Failed
boundary three-way	`['5.73', '5.42', ['2.36', '3.03', '2.74']]`	`['5.73', '5.42', ['2.64', '3.38', '3.07']]`	Failed
boundary no-profit price	`invalid`	`invalid`	Passed
regression: fair price direction	`['3.58', '3.46', ['4.13', '3.65', '1.80']]`	`['3.58', '3.46', ['4.43', '3.92', '1.93']]`	Failed
variant scenario 1	`['12.18', '10.86', ['2.12', '8.11', '1.51']]`	`['12.18', '10.86', ['2.67', '10.21', '1.90']]`	Failed
variant scenario 2	`['2.45', '2.40', ['3.17', '2.73', '2.71']]`	`['2.45', '2.40', ['3.33', '2.87', '2.85']]`	Failed

SHA-256 / a0c4f28a22862f0a4962b90db32ff8391d250457b393d0cc761f15b8c6e67cdd

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(prices):
    def fmt(x):
        c = math.floor(x * 100 + Fraction(1, 2))
        sign = '-' if c < 0 else ''
        c = abs(c)
        return sign + '%d.%02d' % (c // 100, c % 100)
    ds = [Fraction(p) for p in prices]
    if any(d <= 1 for d in ds):
        return 'invalid'
    book = sum(1 / d for d in ds)
    over = (book - 1) * 100
    margin = (1 - 1 / book) * 100
    fair = [fmt(d + (book - 1)) for d in ds]
    return [fmt(over), fmt(margin), fair]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
def run(args):
    try:
        return solve(*args)
    except Exception as exc:
        return 'raised ' + type(exc).__name__
cases = [[('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction',
   (['4.28', '3.78', '1.86'],),
   ['3.58', '3.46', ['4.43', '3.92', '1.93']]),
  ('variant scenario 1',
   (['2.38', '9.10', '1.69'],),
   ['12.18', '10.86', ['2.67', '10.21', '1.90']]),
  ('variant scenario 2', (['3.25', '2.80', '2.78'],), ['2.45', '2.40', ['3.33', '2.87', '2.85']])],
 [('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction',
   (['4.98', '3.07', '3.86', '5.09'],),
   ['-1.79', '-1.83', ['4.89', '3.01', '3.79', '5.00']]),
  ('variant scenario 1', (['2.65', '9.18', '1.83'],), ['3.27', '3.17', ['2.74', '9.48', '1.89']]),
  ('variant scenario 2', (['2.11', '4.77', '2.91'],), ['2.72', '2.65', ['2.17', '4.90', '2.99']])],
 [('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction', (['1.36', '3.90'],), ['-0.83', '-0.84', ['1.35', '3.87']]),
  ('variant scenario 1', (['1.12', '6.59'],), ['4.46', '4.27', ['1.17', '6.88']]),
  ('variant scenario 2', (['1.86', '1.65'],), ['14.37', '12.56', ['2.13', '1.89']])],
 [('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction', (['1.99', '1.97'],), ['1.01', '1.00', ['2.01', '1.99']]),
  ('variant scenario 1', (['2.21', '2.07', '7.52'],), ['6.86', '6.42', ['2.36', '2.21', '8.04']]),
  ('variant scenario 2', (['1.37', '3.08'],), ['5.46', '5.18', ['1.44', '3.25']])],
 [('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction',
   (['1.67', '6.50', '3.71'],),
   ['2.22', '2.17', ['1.71', '6.64', '3.79']]),
  ('variant scenario 1', (['5.20', '1.15'],), ['6.19', '5.83', ['5.52', '1.22']]),
  ('variant scenario 2',
   (['7.11', '3.30', '9.10', '2.32'],),
   ['-1.54', '-1.56', ['7.00', '3.25', '8.96', '2.28']])]]
for label, args, expected in cases[N - 1]:
    check(label, run(args), 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
control fair coin	`['0.00', '0.00', ['2.00', '2.00']]`	`['0.00', '0.00', ['2.00', '2.00']]`	Passed
control standard juice	`['4.71', '4.50', ['1.96', '1.96']]`	`['4.71', '4.50', ['2.00', '2.00']]`	Failed
boundary three-way	`['5.73', '5.42', ['2.56', '3.26', '2.96']]`	`['5.73', '5.42', ['2.64', '3.38', '3.07']]`	Failed
boundary no-profit price	`invalid`	`invalid`	Passed
regression: fair price direction	`['3.58', '3.46', ['4.32', '3.82', '1.90']]`	`['3.58', '3.46', ['4.43', '3.92', '1.93']]`	Failed
variant scenario 1	`['12.18', '10.86', ['2.50', '9.22', '1.81']]`	`['12.18', '10.86', ['2.67', '10.21', '1.90']]`	Failed
variant scenario 2	`['2.45', '2.40', ['3.27', '2.82', '2.80']]`	`['2.45', '2.40', ['3.33', '2.87', '2.85']]`	Failed

SHA-256 / 53cab83fc5458a98fc6ed5f34c84e520a1b0bb1bd63a6bf29da9bd9e0a9e9e90

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(prices):
    def fmt(x):
        c = math.floor(x * 100 + Fraction(1, 2))
        sign = '-' if c < 0 else ''
        c = abs(c)
        return sign + '%d.%02d' % (c // 100, c % 100)
    ds = [Fraction(p) for p in prices]
    if any(d <= 1 for d in ds):
        return 'invalid'
    book = sum(1 / d for d in ds)
    over = (book - 1) * 100
    margin = (1 - 1 / book) * 100
    fair = [fmt(d * book) for d in ds]
    return [fmt(over), fmt(margin), fair]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
def run(args):
    try:
        return solve(*args)
    except Exception as exc:
        return 'raised ' + type(exc).__name__
cases = [[('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction',
   (['4.28', '3.78', '1.86'],),
   ['3.58', '3.46', ['4.43', '3.92', '1.93']]),
  ('variant scenario 1',
   (['2.38', '9.10', '1.69'],),
   ['12.18', '10.86', ['2.67', '10.21', '1.90']]),
  ('variant scenario 2', (['3.25', '2.80', '2.78'],), ['2.45', '2.40', ['3.33', '2.87', '2.85']])],
 [('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction',
   (['4.98', '3.07', '3.86', '5.09'],),
   ['-1.79', '-1.83', ['4.89', '3.01', '3.79', '5.00']]),
  ('variant scenario 1', (['2.65', '9.18', '1.83'],), ['3.27', '3.17', ['2.74', '9.48', '1.89']]),
  ('variant scenario 2', (['2.11', '4.77', '2.91'],), ['2.72', '2.65', ['2.17', '4.90', '2.99']])],
 [('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction', (['1.36', '3.90'],), ['-0.83', '-0.84', ['1.35', '3.87']]),
  ('variant scenario 1', (['1.12', '6.59'],), ['4.46', '4.27', ['1.17', '6.88']]),
  ('variant scenario 2', (['1.86', '1.65'],), ['14.37', '12.56', ['2.13', '1.89']])],
 [('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction', (['1.99', '1.97'],), ['1.01', '1.00', ['2.01', '1.99']]),
  ('variant scenario 1', (['2.21', '2.07', '7.52'],), ['6.86', '6.42', ['2.36', '2.21', '8.04']]),
  ('variant scenario 2', (['1.37', '3.08'],), ['5.46', '5.18', ['1.44', '3.25']])],
 [('control fair coin', (['2.00', '2.00'],), ['0.00', '0.00', ['2.00', '2.00']]),
  ('control standard juice', (['1.91', '1.91'],), ['4.71', '4.50', ['2.00', '2.00']]),
  ('boundary three-way', (['2.50', '3.20', '2.90'],), ['5.73', '5.42', ['2.64', '3.38', '3.07']]),
  ('boundary no-profit price', (['1.00', '5.00'],), 'invalid'),
  ('regression: fair price direction',
   (['1.67', '6.50', '3.71'],),
   ['2.22', '2.17', ['1.71', '6.64', '3.79']]),
  ('variant scenario 1', (['5.20', '1.15'],), ['6.19', '5.83', ['5.52', '1.22']]),
  ('variant scenario 2',
   (['7.11', '3.30', '9.10', '2.32'],),
   ['-1.54', '-1.56', ['7.00', '3.25', '8.96', '2.28']])]]
for label, args, expected in cases[N - 1]:
    check(label, run(args), 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
control fair coin	`['0.00', '0.00', ['2.00', '2.00']]`	`['0.00', '0.00', ['2.00', '2.00']]`	Passed
control standard juice	`['4.71', '4.50', ['2.00', '2.00']]`	`['4.71', '4.50', ['2.00', '2.00']]`	Passed
boundary three-way	`['5.73', '5.42', ['2.64', '3.38', '3.07']]`	`['5.73', '5.42', ['2.64', '3.38', '3.07']]`	Passed
boundary no-profit price	`invalid`	`invalid`	Passed
regression: fair price direction	`['3.58', '3.46', ['4.43', '3.92', '1.93']]`	`['3.58', '3.46', ['4.43', '3.92', '1.93']]`	Passed
variant scenario 1	`['12.18', '10.86', ['2.67', '10.21', '1.90']]`	`['12.18', '10.86', ['2.67', '10.21', '1.90']]`	Passed
variant scenario 2	`['2.45', '2.40', ['3.33', '2.87', '2.85']]`	`['2.45', '2.40', ['3.33', '2.87', '2.85']]`	Passed

SHA-256 / ed8eca29b0958383152ce63384da0957cd28fd6f58545c92a670bdb7b47e4b9d

Verification & scope

Stipulated, bounded toy contract stated in the contract field; not a claim of conformance with any operator, exchange or regulator rule set. 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 2026-09-29T14:50:30.541955+00:00.

Case digest / 3a9070e2672a80c871cb315ecf58a01d7699989b38b04ad20b94f8bc98acad90