FA-84411 / Betting odds conversion / Open access
Bookmaker margin reported as the overround · case 01
The margin column repeats the overround (4.71 instead of 4.50 for 1.91/1.91).
ROOT CAUSE
The margin is computed as book - 1 instead of 1 - 1/book.
THE FAILURE
The margin is computed as book - 1 instead of 1 - 1/book.
Unsuccessful approach: Dividing the overround by the number of outcomes gives a per-outcome figure, not the margin.
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 = (book - 1) * 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: margin versus overround',
(['2.23', '1.91', '5.75'],),
['14.59', '12.73', ['2.56', '2.19', '6.59']]),
('variant scenario 1',
(['5.06', '2.28', '4.51', '3.78'],),
['12.25', '10.91', ['5.68', '2.56', '5.06', '4.24']]),
('variant scenario 2', (['1.14', '3.87'],), ['13.56', '11.94', ['1.29', '4.39']])],
[('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: margin versus overround',
(['3.85', '3.37', '2.18'],),
['1.52', '1.50', ['3.91', '3.42', '2.21']]),
('variant scenario 1', (['1.99', '2.86', '3.67'],), ['12.46', '11.08', ['2.24', '3.22', '4.13']]),
('variant scenario 2',
(['2.92', '8.98', '1.89'],),
['-1.71', '-1.74', ['2.87', '8.83', '1.86']])],
[('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: margin versus overround',
(['3.10', '8.19', '3.32', '3.05'],),
['7.38', '6.87', ['3.33', '8.79', '3.56', '3.27']]),
('variant scenario 1',
(['2.51', '4.38', '4.81', '3.77'],),
['9.99', '9.08', ['2.76', '4.82', '5.29', '4.15']]),
('variant scenario 2', (['2.41', '2.33', '4.15'],), ['8.51', '7.84', ['2.62', '2.53', '4.50']])],
[('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: margin versus overround',
(['3.20', '3.70', '2.55', '7.93'],),
['10.10', '9.18', ['3.52', '4.07', '2.81', '8.73']]),
('variant scenario 1', (['1.21', '4.22'],), ['6.34', '5.96', ['1.29', '4.49']]),
('variant scenario 2',
(['19.30', '2.55', '6.75', '2.08'],),
['7.29', '6.79', ['20.71', '2.74', '7.24', '2.23']])],
[('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: margin versus overround', (['4.37', '1.19'],), ['6.92', '6.47', ['4.67', '1.27']]),
('variant scenario 1', (['1.29', '4.02'],), ['2.40', '2.34', ['1.32', '4.12']]),
('variant scenario 2', (['4.42', '2.56', '2.27'],), ['5.74', '5.43', ['4.67', '2.71', '2.40']])]]
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', '4.71', ['2.00', '2.00']] | ['4.71', '4.50', ['2.00', '2.00']] | Failed |
| boundary three-way | ['5.73', '5.73', ['2.64', '3.38', '3.07']] | ['5.73', '5.42', ['2.64', '3.38', '3.07']] | Failed |
| boundary no-profit price | invalid | invalid | Passed |
| regression: margin versus overround | ['14.59', '14.59', ['2.56', '2.19', '6.59']] | ['14.59', '12.73', ['2.56', '2.19', '6.59']] | Failed |
| variant scenario 1 | ['12.25', '12.25', ['5.68', '2.56', '5.06', '4.24']] | ['12.25', '10.91', ['5.68', '2.56', '5.06', '4.24']] | Failed |
| variant scenario 2 | ['13.56', '13.56', ['1.29', '4.39']] | ['13.56', '11.94', ['1.29', '4.39']] | Failed |
SHA-256 / e53179ba357dcbab17f4e559a846a60d48bc9c045b2157ddb51f5ebd71b54fe9
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 = (book - 1) / len(ds) * 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: margin versus overround',
(['2.23', '1.91', '5.75'],),
['14.59', '12.73', ['2.56', '2.19', '6.59']]),
('variant scenario 1',
(['5.06', '2.28', '4.51', '3.78'],),
['12.25', '10.91', ['5.68', '2.56', '5.06', '4.24']]),
('variant scenario 2', (['1.14', '3.87'],), ['13.56', '11.94', ['1.29', '4.39']])],
[('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: margin versus overround',
(['3.85', '3.37', '2.18'],),
['1.52', '1.50', ['3.91', '3.42', '2.21']]),
('variant scenario 1', (['1.99', '2.86', '3.67'],), ['12.46', '11.08', ['2.24', '3.22', '4.13']]),
('variant scenario 2',
(['2.92', '8.98', '1.89'],),
['-1.71', '-1.74', ['2.87', '8.83', '1.86']])],
[('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: margin versus overround',
(['3.10', '8.19', '3.32', '3.05'],),
['7.38', '6.87', ['3.33', '8.79', '3.56', '3.27']]),
('variant scenario 1',
(['2.51', '4.38', '4.81', '3.77'],),
['9.99', '9.08', ['2.76', '4.82', '5.29', '4.15']]),
('variant scenario 2', (['2.41', '2.33', '4.15'],), ['8.51', '7.84', ['2.62', '2.53', '4.50']])],
[('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: margin versus overround',
(['3.20', '3.70', '2.55', '7.93'],),
['10.10', '9.18', ['3.52', '4.07', '2.81', '8.73']]),
('variant scenario 1', (['1.21', '4.22'],), ['6.34', '5.96', ['1.29', '4.49']]),
('variant scenario 2',
(['19.30', '2.55', '6.75', '2.08'],),
['7.29', '6.79', ['20.71', '2.74', '7.24', '2.23']])],
[('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: margin versus overround', (['4.37', '1.19'],), ['6.92', '6.47', ['4.67', '1.27']]),
('variant scenario 1', (['1.29', '4.02'],), ['2.40', '2.34', ['1.32', '4.12']]),
('variant scenario 2', (['4.42', '2.56', '2.27'],), ['5.74', '5.43', ['4.67', '2.71', '2.40']])]]
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', '2.36', ['2.00', '2.00']] | ['4.71', '4.50', ['2.00', '2.00']] | Failed |
| boundary three-way | ['5.73', '1.91', ['2.64', '3.38', '3.07']] | ['5.73', '5.42', ['2.64', '3.38', '3.07']] | Failed |
| boundary no-profit price | invalid | invalid | Passed |
| regression: margin versus overround | ['14.59', '4.86', ['2.56', '2.19', '6.59']] | ['14.59', '12.73', ['2.56', '2.19', '6.59']] | Failed |
| variant scenario 1 | ['12.25', '3.06', ['5.68', '2.56', '5.06', '4.24']] | ['12.25', '10.91', ['5.68', '2.56', '5.06', '4.24']] | Failed |
| variant scenario 2 | ['13.56', '6.78', ['1.29', '4.39']] | ['13.56', '11.94', ['1.29', '4.39']] | Failed |
SHA-256 / 52d40802950a41e3040733aeeffa40330fe843e45073159d6ae219d669a1ba3e
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Sign in to the archive ↗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 2026-09-29T14:50:30.523871+00:00.
Case digest / 38477139a36fcaaaf71d58ebd1e9d756464257edb9dae2911ed0e1dfb1f59313