FA-84716 / Betting odds conversion / Open access

Breakage rounds dividends to the nearest or next dime · case 01

A 2.8267 dividend is paid as 2.90 or rounded to 2.80 only sometimes.

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

ROOT CAUSE

Breakage rounds to the nearest 10 cents.

VERIFIED REPAIR

Always break down to the 10-cent step below.

Unsuccessful approach: Rounding up pays out money the pool does not have.

Case contract

Pari-mutuel win dividend per unit stake. The net pool is pool * (100 - takeout_pct) / 100; with a dead heat it is split equally among the winning runners. Each runner's dividend is its share divided by the stakes on it, broken down to the 10-cent step below (breakage), with a minimum of 1.10. A winner with no stakes gets None. Return dividends as "D.D0" strings in winners order.

Why this case matters

Tote operators compute dividends with takeout, breakage and minimum-dividend rules.

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(pool_cents, takeout_pct, winners):
    net = Fraction(pool_cents) * (100 - Fraction(takeout_pct)) / 100
    share = net / len(winners)
    out = []
    for s in winners:
        if s == 0:
            out.append(None)
            continue
        dimes = math.floor(share / s * 10 + Fraction(1, 2))
        dimes = max(dimes, 11)
        out.append('%d.%d0' % (dimes // 10, dimes % 10))
    return out
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 single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (50000, '15', [11867]), ['3.50']),
  ('variant scenario 1', (50000, '20', [47992]), ['1.10']),
  ('variant scenario 2', (100000, '20', [75618]), ['1.10'])],
 [('control single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (250000, '16', [62527]), ['3.30']),
  ('variant scenario 1', (250000, '0', [333]), ['750.70']),
  ('variant scenario 2', (50000, '16', [38443]), ['1.10'])],
 [('control single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (100000, '0', [70424]), ['1.40']),
  ('regression: breakage direction', (1234500, '16', [155805]), ['6.60']),
  ('variant scenario 1', (100000, '15', [55625, 0]), ['1.10', None]),
  ('variant scenario 2', (50000, '15', [6485]), ['6.50'])],
 [('control single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (250000, '0', [241772, 1500]), ['1.10', '83.30']),
  ('regression: breakage direction', (50000, '16', [0, 5094, 3128]), [None, '2.70', '4.40']),
  ('variant scenario 1', (250000, '16', [250000]), ['1.10']),
  ('variant scenario 2', (50000, '20', [36563]), ['1.10'])],
 [('control single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (1234500, '20', [896467]), ['1.10']),
  ('regression: breakage direction', (50000, '20', [21393]), ['1.80']),
  ('variant scenario 1', (1234500, '15', [40000, 617250, 518407]), ['8.70', '1.10', '1.10']),
  ('variant scenario 2', (100000, '15', [40000]), ['2.10'])]]
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 single winner	`['3.40']`	`['3.40']`	Passed
boundary breakage down	`['2.80']`	`['2.80']`	Passed
boundary minimum dividend	`['1.10']`	`['1.10']`	Passed
boundary dead heat split	`['4.00', '1.10']`	`['4.00', '1.10']`	Passed
control unbacked winner	`[None]`	`[None]`	Passed
regression: breakage direction	`['3.60']`	`['3.50']`	Failed
variant scenario 1	`['1.10']`	`['1.10']`	Passed
variant scenario 2	`['1.10']`	`['1.10']`	Passed

SHA-256 / f47e7fe600dd91e544c5bac85b4b5854188cac10290e59a30862ce4548268427

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(pool_cents, takeout_pct, winners):
    net = Fraction(pool_cents) * (100 - Fraction(takeout_pct)) / 100
    share = net / len(winners)
    out = []
    for s in winners:
        if s == 0:
            out.append(None)
            continue
        dimes = math.ceil(share / s * 10)
        dimes = max(dimes, 11)
        out.append('%d.%d0' % (dimes // 10, dimes % 10))
    return out
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 single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (50000, '15', [11867]), ['3.50']),
  ('variant scenario 1', (50000, '20', [47992]), ['1.10']),
  ('variant scenario 2', (100000, '20', [75618]), ['1.10'])],
 [('control single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (250000, '16', [62527]), ['3.30']),
  ('variant scenario 1', (250000, '0', [333]), ['750.70']),
  ('variant scenario 2', (50000, '16', [38443]), ['1.10'])],
 [('control single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (100000, '0', [70424]), ['1.40']),
  ('regression: breakage direction', (1234500, '16', [155805]), ['6.60']),
  ('variant scenario 1', (100000, '15', [55625, 0]), ['1.10', None]),
  ('variant scenario 2', (50000, '15', [6485]), ['6.50'])],
 [('control single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (250000, '0', [241772, 1500]), ['1.10', '83.30']),
  ('regression: breakage direction', (50000, '16', [0, 5094, 3128]), [None, '2.70', '4.40']),
  ('variant scenario 1', (250000, '16', [250000]), ['1.10']),
  ('variant scenario 2', (50000, '20', [36563]), ['1.10'])],
 [('control single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (1234500, '20', [896467]), ['1.10']),
  ('regression: breakage direction', (50000, '20', [21393]), ['1.80']),
  ('variant scenario 1', (1234500, '15', [40000, 617250, 518407]), ['8.70', '1.10', '1.10']),
  ('variant scenario 2', (100000, '15', [40000]), ['2.10'])]]
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 single winner	`['3.40']`	`['3.40']`	Passed
boundary breakage down	`['2.80']`	`['2.80']`	Passed
boundary minimum dividend	`['1.10']`	`['1.10']`	Passed
boundary dead heat split	`['4.00', '1.10']`	`['4.00', '1.10']`	Passed
control unbacked winner	`[None]`	`[None]`	Passed
regression: breakage direction	`['3.60']`	`['3.50']`	Failed
variant scenario 1	`['1.10']`	`['1.10']`	Passed
variant scenario 2	`['1.10']`	`['1.10']`	Passed

SHA-256 / 3079de4b8b57775424b91379ee69e64d2f20a9b26521dea99f913aa3f0bfcfb7

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(pool_cents, takeout_pct, winners):
    net = Fraction(pool_cents) * (100 - Fraction(takeout_pct)) / 100
    share = net / len(winners)
    out = []
    for s in winners:
        if s == 0:
            out.append(None)
            continue
        dimes = math.floor(share / s * 10)
        dimes = max(dimes, 11)
        out.append('%d.%d0' % (dimes // 10, dimes % 10))
    return out
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 single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (50000, '15', [11867]), ['3.50']),
  ('variant scenario 1', (50000, '20', [47992]), ['1.10']),
  ('variant scenario 2', (100000, '20', [75618]), ['1.10'])],
 [('control single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (250000, '16', [62527]), ['3.30']),
  ('variant scenario 1', (250000, '0', [333]), ['750.70']),
  ('variant scenario 2', (50000, '16', [38443]), ['1.10'])],
 [('control single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (100000, '0', [70424]), ['1.40']),
  ('regression: breakage direction', (1234500, '16', [155805]), ['6.60']),
  ('variant scenario 1', (100000, '15', [55625, 0]), ['1.10', None]),
  ('variant scenario 2', (50000, '15', [6485]), ['6.50'])],
 [('control single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (250000, '0', [241772, 1500]), ['1.10', '83.30']),
  ('regression: breakage direction', (50000, '16', [0, 5094, 3128]), [None, '2.70', '4.40']),
  ('variant scenario 1', (250000, '16', [250000]), ['1.10']),
  ('variant scenario 2', (50000, '20', [36563]), ['1.10'])],
 [('control single winner', (100000, '15', [25000]), ['3.40']),
  ('boundary breakage down', (100000, '16', [30000]), ['2.80']),
  ('boundary minimum dividend', (100000, '20', [90000]), ['1.10']),
  ('boundary dead heat split', (100000, '20', [10000, 40000]), ['4.00', '1.10']),
  ('control unbacked winner', (100000, '15', [0]), [None]),
  ('regression: breakage direction', (1234500, '20', [896467]), ['1.10']),
  ('regression: breakage direction', (50000, '20', [21393]), ['1.80']),
  ('variant scenario 1', (1234500, '15', [40000, 617250, 518407]), ['8.70', '1.10', '1.10']),
  ('variant scenario 2', (100000, '15', [40000]), ['2.10'])]]
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 single winner	`['3.40']`	`['3.40']`	Passed
boundary breakage down	`['2.80']`	`['2.80']`	Passed
boundary minimum dividend	`['1.10']`	`['1.10']`	Passed
boundary dead heat split	`['4.00', '1.10']`	`['4.00', '1.10']`	Passed
control unbacked winner	`[None]`	`[None]`	Passed
regression: breakage direction	`['3.50']`	`['3.50']`	Passed
variant scenario 1	`['1.10']`	`['1.10']`	Passed
variant scenario 2	`['1.10']`	`['1.10']`	Passed

SHA-256 / 1491fbc9351bcaaba753d8c8332f097cfe4b383ea015b3e60023e32f62bbeb87

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 2026-09-29T14:50:33.684929+00:00.

Case digest / 07e6cc20656ef4f4d7a6f313bf6bcbda1ae35dd1c71b559365a37b8bbe95d4af