FA-84556 / Betting odds conversion / Open access

Kelly computed with decimal odds instead of net odds · case 01

Stakes are sized far too large on every price.

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

ROOT CAUSE

b is taken as the decimal price rather than price - 1.

VERIFIED REPAIR

Use the net odds b = price - 1.

Unsuccessful approach: Using net odds in the numerator but the decimal price in the denominator still misstates the fraction.

Case contract

Kelly staking. With b = price - 1, p = prob and q = 1 - p, the full Kelly fraction is (b * p - q) / b, floored at 0 when the edge is not positive. The stake is bankroll * min(full Kelly * fraction, max_pct / 100), rounded down to a cent. Return [full Kelly fraction rounded half up to four decimals as a string, stake cents].

Why this case matters

Bankroll tools size stakes with fractional Kelly and a hard cap.

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(prob, price, fraction, bankroll_cents, max_pct):
    p = Fraction(prob)
    b = Fraction(price)
    q = 1 - p
    k = (b * p - q) / b
    if k < 0:
        k = Fraction(0)
    use = min(k * Fraction(fraction), Fraction(max_pct) / 100)
    stake = math.floor(bankroll_cents * use)
    r = math.floor(k * 10000 + Fraction(1, 2))
    return ['%d.%04d' % (r // 10000, r % 10000), stake]
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 even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.60', '3.27', '0.5', 50000, '10'), ['0.4238', 5000]),
  ('variant scenario 1', ('0.50', '1.73', '0.5', 100000, '5'), ['0.0000', 0]),
  ('variant scenario 2', ('0.60', '5.99', '1', 12345, '10'), ['0.5198', 1234])],
 [('control even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.80', '4.16', '0.25', 50000, '2'), ['0.7367', 1000]),
  ('variant scenario 1', ('0.60', '3.64', '0.5', 12345, '5'), ['0.4485', 617]),
  ('variant scenario 2', ('0.60', '2.09', '1', 12345, '2'), ['0.2330', 246])],
 [('control even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.60', '2.62', '0.25', 50000, '5'), ['0.3531', 2500]),
  ('variant scenario 1', ('0.60', '5.17', '0.25', 50000, '5'), ['0.5041', 2500]),
  ('variant scenario 2', ('0.57', '3.82', '0.5', 50000, '100'), ['0.4175', 10437])],
 [('control even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.55', '1.34', '1', 100000, '10'), ['0.0000', 0]),
  ('regression: net odds', ('0.57', '2.09', '0.5', 100000, '10'), ['0.1755', 8775]),
  ('variant scenario 1', ('0.60', '2.15', '1', 12345, '100'), ['0.2522', 3113]),
  ('variant scenario 2', ('0.48', '3.64', '0.5', 50000, '2'), ['0.2830', 1000])],
 [('control even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.55', '3.59', '0.25', 12345, '100'), ['0.3763', 1161]),
  ('variant scenario 1', ('0.60', '2.93', '0.25', 12345, '10'), ['0.3927', 1212]),
  ('variant scenario 2', ('0.78', '1.41', '0.25', 100000, '100'), ['0.2434', 6085])]]
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 even-money edge	`['0.3250', 32500]`	`['0.1000', 10000]`	Failed
control half kelly	`['0.3250', 16250]`	`['0.1000', 5000]`	Failed
boundary capped stake	`['0.4000', 5000]`	`['0.2000', 5000]`	Failed
boundary no edge	`['0.1000', 5000]`	`['0.0000', 0]`	Failed
control underdog edge	`['0.1250', 12500]`	`['0.0667', 6666]`	Failed
regression: net odds	`['0.4777', 5000]`	`['0.4238', 5000]`	Failed
variant scenario 1	`['0.2110', 5000]`	`['0.0000', 0]`	Failed
variant scenario 2	`['0.5332', 1234]`	`['0.5198', 1234]`	Failed

SHA-256 / 149e954f772927e42934efcc85c1f85e6989903261d84d7b385e985616b983d8

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(prob, price, fraction, bankroll_cents, max_pct):
    p = Fraction(prob)
    b = Fraction(price) - 1
    q = 1 - p
    k = (b * p - q) / (b + 1)
    if k < 0:
        k = Fraction(0)
    use = min(k * Fraction(fraction), Fraction(max_pct) / 100)
    stake = math.floor(bankroll_cents * use)
    r = math.floor(k * 10000 + Fraction(1, 2))
    return ['%d.%04d' % (r // 10000, r % 10000), stake]
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 even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.60', '3.27', '0.5', 50000, '10'), ['0.4238', 5000]),
  ('variant scenario 1', ('0.50', '1.73', '0.5', 100000, '5'), ['0.0000', 0]),
  ('variant scenario 2', ('0.60', '5.99', '1', 12345, '10'), ['0.5198', 1234])],
 [('control even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.80', '4.16', '0.25', 50000, '2'), ['0.7367', 1000]),
  ('variant scenario 1', ('0.60', '3.64', '0.5', 12345, '5'), ['0.4485', 617]),
  ('variant scenario 2', ('0.60', '2.09', '1', 12345, '2'), ['0.2330', 246])],
 [('control even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.60', '2.62', '0.25', 50000, '5'), ['0.3531', 2500]),
  ('variant scenario 1', ('0.60', '5.17', '0.25', 50000, '5'), ['0.5041', 2500]),
  ('variant scenario 2', ('0.57', '3.82', '0.5', 50000, '100'), ['0.4175', 10437])],
 [('control even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.55', '1.34', '1', 100000, '10'), ['0.0000', 0]),
  ('regression: net odds', ('0.57', '2.09', '0.5', 100000, '10'), ['0.1755', 8775]),
  ('variant scenario 1', ('0.60', '2.15', '1', 12345, '100'), ['0.2522', 3113]),
  ('variant scenario 2', ('0.48', '3.64', '0.5', 50000, '2'), ['0.2830', 1000])],
 [('control even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.55', '3.59', '0.25', 12345, '100'), ['0.3763', 1161]),
  ('variant scenario 1', ('0.60', '2.93', '0.25', 12345, '10'), ['0.3927', 1212]),
  ('variant scenario 2', ('0.78', '1.41', '0.25', 100000, '100'), ['0.2434', 6085])]]
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 even-money edge	`['0.0500', 5000]`	`['0.1000', 10000]`	Failed
control half kelly	`['0.0500', 2500]`	`['0.1000', 5000]`	Failed
boundary capped stake	`['0.1000', 5000]`	`['0.2000', 5000]`	Failed
boundary no edge	`['0.0000', 0]`	`['0.0000', 0]`	Passed
control underdog edge	`['0.0500', 5000]`	`['0.0667', 6666]`	Failed
regression: net odds	`['0.2942', 5000]`	`['0.4238', 5000]`	Failed
variant scenario 1	`['0.0000', 0]`	`['0.0000', 0]`	Passed
variant scenario 2	`['0.4331', 1234]`	`['0.5198', 1234]`	Failed

SHA-256 / f04de6a2d7fe538620b2987cbd4f6e52a3e7537923811dbe09ed0ea671bcc0b4

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(prob, price, fraction, bankroll_cents, max_pct):
    p = Fraction(prob)
    b = Fraction(price) - 1
    q = 1 - p
    k = (b * p - q) / b
    if k < 0:
        k = Fraction(0)
    use = min(k * Fraction(fraction), Fraction(max_pct) / 100)
    stake = math.floor(bankroll_cents * use)
    r = math.floor(k * 10000 + Fraction(1, 2))
    return ['%d.%04d' % (r // 10000, r % 10000), stake]
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 even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.60', '3.27', '0.5', 50000, '10'), ['0.4238', 5000]),
  ('variant scenario 1', ('0.50', '1.73', '0.5', 100000, '5'), ['0.0000', 0]),
  ('variant scenario 2', ('0.60', '5.99', '1', 12345, '10'), ['0.5198', 1234])],
 [('control even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.80', '4.16', '0.25', 50000, '2'), ['0.7367', 1000]),
  ('variant scenario 1', ('0.60', '3.64', '0.5', 12345, '5'), ['0.4485', 617]),
  ('variant scenario 2', ('0.60', '2.09', '1', 12345, '2'), ['0.2330', 246])],
 [('control even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.60', '2.62', '0.25', 50000, '5'), ['0.3531', 2500]),
  ('variant scenario 1', ('0.60', '5.17', '0.25', 50000, '5'), ['0.5041', 2500]),
  ('variant scenario 2', ('0.57', '3.82', '0.5', 50000, '100'), ['0.4175', 10437])],
 [('control even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.55', '1.34', '1', 100000, '10'), ['0.0000', 0]),
  ('regression: net odds', ('0.57', '2.09', '0.5', 100000, '10'), ['0.1755', 8775]),
  ('variant scenario 1', ('0.60', '2.15', '1', 12345, '100'), ['0.2522', 3113]),
  ('variant scenario 2', ('0.48', '3.64', '0.5', 50000, '2'), ['0.2830', 1000])],
 [('control even-money edge', ('0.55', '2.00', '1', 100000, '100'), ['0.1000', 10000]),
  ('control half kelly', ('0.55', '2.00', '0.5', 100000, '100'), ['0.1000', 5000]),
  ('boundary capped stake', ('0.60', '2.00', '1', 100000, '5'), ['0.2000', 5000]),
  ('boundary no edge', ('0.40', '2.00', '1', 100000, '5'), ['0.0000', 0]),
  ('control underdog edge', ('0.30', '4.00', '1', 100000, '100'), ['0.0667', 6666]),
  ('regression: net odds', ('0.55', '3.59', '0.25', 12345, '100'), ['0.3763', 1161]),
  ('variant scenario 1', ('0.60', '2.93', '0.25', 12345, '10'), ['0.3927', 1212]),
  ('variant scenario 2', ('0.78', '1.41', '0.25', 100000, '100'), ['0.2434', 6085])]]
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 even-money edge	`['0.1000', 10000]`	`['0.1000', 10000]`	Passed
control half kelly	`['0.1000', 5000]`	`['0.1000', 5000]`	Passed
boundary capped stake	`['0.2000', 5000]`	`['0.2000', 5000]`	Passed
boundary no edge	`['0.0000', 0]`	`['0.0000', 0]`	Passed
control underdog edge	`['0.0667', 6666]`	`['0.0667', 6666]`	Passed
regression: net odds	`['0.4238', 5000]`	`['0.4238', 5000]`	Passed
variant scenario 1	`['0.0000', 0]`	`['0.0000', 0]`	Passed
variant scenario 2	`['0.5198', 1234]`	`['0.5198', 1234]`	Passed

SHA-256 / 4c27a2ab0929bf143234d6d88ca6e0a8f1037292da2b66d767c27b720c353a01

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 2026-09-29T14:50:31.900680+00:00.

Case digest / e0e77f7abccd3e92f7afb723c7aec140b978fbd4bb9ae674d1f3d800378d4649