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Kelly Criterion Calculator

Math Calculators

Optimal bet size, half Kelly

Quick Answer

Kelly Criterion Calculator: Optimal bet size, half Kelly. Kelly Criterion Calculator uses standard math formulas to compute accurate results instantly.

f* = (bp − q) / b
10%
Bet 10% of bankroll each round; with fraction 1 → 10%

Full Kelly stake scale

Conservative <5%
Moderate 5-15%
Aggressive 15-30%
Very risky 30-50%
Dangerous >50%

10%

Edge (EV per unit)10%
Half Kelly5%
Max growth rate0.50%
q = 1 − p45%

Calculation steps

  1. 1p = 0.55, q = 1 − p = 0.45, b = 1
  2. 2f* = (b·p − q) / b = (1×0.55 − 0.45) / 1 = 0.1 / 1
  3. 3f* = 0.1 = 10% of bankroll
  4. 4Derivation: maximize g(f) = p·ln(1+b·f) + q·ln(1−f) → derivative zero at f* = (bp−q)/b.

Kelly in practice

StrategyGrowthVolatility
Full KellyMaximum long-run growthVery high drawdowns (can dip 50%+)
Half Kelly (1/2)~3/4 of max growthMuch smoother ride
Quarter Kelly~Half of max growthConservative
2× KellyLOWER than full KellyRuin risk spikes
💡 Kelly maximizes log-wealth growth, invented by John Kelly at Bell Labs (1956) and famously used by Ed Thorp in blackjack and markets. Two catches: (1) it assumes you KNOW your true edge — overestimating p by a few points turns optimal into ruinous; (2) full Kelly is emotionally unbearable. Pros use fractional Kelly (1/2 or 1/4).

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How to Use

  1. Enter values or expressions: type directly into the Kelly Criterion Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Kelly Criterion Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: Optimal bet size, half Kelly.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Kelly Criterion Calculator formula

Kelly Criterion Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Kelly Criterion Calculator?
Open the page and fill in the input fields — results update automatically. Optimal bet size, half Kelly.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Kelly Criterion Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/kelly

Results provided by this tool are for reference only and do not constitute professional advice.