🎯 Kelly calculator

What it is

The Kelly criterion is a bet-sizing formula that maximizes the long-term growth rate of your bankroll when you have a clear edge. It calculates the optimal fraction of your bankroll to stake based on the odds and your estimated probability, balancing profit potential against risk of ruin.

How it works

The formula is f = (odds × p − 1) / (odds − 1), where p is your estimated probability (as a decimal). For example, with odds 2.00 and p = 0.55 (55%), f = (2 × 0.55 − 1) / (2 − 1) = (1.10 − 1) / 1 = 0.10, or 10%. Full Kelly suggests staking 10% of your bankroll.

Now suppose you overestimate p by 5 points: true p is 50%, but you use 55%. The formula still gives f = (2 × 0.55 − 1) / 1 = 0.10, so you bet 10% on a bet with zero edge (true f = 0). This turns a no-bet situation into a risky wager that can cause large losses. Using a fraction like Half Kelly (5%) or Quarter Kelly (2.5%) reduces the damage from misestimation.

How to use it

1. Enter your entire bankroll in US dollars in the 'Total bankroll' field (e.g., 1000 for $1,000).
2. Input the decimal odds from your betting slip into the 'Odds (decimal)' field (e.g., 2.50).
3. Type your estimated probability as a percentage in 'Estimated probability (%)' (e.g., 45 for 45%).
4. Select a 'Kelly fraction' from the dropdown: Full, Half, Quarter, or Eighth Kelly.
5. Read the 'Suggested stake' output—this is the dollar amount you would wager according to the chosen fraction.
6. Review 'Expected value' to confirm your edge is positive (above 0%) before betting.

How to read the result

• Kelly (%) is the fraction of your bankroll to stake based on the formula and fraction selected—e.g., 5% means bet 5% of current bankroll.
• Suggested stake is the actual dollar amount for that bet; it changes as your bankroll grows or shrinks if you recalculate.
• Potential profit shows gross profit if the bet wins (stake × (odds − 1)), not net including stake.
• Bankroll after win and Bankroll after loss show what your bankroll would be in each outcome—useful for scenario planning but not a prediction.

When not to trust the result

• Full Kelly assumes your probability estimate is exactly correct; a small overestimation turns the formula into a dangerous overbet that can lead to large drawdowns or ruin.
• Real-world constraints like maximum bet limits, minimum odds restrictions, and account limits often prevent using the full Kelly stake, forcing you to bet smaller fractions or skip the bet.
• Kelly is a long-run strategy; it requires a large number of bets to realize growth, and even with positive expected value you can experience extended losing streaks that shrink your bankroll significantly.
• The formula only accounts for the bet's edge and odds, ignoring correlation between bets or the need to preserve capital across a portfolio—betting full Kelly on each of several simultaneous bets can overexpose you.

Frequently asked questions

What does the Kelly fraction do?

The Kelly fraction reduces the suggested stake to manage risk. Half Kelly multiplies the full Kelly percentage by 0.5, Quarter by 0.25, and so on. Lower fractions lower volatility and reduce the chance of large losses, but also slow growth.

Should I always use full Kelly?

No. Full Kelly is only optimal if you are 100% confident in your probability estimate and can tolerate large swings. Most bettors use a fraction (e.g., 1/4 or 1/8) to protect against overestimation and variance.

How do I estimate probability accurately?

That is the hardest part. You need a model or method that gives you a consistent edge over the market odds. Without a demonstrable track record of accurate estimates, the Kelly output is only as good as your input—and can mislead you into overbetting.

Does Kelly guarantee profit?

No. Kelly maximizes long-term growth only if your probability estimates are correct. Even then, short-term results are random and you can lose money. It is a risk-management tool, not a profit guarantee.