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Home Page > Financial Calculators > Investment Calculators

Kelly Criterion Calculator

MiniWebtool’s Kelly Criterion Calculator estimates a capital fraction from your assumed probability and payoff. Full and fractional Kelly comparisons illustrate the model’s risk implications; inaccurate input assumptions can substantially change the suggested fraction.

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Kelly criterion: bet (p × b − q) / b of your bankroll

Enter your win probability and win/loss ratio (or odds), plus an optional bankroll, to get the full, half, third and quarter Kelly percentages and amounts, with the steps.

Try example scenarios:

Coin Flip Edge Sports Betting Trading Setup High Risk/Reward
Size a whole slate of bets (one per line)
Tip: Be conservative with your win probability estimate. Overestimating leads to overbetting. When in doubt, use Half Kelly or less.

Embed Kelly Criterion Calculator Widget

Video Guide: Kelly Criterion Calculator

Video guide with full transcript

About Kelly Criterion Calculator

Welcome to the Kelly Criterion Calculator, a professional-grade tool for determining the optimal percentage of your capital to risk on any bet or investment. Whether you are a sports bettor, poker player, stock trader, or cryptocurrency investor, the Kelly Criterion helps you maximize long-term growth while managing risk scientifically.

At a Glance

Kelly Criterion Calculator computes the Kelly fraction, K% = (p x b - q) / b, from your estimated win probability and win/loss ratio. It compares full and fractional Kelly and can convert the fraction into amounts for a bankroll.

Kelly Criterion Calculator: features at a glance
FeatureWhat you getGood for
InputsWin probability from 1% to 99%, the win/loss ratio (1 for even money, 2 for 2:1), and an optional bankroll. Results depend entirely on these assumptions.Sizing a bet or position from your own estimates
Result valuesShows the Kelly percentage, the edge and the expected value per unit risked. A negative Kelly value means the inputs give no edge.Checking whether a bet has a positive expected value
Fractional KellyCompares Full, Half, Third and Quarter Kelly with their approximate growth rates (about 100%, 75%, 55% and 44%) and relative volatility.Seeing how risk drops as the fraction shrinks
Bankroll amountsWith a bankroll entered, each Kelly fraction is shown as a specific amount.Turning a percentage into a stake
ChartsAn interactive growth curve and a bet-size risk chart illustrate the effect of betting more or less than the Kelly fraction.Visualizing the cost of overbetting
Step-by-step workingDisplays the calculation, and the page explains converting decimal odds with b = odds - 1 or using average win divided by average loss for trading.Working out the win/loss ratio from odds or trade history

What is the Kelly Criterion?

The Kelly Criterion, also known as the Kelly Strategy or Kelly Formula, is a mathematical formula developed by John L. Kelly Jr. at Bell Labs in 1956. Originally designed to optimize signal-to-noise ratios in telecommunications, it was quickly adopted by gamblers and investors as the optimal strategy for sizing bets and positions.

The Kelly Criterion answers a fundamental question: Given your edge and odds, what percentage of your bankroll should you bet to maximize long-term growth? Bet too little and you leave money on the table; bet too much and you risk catastrophic losses.

The Kelly Formula

Kelly Criterion Formula
$$K\% = \frac{p \times b - q}{b}$$

Where:

Alternative Kelly Formula

The formula can also be written as:

Simplified Kelly Formula
$$K\% = p - \frac{q}{b} = p - \frac{1-p}{b}$$

How to Use This Calculator

  1. Enter your win probability: Estimate your probability of winning the bet as a percentage (1-99%). Be realistic and conservative in your estimates.
  2. Enter your win/loss ratio: This is how much you win relative to how much you lose. For even-money bets, this is 1. For 2:1 odds, this is 2.
  3. Enter your bankroll (optional): Add your total capital to see specific dollar amounts for each Kelly fraction.
  4. Review results: Examine the optimal Kelly percentage, fractional options, and growth visualization.
  5. Apply fractional Kelly: Choose Half Kelly or less for practical applications.

Understanding Your Results

Primary Results

Fractional Kelly Options

Kelly Criterion Calculator: Fractional Kelly Options
FractionGrowth RateVolatilityBest For
Full Kelly100%HighestTheoretical maximum (not recommended)
Half Kelly~75%Much LowerMost practical applications (recommended)
Third Kelly~55%LowConservative approach
Quarter Kelly~44%LowestMaximum safety, minimal drawdowns

Why Use Fractional Kelly?

Full Kelly betting assumes perfect knowledge of win probability and odds, which is impossible in practice. Fractional Kelly provides:

  • Protection against estimation errors in your win rate
  • Dramatically reduced volatility and drawdowns
  • Better psychological sustainability during losing streaks
  • Nearly the same long-term growth with much less risk

Calculating Win/Loss Ratio

For Sports Betting

Convert decimal odds to win/loss ratio:

Win/Loss Ratio from Decimal Odds
$$b = \text{Decimal Odds} - 1$$

Example: Decimal odds of 2.5 means b = 2.5 - 1 = 1.5

For Trading

Calculate from your historical performance:

Win/Loss Ratio for Trading
$$b = \frac{\text{Average Winning Trade}}{\text{Average Losing Trade}}$$

Practical Applications

Sports Betting

Professional sports bettors use Kelly Criterion to size their wagers. With accurate win probability estimates, Kelly helps maximize long-term profits while avoiding the risk of ruin from overbetting.

Stock and Options Trading

Traders use Kelly for position sizing in their portfolios. By calculating the Kelly percentage for each trade based on historical win rates and average gains/losses, traders can optimize their capital allocation.

Poker

Poker players use Kelly to manage their bankroll for cash games and tournaments. The formula helps determine appropriate stakes and buy-in levels based on edge and variance.

Cryptocurrency Trading

Given the high volatility in crypto markets, fractional Kelly is essential. Most crypto traders use Quarter Kelly or less to survive the extreme swings while still capitalizing on their edge.

Important Limitations

  • Accurate probability estimation is critical: Kelly assumes you know your true win probability, which is difficult in practice
  • Full Kelly has extreme volatility: You can expect 50%+ drawdowns even with a positive edge
  • Independent bets assumption: Kelly assumes each bet is independent, which may not hold for correlated positions
  • Fractional bankroll constraint: In practice, you cannot bet fractional cents, which matters with small bankrolls

The Mathematics Behind Kelly

Maximizing Geometric Growth

The Kelly Criterion maximizes the expected logarithm of wealth, which is equivalent to maximizing long-term geometric growth rate. The expected log growth rate is:

Expected Log Growth
$$G = p \times \ln(1 + b \times f) + q \times \ln(1 - f)$$

Where f is the fraction of bankroll bet. Taking the derivative and setting it to zero gives the Kelly formula.

Why Half Kelly Works

The growth function is concave (bell-shaped) around the Kelly point. This means:

Frequently Asked Questions

What is the Kelly Criterion?

The Kelly Criterion is a mathematical formula that determines the optimal percentage of your bankroll to bet or invest to maximize long-term growth. Developed by John Kelly in 1956 at Bell Labs, it balances the trade-off between risk and reward by considering your win probability and the odds offered.

Why should I use Half Kelly instead of Full Kelly?

Half Kelly is recommended because it provides approximately 75% of the growth rate of Full Kelly while dramatically reducing volatility and drawdowns. Full Kelly assumes perfect knowledge of win probability and odds, which is rarely the case. Half Kelly provides a significant safety margin for estimation errors.

What does a negative Kelly value mean?

A negative Kelly value means you have no edge in the bet - your expected value is negative. The Kelly Criterion recommends not betting at all. A negative Kelly indicates that over time, you would lose money by placing this bet, regardless of bet size.

How do I calculate my win/loss ratio?

Divide your average win amount by your average loss amount. For sports betting, it is the decimal odds minus 1 (e.g., 2.5 odds = 1.5 ratio). For trading, analyze your historical trades to calculate this ratio.

Can Kelly Criterion be used for stock trading?

Yes, the Kelly Criterion is widely used in stock trading and portfolio management. Many professional traders and hedge funds use fractional Kelly (typically 1/4 to 1/2) to determine position sizes. Accurately estimating probabilities in financial markets is challenging, making conservative Kelly fractions advisable.

What is the relationship between Kelly and risk of ruin?

Kelly theoretically minimizes risk of ruin while maximizing growth. Betting exactly Kelly ensures you never go bankrupt mathematically (since you always bet a percentage). However, fractional Kelly further reduces short-term drawdown risk, making it more sustainable.

How do I size a bet when I have a $1,000 bankroll, a 55% win chance, and even-money odds?

At even-money odds, the win/loss ratio is 1. The Kelly fraction is p minus (1 minus p) divided by b, so with p = 0.55 and b = 1, the full Kelly fraction is 10%. That corresponds to $100 of a $1,000 bankroll. Because the probability estimate may be wrong and full Kelly can produce large swings, many people use a fraction of that amount, such as half Kelly, or $50.

How should I use Kelly when my estimate of the win probability is uncertain?

Use a cautious probability estimate, since overstating your chance of winning can make the calculated stake too large. For example, if your estimate is 55% but the true chance is closer to 50% at even-money odds, a 10% full-Kelly stake is no longer justified. You can test a lower probability estimate and consider a fractional Kelly amount to reduce the impact of estimation errors. Kelly gives a mathematical result from its inputs; it cannot verify that those inputs are accurate.

Can I use one Kelly percentage for several bets at once?

A single Kelly percentage is calculated for one wager with a particular win probability and payout ratio. Several bets may have different edges, and their outcomes may be related. For instance, two bets on the same game can both lose for the same reason, so treating them as independent can understate risk. Evaluate each opportunity on its own assumptions and be cautious about total exposure when bets are correlated. The calculation does not make uncertain outcomes predictable.

Additional Resources

Reference this content, page, or tool as:

"Kelly Criterion Calculator" at https://MiniWebtool.com/kelly-criterion-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Jan 19, 2026

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