Kelly Criterion Calculator

📐 Kelly Criterion Calculator

Enter your win probability and the odds offered to calculate the optimal bet size. The calculator shows both full Kelly and conservative fractional Kelly recommendations.

Your Estimated Win Probability (%) Your assessment of the true probability of winning

Decimal Odds e.g., 2.00 = even money (1:1)

Bankroll ($) Your total betting bankroll

Full Kelly Bet Size

10.00%

Bet $100.00 of your $1,000 bankroll

Fractional Kelly (Reduce Volatility)

50% Kelly

10% (Very Conservative) 25% 50% (Recommended) 75% 100% (Full)

$50.00
Fractional Kelly Bet

10.00%

Your Edge

+$5.00

Expected Value

50.00%

Implied Probability

📖 The Kelly Formula

f* = (bp - q) / b

f* = Fraction of bankroll to bet

b = Net odds received (decimal odds - 1)

p = Probability of winning

q = Probability of losing (1 - p)

Example: If you believe you have a 55% chance of winning a bet at 2.00 decimal odds (even money), the Kelly formula gives: f* = (1.00 × 0.55 - 0.45) / 1.00 = 0.10, meaning you should bet 10% of your bankroll.

🎯 Example Scenarios

Click a scenario to load it into the calculator:

Slight Edge - Even Money

55% win rate at 2.00 odds

Edge: 10% Kelly: 10%

Strong Edge - Even Money

60% win rate at 2.00 odds

Edge: 20% Kelly: 20%

Underdog Bet

40% win rate at 3.00 odds

Edge: 20% Kelly: 10%

Heavy Favorite

70% win rate at 1.50 odds

Edge: 5% Kelly: 10%

Long Shot Value

25% win rate at 5.00 odds

Edge: 25% Kelly: 6.25%

Slight Value

48% win rate at 2.10 odds

Edge: 0.8% Kelly: 0.73%

Understanding the Kelly Criterion: The Science of Optimal Bet Sizing

The Kelly Criterion is a formula for determining the optimal size of a series of bets. It was developed by John L. Kelly Jr., a researcher at Bell Labs, and published in 1956. Originally designed for maximizing the growth rate of investments, it has become a fundamental tool in both gambling theory and portfolio management.

The genius of Kelly's formula is that it balances two competing forces: betting more when you have an edge to maximize growth, while not overbetting and risking ruin. The formula was later championed by legendary investors like Warren Buffett's partner Charlie Munger and mathematician Edward Thorp, who used it to beat casinos at blackjack—as documented in his classic book "Beat the Dealer".

Why Kelly Matters: Mathematical Foundations

Kelly proved that his formula maximizes the geometric growth rate of capital. This is crucial because in the real world, you can't average your returns—you experience compounded results. According to research from the Journal of Finance, geometric mean maximization provides better long-term outcomes than simple expected value maximization.

Here's what makes Kelly mathematically optimal:

Maximizes long-term growth: No other betting strategy produces faster bankroll growth over time
Never risks ruin: Kelly never bets your entire bankroll, so you can never go completely broke
Self-adjusting: Bet sizes automatically scale with your bankroll—bet more when winning, less when losing
Edge-proportional: Larger edges warrant larger bets, smaller edges require smaller bets

Fractional Kelly: Why Professionals Use Less

While full Kelly is mathematically optimal, most professionals use fractional Kelly (typically 25-50% of the full Kelly amount). Here's why:

Kelly Fraction	Growth Rate	Max Drawdown	Volatility
100% (Full Kelly)	Highest	~50%+ possible	Very High
75% Kelly	~94% of max	~35-40%	High
50% Kelly (Recommended)	~75% of max	~25%	Moderate
25% Kelly	~44% of max	~12-15%	Low

As discussed in academic finance literature and validated by the CFA Institute, the 50% Kelly (half-Kelly) provides about 75% of the maximum growth rate while dramatically reducing volatility and drawdowns—making it the sweet spot for most bettors.

Key Requirements for Using Kelly

Critical: Kelly Only Works With Positive Expected Value

The Kelly Criterion is only applicable when you have an edge (positive expected value). In most casino games, the house has the edge, meaning Kelly would recommend betting $0. Kelly is primarily used for sports betting, poker, advantage play (like card counting), and financial investments where you can identify value.

For Kelly to work effectively, you need:

Accurate probability estimates: Your edge calculation is only as good as your win probability estimate. Overconfidence leads to overbetting.
Positive expected value: If your true probability doesn't exceed the implied probability from the odds, Kelly says don't bet.
Sufficient bankroll: You need enough capital to weather losing streaks without going broke.
Consistent application: Kelly works over many bets; results in any single bet are still random.

Kelly vs. Other Betting Strategies

Unlike betting systems like Martingale or Fibonacci which are mathematically doomed to fail (as we explain in our betting systems truth article), the Kelly Criterion is scientifically proven to maximize wealth over time—provided you actually have an edge. The difference is that those systems try to overcome the house edge through bet sizing (impossible), while Kelly optimizes bet sizing when you already have an edge.

For more on how variance and expected value interact, see our complete guide to gambling mathematics. Understanding these concepts is essential for properly applying the Kelly Criterion.

Practical Tips for Using This Calculator

Be conservative with your probability estimates. If you think you have a 60% edge, input 55%. Overconfidence is the enemy.
Start with quarter-Kelly. Until you've proven your edge over hundreds of bets, use 25% Kelly to protect against estimation errors.
Track your results. Compare your actual win rate to your estimated probability. Adjust over time.
Never bet more than Kelly suggests. Overbetting is mathematically worse than underbetting—it can lead to ruin.
Use a separate betting bankroll. Only apply Kelly to money you've set aside specifically for betting.

Educational Disclaimer: This calculator is for educational purposes only. The Kelly Criterion assumes you can accurately estimate win probabilities and have a genuine edge—conditions rarely met in practice. Never gamble with money you cannot afford to lose. For gambling help resources, visit the National Council on Problem Gambling or see our responsible gambling page. 18+ Only.

Frequently Asked Questions

What is the Kelly Criterion?

The Kelly Criterion is a mathematical formula developed by John Kelly in 1956 at Bell Labs. It calculates the optimal percentage of your bankroll to wager on a bet with positive expected value, maximizing long-term growth while minimizing risk of ruin. It's used by professional gamblers, poker players, and financial investors.

How do you calculate Kelly Criterion?

The Kelly formula is: f* = (bp - q) / b, where f* is the fraction of bankroll to bet, b is the decimal odds minus 1 (net odds), p is the probability of winning, and q is the probability of losing (1 - p). For example, with 55% win probability and even money odds (2.00), Kelly recommends betting (1.00 × 0.55 - 0.45) / 1.00 = 10% of your bankroll.

Why use fractional Kelly?

Fractional Kelly (betting 25-50% of the full Kelly amount) reduces volatility and drawdowns while still capturing most of the growth. Full Kelly can lead to bankroll swings of 50% or more, which is psychologically difficult. Half-Kelly (50%) provides about 75% of maximum growth with much smoother results—that's why most professionals prefer it.

Can Kelly Criterion be used in casino games?

The Kelly Criterion only applies when you have a positive edge (expected value). In most casino games—slots, roulette, craps—the house has the edge, so Kelly would recommend betting $0. Kelly is primarily useful for sports betting, poker (where skill matters), card counting in blackjack, and financial investments where you can identify undervalued opportunities.

What happens if Kelly recommends a negative bet?

A negative Kelly result means you have negative expected value—the odds don't justify the bet based on your probability estimate. In this case, the optimal strategy is to not bet at all. If you could bet the other side (like the house), that would be the profitable position. This calculator shows "No Bet" when Kelly is negative.