Kelly Criterion Calculator

Calculate the optimal bet size to maximize long-term geometric growth rate.

0 to 1 (e.g., 0.6 = 60%)
Net profit per $1 wagered
$
Optimal Kelly Fraction (f*)
20.00%
Bet 20% of your bankroll on each wager
Full Kelly Amount
$2,000
Half-Kelly Amount
$1,000
Quarter-Kelly Amount
$500
Expected Growth Rate
+2.01% per bet
Expected Value per $1
$0.20
Edge
20.00%

How to Use the Kelly Criterion Calculator

  1. Enter the probability of winning — your estimated chance of the bet succeeding, as a decimal (0.6 = 60%).
  2. Enter the payout odds — the net profit per dollar wagered. For example, "2.0" means you win $2 for every $1 bet (plus your original $1 back).
  3. Optionally enter your bankroll — to see the dollar amounts for full, half, and quarter Kelly.
  4. Read the results — the Kelly fraction tells you what percentage of your bankroll to risk.

Understanding the Kelly Criterion

The Kelly Criterion, developed by John L. Kelly Jr. at Bell Labs in 1956, solves one of the most important problems in finance and gambling: how much to bet. While most people focus on finding positive expected value (+EV) opportunities, the Kelly Criterion addresses the equally critical question of position sizing — betting too much risks ruin, while betting too little leaves money on the table.

The Kelly Formula

The formula is elegantly simple:

f* = (bp - q) / b

Where f* is the optimal fraction of bankroll to wager, b is the net odds (profit per $1 bet), p is the probability of winning, and q is the probability of losing (1 - p). The result is the exact fraction that maximizes the geometric growth rate of your wealth over time.

Why Geometric Growth Matters

The Kelly Criterion maximizes the expected logarithm of wealth, not the expected wealth itself. This is critical because compounding returns are multiplicative, not additive. A 50% loss followed by a 50% gain does not return you to break-even — you end up at 75% of your starting wealth. Kelly accounts for this asymmetry, ensuring you never overbet into ruin while still growing aggressively.

Expected Geometric Growth Rate

The growth rate per bet at the Kelly fraction is:

g = p × ln(1 + f*×b) + q × ln(1 - f*)

This value represents the average percentage growth of your bankroll per bet when wagering the Kelly fraction. A positive growth rate means your bankroll trends upward over time despite individual losses.

Half-Kelly and Fractional Kelly

In practice, most professionals use Half-Kelly (betting half the recommended fraction). Why? Because the Kelly Criterion assumes you know the exact probability of winning, which you rarely do. Half-Kelly provides 75% of the growth rate with significantly reduced variance. It also protects against estimation errors — if your probability estimate is off, half-Kelly is much more forgiving than full Kelly.

The Danger of Over-Betting

Betting more than the Kelly fraction is mathematically destructive. At exactly 2x Kelly, your expected growth rate drops to zero — the same as not betting at all. Above 2x Kelly, your bankroll is mathematically guaranteed to approach zero over time, even though each individual bet has positive expected value. This counterintuitive result is why position sizing matters as much as edge.

Real-World Applications

The Kelly Criterion is used by poker professionals (Chris Ferguson famously grew $0 into $10,000 using Kelly), sports bettors, hedge fund managers, and venture capitalists. Edward Thorp, who pioneered card counting in blackjack, used Kelly to size his bets and later applied it to building one of the most successful quantitative hedge funds in history.

Frequently Asked Questions

The Kelly Criterion is a formula that determines the optimal percentage of your bankroll to wager on a bet or investment to maximize long-term geometric growth. Developed by John L. Kelly Jr. at Bell Labs in 1956, it balances risk and reward by considering both the probability of winning and the odds offered.
A negative Kelly fraction means you have a negative expected value — the bet is mathematically against you. You should not place the bet at all. A negative Kelly indicates that the probability of winning multiplied by the payout is less than the probability of losing.
Half-Kelly means wagering exactly half of the full Kelly fraction. Many professionals use half-Kelly because it provides 75% of the growth rate with significantly reduced volatility. It serves as a practical compromise between theoretical optimality and real-world uncertainty in probability estimates.
Yes, the Kelly Criterion applies to any situation with a positive expected value and known probabilities. Hedge funds, poker players, and sports bettors all use variants of Kelly. Warren Buffett and Charlie Munger are known advocates of Kelly-style concentrated position sizing.
Betting more than the Kelly fraction ("over-betting") mathematically guarantees lower long-term growth and increases the risk of ruin. At exactly 2x Kelly, expected growth drops to zero. Above 2x Kelly, your bankroll is guaranteed to approach zero over time despite having a positive edge.