Kelly Criterion Calculator

Determine optimal bet sizing for maximizing long-term growth rate while avoiding ruin

About the Kelly Criterion Calculator

The Kelly Criterion Calculator is a financial tool used by gamblers and investors to determine the mathematically optimal size of a series of bets. Originally developed by John L. Kelly Jr. in 1956 while working at Bell Labs, the formula was designed to maximize the long-term growth of a bankroll. It is widely utilized by professional sports bettors and value investors like Warren Buffett to balance the trade-off between aggressive growth and the risk of total loss.

This tool computes the precise percentage of your capital that should be committed to a specific opportunity based on the perceived edge and the offered odds. Unlike flat-betting or arbitrary staking, the Kelly Criterion adjusts dynamically to your confidence levels and the potential return on investment. It provides a systematic approach to money management, helping users avoid the 'gambler's ruin'—a scenario where even a winning strategy fails due to poor position sizing that leads to a depleted bankroll during a normal variance cycle.

Formula

f* = (bp - q) / b

In this formula, f* represents the fraction of your current bankroll to wager. The variable 'b' stands for the decimal odds minus one (total potential profit divided by the stake), 'p' is the probability of winning expressed as a decimal, and 'q' is the probability of losing (which is 1 - p).

The numerator (bp - q) effectively represents your 'edge.' If this value is not greater than zero, the formula will yield a zero or negative percentage, indicating the bet has no value. The denominator 'b' normalizes the stake relative to the payout odds, ensuring that lower-odds favorites require a larger stake to achieve the same growth as higher-odds underdogs.

Worked examples

Example 1: An investor identifies a bond with a 2-to-1 payout (b=2) and estimates a 40% chance of success (p=0.40).

p = 0.40\nq = 0.60\nb = 2.0\nf* = (2 * 0.40 - 0.60) / 2\nf* = (0.80 - 0.60) / 2\nf* = 0.20 / 2 = 0.10\n(Half-Kelly adjustment used here for safety) f* = 0.05

Result: 0.05 or 5% of bankroll. The investor should risk 5% of their total capital on this high-yield bond opportunity.

Example 2: A sports bettor finds a value bet with decimal odds of 2.0 (even money, b=1) where they have a 60% estimated win probability.

p = 0.60\nq = 0.40\nb = 1.0\nf* = (1 * 0.60 - 0.40) / 1\nf* = 0.20 / 1\nf* = 0.20\n(Standard Full-Kelly) = 0.20\n(Using Quarter-Kelly for risk management) = 0.10

Result: 0.10 or 10% of bankroll. This represents a significant edge where a one-tenth allocation of the bankroll is mathematically optimal.

Common use cases

A sports bettor determining how much of their $5,000 bankroll to place on a football game where they believe the win probability is 55%.
An options trader calculating the position size for a trade where the potential payout is 3 to 1 but the success rate is only 30%.
A value investor deciding what percentage of a portfolio to allocate to a distressed stock with a high potential upside but a significant chance of bankruptcy.

Pitfalls and limitations

Assuming 100% accuracy in win probability leads to aggressive over-betting and high risk of ruin.
The formula does not account for simultaneous bets, which requires a more complex multi-Kelly calculation.
High volatility is inherent in full-Kelly staking; many users prefer half-Kelly to smooth out the equity curve.
The calculator does not consider minimum or maximum table limits set by bookmakers or exchanges.

Frequently asked questions

can I bet my whole bankroll if the kelly criterion is high?

The Kelly Criterion suggests the percentage of your total wealth that can be risked on a single bet to maximize growth. Using your full bankroll on a single investment is almost never recommended because one loss would result in total liquidation.

what does it mean if the kelly calculator gives a negative number?

A negative result indicates that the bet has a negative expected value (EV-). In this scenario, the mathematically optimal strategy is to not bet at all, as the odds are stacked against you and will lead to long-term loss.

is half kelly better than full kelly for sports betting?

Fractional Kelly (like half-Kelly) involves betting a fixed fraction of the suggested amount, such as 50%. This reduces the volatility and the risk of massive drawdowns while still maintaining a positive growth trajectory, albeit at a slower pace.

how does overestimating win probability affect kelly staking?

The Kelly Criterion assumes you know the exact probability of an outcome, which is rarely true in sports. If you overestimate your edge, the formula will suggest an over-bet, which can lead to rapid bankruptcy if a losing streak occurs.

can i use the kelly criterion for stock market trading?

Yes, the formula works for any scenario with a defined risk-reward profile, including stock options or forex. However, it is most effective when the outcomes are discrete and the probability can be estimated with reasonable confidence.