# Kelly Criterion Calculator

## How to Use This Kelly Criterion Calculator

To use this Kelly criterion calculator:

- Select your odds format (American, decimal, fractional, etc.)
- Enter valid odds for your chosen format in the "Odds" field.
- Enter your estimated win probability as a percentage into the "Win Probability %" field.
- Enter your Kelly multiplier. The default is 1, but many people use a 0.25, 0.33, or 0.5 Kelly multiplier to reduce the risk to their bankroll from any one bet.
- Optionally, enter your bankroll (needed to calculate Amount to Bet & Expected Value).

"% of Bankroll to Bet" tells you what fraction of your bankroll the Kelly criterion formula suggests betting based on the criteria you entered. If you enter your bankroll into the calculator, you'll also see the amount to bet in your currency.

The calculator also outputs your expected ROI and expected value (if you entered your bankroll).

## What is the Kelly Criterion?

The Kelly criterion (Kelly strategy) is a formula developed by John Kelly to determine the optimal bet size to maximize profit. Assuming the expected win probability and thus the expected value is known, utilizing the Kelly criterion maximizes wealth growth.

### Kelly Criterion Bet Formula

Here's the formula for determining bet size using the Kelly criterion in betting:

% of Bankroll to Bet as a Decimal = Probability of a Win as a Decimal - (Probability of a Loss as a Decimal / Proportion of a Bet Gained With a Win)

"Proportion of a Bet Gained With a Win" is the Profit / Bet Amount.

#### Kelly Criterion Example

For this example, we'll calculate the % of your bankroll that the Kelly criterion recommends betting on +110 American odds (2.1 decimal odds, 11/10 fractional) if the probability of winning the bet is 55%.

First, we'll need to find the "Proportion of a Bet Gained With a Win". Using our bet calculator, we can see that a $100 bet at +110 profits $110 if it wins. Therefore, the "Proportion of a Bet Gained With a Win" is 1.1 ($110 profit / $100 bet amount = 1.1). We can now use the Kelly criterion formula to calculate the percentage of our bankroll it recommends betting.

% of Bankroll to Bet As a Decimal = 0.55 - ((1 - 0.55) / 1.1) = 0.14090909 or 14.09%

If our bankroll is $1,000, the Kelly criterion recommends betting $140.91 (1000 * 0.14090909).

## Caveats to Using the Kelly Criterion for Sports Betting

If you want to implement the Kelly criterion into your sports betting strategy, there are a few important things to consider.

- The Kelly criterion assumes we know an event's exact win probability, but we can only make estimates. No betting model exists that can perfectly predict win probabilities.
- Sports bettors often have many bets in play at any given time (I've frequently had hundreds of bets in play at a time), while the Kelly criterion formula assumes you place one bet at a time and then adjust your bankroll for the subsequent bet.
- Using the Kelly strategy can lead to massive swings. It's been shown that a Kelly bettor has a 1/3 chance of losing half the starting bankroll before doubling it.

For these reasons and more, many bettors use a Kelly multiplier to reduce their bet sizes and limit swings. Common strategies are 1/4 Kelly (0.25 multiplier), 1/3 Kelly (0.33 multiplier), and half Kelly (0.5 multiplier). These multipliers are multiplied by the bet amount the Kelly criterion recommends, thus reducing bet size.

Whereas Full Kelly has a 1/3 chance of halving the bankroll before doubling it, a Half Kelly strategy has only a 1/9 chance of halving the bankroll before doubling it.

Additionally, it's often recommended to use some margin of error for your estimated win probability.