# Kelly Criterion Explained: Optimize Betting and Investing Strategies

## What Is the Kelly Criterion?

John L. Kelly Jr. created the Kelly criterion formula in 1956 at AT&T's Bell Laboratories. It helps determine how much to invest in a given asset to maximize wealth growth over time.

### Key Takeaways

*   The Kelly Criterion is a formula created by John L. Kelly Jr. in 1956 to help maximize wealth growth by determining optimal investment sizes.  
    
*   Originally intended for gambling, the Kelly Criterion calculates how much to invest in a single trade based on winning probability and win/loss ratio.  
    
*   While beneficial for identifying investment proportions, the Kelly Criterion is not a standalone strategy, as it lacks consideration for portfolio diversification.  
    
*   Some economists argue against the Kelly Criterion due to personal investment constraints that can affect optimal growth rates.

## Understanding the Kelly Criterion Formula and Its Applications

Gamblers began using the Kelly criterion in 1956 to make bets on horse racing. Later, investors like [Warren Buffett](https://www.investopedia.com/terms/o/oracleofomaha.asp) and [Bill Gross](https://www.investopedia.com/terms/w/william-h-gross.asp) reportedly used the Kelly criterion in their strategies. The formula helps determine the ideal amount to invest in a trade. There are two key components to the formula for the Kelly criterion:

*   **Winning probability factor (W)**: Probability a trade will have a positive return.
*   **Win/loss ratio (R)**: Equal to the total positive trade amounts, divided by the total negative trading amounts.

The result tells investors what percentage of their total capital should apply to each investment. The term is often called the Kelly strategy, Kelly formula, or Kelly bet.

> $\begin{aligned} &Kelly~\% = W - \Big[\dfrac{(1-W)}{R}\Big] \\ &\textbf{where:}\\ &\begin{aligned} Kelly~\% = &\text{ Percent of investor's capital to put into}\\ &\text{ a single trade} \end{aligned}\\ &W = \text{Historical win percentage of trading system}\\ &R = \text{Trader's historical win/loss ratio}\\ \end{aligned}$
> 
> > **Warning**
> >
> > The Kelly Criterion can be useful, but investors should also consider diversification. Many investors should be wary about investing only in a single asset even if the formula suggests a high probability of success.
> 
> ## Recognizing the Limitations of the Kelly Criterion
> 
> Despite its appeal, some economists argue it's not always effective because personal investment constraints can limit growth. In reality, an investor's constraints, whether self-imposed or not, are a significant factor in decision-making capability. A common alternative is [Expected Utility Theory](https://www.investopedia.com/terms/e/expectedutility.asp), suggesting bets should maximize the expected benefit.
> 
> ## How Do Investors Find Their Win Probability With the Kelly Criterion?
> 
> Most investors [using the Kelly Criterion](https://www.investopedia.com/articles/trading/04/091504.asp) try to estimate this value based on their historical trades by looking at the last 50 or 60 trades and counting how many of them had positive returns.
> 
> ## How Do Investors Input Odds Into the Kelly Criterion?
> 
> To enter odds into the Kelly Criterion, one first needs to determine W, the probability of a favorable return, and R, the size of the average win divided by the size of the average loss. The easiest way to estimate these percentages is from the investor's recent investment returns. These figures are then entered into the formula: K= W- (1-W) / R—where K represents the percentage of the investor's bankroll that they should invest.  
> 
> ## How Are the Black-Scholes Model and the Kelly Criterion Related?
> 
> The [Black-Scholes Model](https://www.investopedia.com/terms/b/blackscholes.asp#:~:text=The%20Black%2DScholes%20model%20is,other%20risk%20factors%20into%20account.) and the Kelly Criterion are mathematical systems that estimate investment returns when some key variables depend on unknown probabilities. The Black-Scholes model calculates the theoretical value of options contracts, based upon their time to maturity and other factors. The Kelly Criterion is used to determine the optimal size of an investment, based on the probability and expected size of a win or loss.
> 
>   
> 
> ## Key Insights into the Kelly Criterion
> 
> The Kelly Criterion is a strategic formula designed to maximize wealth by determining the optimal allocation of an investor's capital in each trade. Developed by John L. Kelly Jr., it uses the probability of a positive return and the win/loss ratio to suggest precise investment amounts.
> 
> While offering a method to grow capital, it is critical for investors to balance this strategy with diversification and consider personal investment constraints. The Kelly Criterion provides insights, but investors should apply it with caution, especially when applied to single trades.  
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