Betting on sports and other events can be an entertaining pastime, but it also carries risks of losses. The Kelly criterion provides a mathematical approach to optimizing bet sizing in order to maximize long-term growth of your bankroll while minimizing risk. This formula allows bettors to determine the optimal stake to place on each wager based on the perceived odds and probability of winning. In this article, we will explore how the Kelly criterion works and how it can be applied to make informed betting decisions.
Origins and Definition of the Kelly Criterion
The Kelly Criterion, a mathematical formula, was conceived by John L. Kelly Jr. during his tenure at AT&T’s Bell Laboratories. Its primary purpose is to guide the long-term growth of capital.
Initially designed as a system for gambling, it was later adopted by investors to determine the optimal amount of money to invest in a particular asset to maximize wealth growth over time.
The Kelly Criterion Formula
K = (bp – q) / b
Where:
- K is the fraction of the bankroll to wager.
- b is the odds received on the bet (decimal odds minus 1). For example, if you’re getting odds of 5.0, then b would be 5.0 – 1 = 4.0.
- p is the probability of winning the bet.
- q is the probability of losing the bet, which is q = 1 − p.
Example:
Let’s say you’re betting on a horse race, and you believe a particular horse has a 50% chance of winning. The bookmaker is offering odds of 2.5 (or 6/4 in fractional terms) for that horse to win.
Given:
- b = 2.5 – 1 = 1.5
- p = 0.50
- q = 1 – 0.50 = 0.50
Plugging these values into the formula:
K = (1.5 (0.50)) − 0.50 / 1.5
K = (0.75 − 0.50) / 1.5
K = 0.25 / 1.5
K = 0.1667
This result means that, according to the Kelly Criterion, you should bet approximately 16.67% of your bankroll on that horse to maximize the growth rate of your bankroll over the long term.
It’s important to note that the Kelly Criterion assumes you can accurately estimate the probability of the event. If your estimation is off, it can lead to suboptimal bet sizes. Always use the formula with caution and consider other factors before placing a bet.
Key Benefits of the Kelly Criterion
- Maximizes long-term capital growth. Kelly betting aims to steadily grow your bankroll over time rather than maximize short-term gains.
- Minimizes risk. By calculating an optimal stake, Kelly prevents overbetting and getting wiped out by losses.
- Easy to calculate. The formula only requires your perceived edge and odds of winning.
- Flexible. The stake can be adjusted based on your risk tolerance and bet size limits.
The Kelly criterion provides an objective, mathematical way to size bets that can maximize returns over the long run. However, discipline is required to overcome emotional biases and stick to the strategy through inevitable losses. Used properly, the Kelly Criterion can make betting a bit smarter.
Comparison of the Kelly Criterion with Other Financial Betting Systems
| System/Strategy | Description | Pros | Cons |
|---|---|---|---|
| Kelly Criterion | Determines the optimal bet size to maximize long-term growth. |
Maximizes long-term capital growth. | Requires accurate probability estimates. |
| Martingale System | After a loss, double the bet size. Return to initial bet after a win. |
Can recover losses with a win. | Can lead to huge losses in a losing streak. |
| Fixed Betting | A fixed amount or percentage of bankroll is bet each time. |
Simple and easy to follow. | Doesn’t optimize for growth. |
| Fibonacci System | Bet size follows the Fibonacci sequence. Increase bet after a loss and move back two steps after a win. |
Can recover losses over time. | Can lead to large bets after a series of losses. |
| Labouchère System | Bet the sum of the first and last numbers in a sequence. Numbers are added or crossed out based on wins or losses. |
Can recover losses with multiple wins. |
Can lead to large bets and long sequences. |
To summarize, The Kelly criterion provides an objective, mathematical way to size bets that can maximize returns over the long run. However, discipline is required to overcome emotional biases and stick to the strategy through inevitable losses. Used properly, the Kelly Criterion can make betting a bit smarter.
