Continuing the theme of money management, let’s delve into the Kelly Formula, a strategy designed to optimize bet sizes and manage risk effectively.
Who Was Kelly, and What Is His Formula?
John Larry Kelly Jr. was a scientist at Bell Labs who, in the 1950s, developed the Kelly Criterion, a formula for determining the optimal size of stakes in a series of bets. The formula helps balance the risk of ruin with the opportunity to maximize long-term growth of capital.
Here’s the formula:
Stake % = ((odds offered × win probability) – loss probability) ÷ odds offered
A Simple Example
Let’s use a straightforward gambling scenario to illustrate. Suppose a casino offers odds of 2-to-1 on a coin toss, meaning they pay you twice as much if you win as you would lose if you guess wrong. The calculation would look like this:
((2 × 0.5) – 0.5) ÷ 2 = 0.25
In this case, the formula recommends staking 25% of your available funds on each toss.
Now, suppose you have a biased coin that gives you a 70/30 chance of winning, and the same odds of 2-to-1 are offered. The calculation would be:
((2 × 0.7) – 0.3) ÷ 2 = 0.55
Here, the Kelly Formula suggests staking 55% of your available funds on each toss.
Who Can Use the Kelly Formula?
The Kelly Criterion can be applied to a variety of scenarios, including:
- Casino games
- Sports betting
- Financial spread betting
However, it’s important to note that the formula is not a magic bullet. It does not guarantee success but aims to preserve capital long enough for you to realize an edge—if you have one.
For example, in Blackjack, skilled players can gain an edge through card counting. However, betting your entire bankroll on the first hand is a quick way to lose it all. The Kelly Formula helps prevent this by recommending a percentage-based stake that adjusts dynamically with wins and losses.
An Anti-Martingale Approach
The Kelly Criterion works as an anti-Martingale strategy, reducing the risk of ruin. By staking a percentage of available funds:
- Bet sizes decrease after losses, preserving capital.
- Bet sizes increase after wins, capitalizing on growth.
This dynamic adjustment prevents overexposure and keeps you “in the game.”
Application to Financial Spread Betting
The Kelly Formula is particularly relevant for financial traders, though it has its challenges:
- Large Recommended Bet Sizes:
When trading high-risk, deep-value stocks, the Kelly Formula may suggest staking a large percentage of your capital—often more than is prudent or comfortable. To address this, many traders adopt a fractional Kelly approach, staking a fraction (e.g., 10% or 20%) of the recommended amount. For instance, if the formula suggests a 50% stake, you might choose to stake only 5%. - Difficulty Estimating Probabilities:
Unlike casino games, where probabilities are often known, financial markets are far less predictable. Many traders find it challenging, if not impossible, to accurately estimate the probabilities of success and failure for a given trade. - Simplified Alternatives:
Due to these difficulties, some traders opt for a simpler strategy: staking a fixed percentage of their available funds, such as 1% per trade, regardless of market conditions or perceived probabilities. This ensures consistent risk management while avoiding the complexities of probability calculations.
While the formula is applicable to any “betting game” including casino games and sports betting as well as financial spread betting, it is not a panacea in the sense of guaranteeing success. It is designed merely to keep you in the game long enough to realise your edge if you have one.
For example: although it will get you thrown out of the casino (or worse) the practice of ‘card counting’ gives you an edge in the game of Blackjack, but this edge will not be realised at all (unless you are very lucky) if you bet the farm on the first game that is dealt.
This formula prevents you from betting the farm, and since it recommends a ‘percentage of available funds’ to bet at each turn, the actual amount staked at each turn will fall and rise as your available funds are depleted through losses and replenished through wins. In this respect, it’s anti-Martingale – and that’s good!
Final Thoughts
The Kelly Formula is a powerful tool for optimizing bet sizes, particularly for those who can accurately assess probabilities and have a clear edge in their chosen domain. However, its practical application in financial spread betting and trading in general requires caution. The Kelly Formula’s challenges in financial trading such as difficulties in estimating probabilities and the high-risk bet sizes it often recommends are well-documented. Whether you use the full Kelly stake, a fractional approach, or a simplified fixed-percentage strategy, the key is to manage risk effectively and preserve your capital.
As always, the ultimate goal of money management is not just to win but to stay in the game long enough to realize your strategy’s potential.
