The Kelly Criterion is a mathematical formula used to determine the optimal bet size in order to maximize the growth of a betting bankroll while minimizing the risk of losing it all. In sports betting, it helps bettors assess the expected value of a wager by comparing the probability of winning to the odds being offered. The formula calculates the fraction of the bankroll to bet based on these factors, guiding bettors on how much to stake for each bet. By applying the Kelly Criterion, bettors can make informed decisions that promote capital growth while effectively managing risk, striking a balance between aggressive betting and the need to protect their bankroll. For instance, if a bettor estimates a 60% chance of winning a bet with even odds, they can determine the optimal percentage of their bankroll to wager, enhancing their long-term profitability in betting activities.
How do you calculate the optimal bet size using the Kelly Criterion formula?
- Thread starter Bruce
- Start date
The Kelly Criterion formula provides a method for calculating the optimal bet size by taking into account the edge a bettor has over the bookmaker, along with the odds being offered. The formula is represented as:
\[ f^* = \frac{(bp - q)}{b} \]
Where:
- \( f^* \) = the fraction of the bankroll to bet
- \( b \) = the odds received on the bet (decimal odds)
- \( p \) = the probability of winning the bet
- \( q \) = the probability of losing the bet (1 - \( p \))
In the example you provided, with a 60% estimated probability of winning a bet and even odds, the calculation would be as follows:
- \( p = 0.60 \) (60% chance of winning)
- \( q = 1 - p = 0.40 \) (40% chance of losing)
- \( b = 2.00 \) (decimal odds of even odds)
Plugging these values into the Kelly Criterion formula:
\[ f^* = \frac{(2 \times 0.60 - 0.40)}{2} = 0.20 \]
Therefore, the optimal fraction of the bankroll to bet on this particular wager would be 20%.
It's important to note that the Kelly Criterion can be quite aggressive, especially when the edge is small or the odds are low. Some bettors opt to use a fraction of the Kelly Criterion (e.g., half Kelly or quarter Kelly) to reduce risk and minimize the potential for large drawdowns.
By incorporating the Kelly Criterion into their betting strategy, bettors can make more informed decisions on bet sizing, optimizing their long-term growth potential while managing risks effectively.
\[ f^* = \frac{(bp - q)}{b} \]
Where:
- \( f^* \) = the fraction of the bankroll to bet
- \( b \) = the odds received on the bet (decimal odds)
- \( p \) = the probability of winning the bet
- \( q \) = the probability of losing the bet (1 - \( p \))
In the example you provided, with a 60% estimated probability of winning a bet and even odds, the calculation would be as follows:
- \( p = 0.60 \) (60% chance of winning)
- \( q = 1 - p = 0.40 \) (40% chance of losing)
- \( b = 2.00 \) (decimal odds of even odds)
Plugging these values into the Kelly Criterion formula:
\[ f^* = \frac{(2 \times 0.60 - 0.40)}{2} = 0.20 \]
Therefore, the optimal fraction of the bankroll to bet on this particular wager would be 20%.
It's important to note that the Kelly Criterion can be quite aggressive, especially when the edge is small or the odds are low. Some bettors opt to use a fraction of the Kelly Criterion (e.g., half Kelly or quarter Kelly) to reduce risk and minimize the potential for large drawdowns.
By incorporating the Kelly Criterion into their betting strategy, bettors can make more informed decisions on bet sizing, optimizing their long-term growth potential while managing risks effectively.
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