Kelly Criterion Calculator

A Kelly Criterion Calculator helps you decide how much money to bet to get the best chance of growing your money without losing too much.
Kelly Criterion Calculator

Kelly Criterion Calculator

What is Kelly Criterion?

The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets to maximize the growth of capital over time while minimizing the risk of losing everything. It is widely used in gambling, investing, and trading.

Formula:

The Kelly Criterion formula is:f∗=bp−qbf^* = \frac{bp – q}{b}f∗=bbp−q​

Where:

  • f∗f^*f∗ = Fraction of capital to wager.
  • bbb = Odds received on the bet (decimal odds minus 1).
  • ppp = Probability of winning.
  • qqq = Probability of losing (1−p1 – p1−p).

Key Concepts:

  1. Maximizes Growth: The formula aims to maximize the logarithmic growth of capital, ensuring the best possible compounding effect over time.
  2. Balances Risk and Reward: It avoids over-betting (risking too much) and under-betting (not leveraging the opportunity sufficiently).
  3. Assumes Known Probabilities: It requires the bettor or investor to accurately estimate the probabilities of outcomes.

Example:

Suppose you are betting on a coin toss where:

  • The coin lands heads 60% of the time (p=0.6p = 0.6p=0.6).
  • The odds are 2-to-1 (b=2b = 2b=2).

Using the formula:f∗=2(0.6)−0.42=1.2−0.42=0.82=0.4f^* = \frac{2(0.6) – 0.4}{2} = \frac{1.2 – 0.4}{2} = \frac{0.8}{2} = 0.4f∗=22(0.6)−0.4​=21.2−0.4​=20.8​=0.4

This means you should bet 40% of your capital on each toss.

Applications:

  1. Gambling: Used to determine bet sizes in games like poker or sports betting.
  2. Investing and Trading: Helps in portfolio management and position sizing, especially in environments with probabilistic outcomes.

Limitations:

  • Requires Accurate Probabilities: Incorrect estimates can lead to suboptimal or disastrous results.
  • Assumes Independent Events: Works best when the outcomes of bets or trades are independent.
  • Risk Tolerance Not Considered: The Kelly Criterion focuses purely on maximizing growth, which may involve higher risk than some individuals are comfortable with.

The Kelly Criterion is a powerful tool but should be used cautiously, particularly when probabilities or outcomes are uncertain.

Who can use Kelly Criterion Calculator?

  • Sports Bettors: In determining the size of the optimal bet given the odds and their estimated probability of an outcome. You can use it with Bundesliga betting odds for example.

  • Casino Players: Especially in those games that involve a better probability estimation based on players’ skills or known advantages, such as blackjack or poker.

  • Horse Racing Enthusiasts: To determine how much to wager on each race when odds and probabilities vary.

FAQ

1. What is the Kelly Criterion and how does it work?

The Kelly Criterion is a mathematical formula used to determine the optimal percentage of your bankroll to wager on a bet to maximize long-term growth while minimizing the risk of ruin. It considers the probability of winning and the odds being offered to calculate the ideal stake for each bet.

By following the Kelly Criterion, bettors aim to grow their bankroll consistently without overexposing themselves to excessive risk.

2. How do I use the Kelly Criterion Calculator?

To use the Kelly Criterion Calculator:
– Enter the probability of winning (your estimation of how likely the bet will succeed).
– Input the odds offered by the bookmaker.
– Provide your current bankroll amount (optional, if the calculator includes a bankroll percentage).
The calculator will then compute the optimal percentage of your bankroll to wager on this particular bet.

3. Can I use the Kelly Criterion for any type of betting?

Yes, the Kelly Criterion can be applied to various types of betting, including sports betting, casino games, and even investing. You can use it with Premier league betting odds etc.

However, it is most effective when you can accurately estimate the probability of an outcome.

If your probabilities are inaccurate or biased, the formula may suggest inappropriate stakes, potentially leading to losses. It is important to combine it with careful research and analysis for the best results.

Minimum Accepted Stake

Enter the minimum stake accepted by your betting exchange. For example, bookmaker has a $5.00 minimum stake for Australian currency accounts. You would input 5.00 in this example. Do not enter currency symbols as part of your input.

Fractional Kelly Betting

The calculated Kelly criterion stake will be adjusted by this factor. To use the standard Kelly method, set this value to 1.00. For a more conservative approach, input a value below 1. For example, to stake 50% of the recommended amount, enter 0.5.