Kelly Fraction for a Single Bet

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Returns Probabilities Simulation
Bet Fraction Bet Fraction
Cash Fraction Number of bets

Final bankroll :
Expected bankroll :


For the theory behind this calculator see: Bet Smart: The Kelly System for Gambling and Investing

The Kelly fraction is the percentage of your assets that you should place on a bet or investment. The calculation is based upon the possible returns and their probabilities.

The Kelly fraction will be positive if the expected (average) return is positive. For a negative expected return the Kelly fraction will be negative. For a stock investment you can interpret this as selling the stock short.

If the Kelly fraction is positive and you play the bet multiple times, your assets will grow at the maximum possible rate with the smallest chance of going bankrupt.

As a simple example, imagine a stock that can either double in value or lose half its value, with equal probability, in a given day. The two returns are then +1 (100%) and -0.5 (-50%), each with probability 0.5. The Kelly fraction in this case is 0.5 which means that at the beginning of each day, you should have exactly half of your assets invested in this stock.

In the boxes you can enter a return per line and a probability per line. You should have at least one positive and one negative return. The returns should be expressed as fractions, so that a return of 30% would be 0.3. The probabilities for all returns should add up to 1.


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