Kelly Betting
A betting system betting a percentage of a bankroll equal to the percentage advantage.
Kelly Betting, or the Kelly Criterion, is a mathematical formula used to determine the optimal size of a series of bets in order to maximize the logarithm of wealth over time. It was developed by John L. Kelly Jr. in 1956 and is widely used in gambling, investing, and other scenarios where probability and risk are involved.
The formula calculates the fraction of a bankroll to wager based on the edge you have over the bet and the odds being offered. The basic formula is:
[ f^* = \frac{bp - q}{b} ]
Where:
- ( f^* ) = the fraction of the bankroll to wager
- ( b ) = the odds received on the wager (in decimal form, minus 1)
- ( p ) = the probability of winning
- ( q ) = the probability of losing (which is ( 1 - p ))
The key idea behind the Kelly Criterion is to find a balance between risk and reward, ensuring that you do not bet too much (which could lead to significant losses) or too little (which could lead to suboptimal growth of your bankroll). By following the Kelly Criterion, bettors aim to maximize their expected logarithmic growth, which can lead to substantial long-term gains. However, it is important to note that the criterion assumes that the bettor can accurately estimate the probabilities and odds, which can be challenging in practice.
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