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Deriving the Kelly Criterion to Maximise Profits
If you want to put some fraction of your money into a risky venture, how much should you invest? In order to maximise long term wealth, the Kelly Criterion is often used to size the bet. This post shows how to derive the gambling formula from the Kelly Criterion and it’s application to different games. It can be used in a simple simulation or to maximise profits in more complicated scenarios, such as Blackjack.
To succeed in the harsh business climate of past times and win the game, we always need to choose an investment that maximises our long-term wealth. I wrote a simulation that plays about ten thousand hands of blackjack for each true count, determining the probabilities of the different payouts. To calculate the growth rate in Blackjack (assuming we know the different probabilities) we have to determine the limit of the logarithm of the expected wealth for the number of hands played approaching infinity, as done above with the ship investor situation.
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