What are some log-optimal portfolios in blackjack?

[Julio88]

Log-optimal portfolios in blackjack are portfolios that aim to maximize the logarithmic utility of the returns over time. The Kelly Criterion, which is a formula for sizing a bet in probability theory, can be used to calculate the growth-optimal strategy for betting in blackjack. The Kelly criterion is also used in the log-optimal portfolio approach for investing in the stock market, and transaction costs can affect the log-optimal portfolio's performance. However, optimizing a portfolio with the Kelly criterion may be too aggressive for some investors, as a log-optimal investment portfolio can be impractical and cost-prohibitive due to the need for continuous rebalancing.

 

[CR7]

In the context of blackjack, a log-optimal portfolio would involve making bets based on the optimal strategy determined by the Kelly criterion. This strategy involves determining the edge that the player has over the casino in a particular game, and then making a bet that is proportional to this edge. The aim is to maximize the logarithmic growth rate of the player's bankroll over time.

It's worth noting that while the Kelly criterion is considered optimal for maximizing long-term growth, it can also be risky. A player who bets too aggressively using the Kelly criterion may end up losing their entire bankroll if they experience a long losing streak. For this reason, some players may choose to use a less aggressive betting strategy that still aims to maximize their expected value while limiting their risk.

In addition to the Kelly criterion, other approaches to log-optimal portfolio construction in blackjack include simulation-based methods and reinforcement learning algorithms. These methods can take into account factors such as the player's skill level and the specific rules of the game being played, and can be used to generate optimal betting strategies that are tailored to the individual player's preferences and risk tolerance.