Following a quick Google search I found a couple of interesting papers on this topic. The first was “The Evolution of Blackjack Strategies” by Kendall and Smith,2003. In this work they look to evolve an optimum blackjack strategy without using card counting. Kendall and Smith state the house advantage over the player based on a series of known strategies, these have been reproduced here:
Thorpe’s Basic Strategy – 0.5%
Mimic the dealer – 5.7%
Never bust – 6.0% (est)
Typical casino player – 2.0% to 15%
I found it extremely interesting that a strategy has already been developed that doesn’t involve card counting that gives the house such a small edge, i.e. that developed by Thorpe.
The second paper was “Who’s Counting? Real-Time Blackjack Monitoring for Card Counting Detection” by Zutis and Hoey, 2009. This paper doesn’t aim to evolve a card counting strategy, rather it attempts to highlight players that may be using card counting to swing the edge in their favour. Zutis and Hoey state that “70-90% of the edge developed by a player is applied by changing the size of the bet as the count fluctuates, whereas the remaining 10-30% of the advantage goes towards the ability to alter game decisions which, therefore, lead to a higher proficiency.”
My aim is to develop a series of card counting strategies and compare them in terms of profitability and simplicity. For example, if a system is very simple, but you break even, then it is not really worth doing. However, if the system allows you a massive advantage, but it is not humanly possible to carry it out, again, it is no use.
Since the majority of the edge developed by the player through card counting is via fluctuating bet size and that Thorpe’s Basic Strategy provided the house with the smallest advantage I decided to implement a basic game of blackjack and implement Thorpe’s strategy using card counting to influence bet amounts. The basic game consisted of the normal game, minus the option of split and double down and all aces are counted as 11. Each game cost $10 to play and the player started with $1000. The fitness of each player was based on the number of hands played until the player went bust. After 500 generations I found that my average number of hands played was very similar to that if I had just used Thorpe’s Basic Strategy without card counting (around 1,600 hands), whereas on occasion the maximum number experienced in a generation topped 10,000 hands. I decided that my fitness function needs more work and that I should probably look to rate fitness based on average and variance of the return. In this way I can reward good play instead of potentially rewarding lucky players that won through high risks.
That’s all for now.