By: Jonathan Quenzer

To have a computer learn how to play Blackjack through reinforcement learning Computer starts off with no memory. After each hand is played, the computer learns more. Goal is to have computer make the best possible decision of how much to bet and when to hit/stay Splitting hands and doubling down will not be included. This decreases the odds of winning.

The dealer has a 5-8% advantage depending on the specific rules without using card counting The player through correct strategy and using card counting can obtain at most a 2% advantage on the dealer

I wrote a Matlab program to simulate Black Jack. Feature vectors were generated by running the program and analyzing each hand played. All of the features were scaled to have a mean of ½, minimum of 0, and maximum of 1.

Hand History Ace The number of cards remaining in the deck for each value of card 2 … 10 PTPlayer Total Without Aces PANumber of Aces in Player's Hand DSCThe Dealers Showing Card Hit/Stay+1 = Hit, -1 = Stay Win1.5 = Black Jack, 1 = Win, 0 = Lose Lose1 = Lose, 0 = Win Push1 = Push, 0 = Win Feature Set Hit/Stay Ace The number of cards remaining in the deck for each value of card 2 … 10 CC Calculated Card Count: Hi-Opt II used PTPlayer Total Without Aces PANumber of Aces in Player's Hand DSCThe Dealers Showing Card Hit/Stay +1 = Hit, -1 = Stay: Opposite of Hit/Stay from Hand History if the player lost Feature Set Bet Amount Ace The number of cards remaining in the deck for each value of card 2 … 10 CC Calculated Card Count: Hi-Opt II used Bet Min/Max +1.5 if hand was Black Jack, +1 if won, -1 if lost = Classification

Example of 5 nearest neighbors Neighbors sum to +3, so decide to Hit

Computer started with no knowledge The player gained advantage over dealer using 10 nearest neighbors

Computer simulated three players playing 1000 hands Computer started with large feature set from 5000 hands