Simulation of Blackjack. Able to run experiments that play a large number of rounds. Does calculation of player edge for a variety of strategies.
pip install jupyter
pip install pandas
pip install matplotlib
For list of installed packeges, see requirements.txt file.
Player Edge means the percentage advantage that the player can expect in the long-run when playing a particular strategy for many rounds in a long session. For most strategies, the Player Edge is negative, meaning that - in fact - the House has the edge.
For example a Player Edge of -1% means that. on average, the player will be down by 1% of their staked money by the end the session. In this case, if the player stakes a total of £100, they can expect to be left with just £99 at the end of the session.
A positive Player Edge means that the player is likely to be ahead at the end of the session :)
Cards are represented as tuples, (name, value_list, card_value).
For example,
("6♥", [6], "6")
("10♣", [10], "10")
("Q♦", [10], "10")
("A♠", [1, 11], "A")
card_value is used to lookup cards in the strategy tables described below. All cards worth 10 points have a card_value of "10". Aces have acard_value of "A".
The Shoe is configured to contain 4 packs of cards. It is configured to have remaining cards discarded, and the shoe re-filled with a fresh set of 4 packs of cards when the penetration level of 75% is reached. Both of these settings can be altered by changing these attributes of the Shoe class,
self.decks = 4 # Number of decks in the shoe when full.
self.penetration = 75 / 100 # Percentage of cards to be dealt before refilling shoe.
At the end of each game, the replenish method is called, to check whether the shoe has been depleted below the penetration level. If it has, then the shoe will be re-filled and all cards in the shoe shuffled.
A Blackjack can only be won with the first two cards of the first hand of a game. The attribute blackjack_value of the Table class is set to "3 for 2", which is the standard Blackjack value in Vegas casinos (stake also returned).
self.blackjack_value = 3 / 2 # Eg. £10 bet wins £15.
The following strategies are implemented in the program.
Implemented in the dealer_stategy method. The most basic strategy; it is the strategy that dealers must follow when playing the House's hands in Vegas casinos. It is also possible to run experiments where the player uses this strategy too.
If current value of hand is 16 or less, then Hit, otherwise Stand.
As illustrated on this card, https://www.ebay.co.uk/itm/303101632202
More details here, https://github.com/johntelforduk/blackjack/blob/master/basic_strategy.md
Basic strategy has 4 sections, implemented in 4 methods as follows,
basic_strategy_section_1 : Basic rules about when to Hit or Stand.
basic_strategy_section_2 : Double Down rules.
basic_strategy_section_3 : Special rules when the player has an Ace in his first 2 cards of the hand.
basic_strategy_section_4 : Rules for player hands with matching card values, which may be Split.
These rules form a hierachy. For example, if the conditions for Section 4's rules are not met, then Section 3 is tested, and so on.
Hi-Lo card counting is described here, https://youtu.be/G_So72lFNIU
The effectiveness of Hi-Lo card counting strategy can be tested by the program. A running count of cards dealt from the shoe (face up cards only) is kept. The true count and recommended bet size is also calculated.
Card counting varies the size of the initial bet in each round. But after the bet is made, Basic Strategy Section 4 is used to play the hand(s).
The program can be used to automatically do a Study, which consists of many sessions of Blackjack. Each session is like sitting down at a table and playing many rounds. Statistics about the sessions are stored, and then analysed.
amount_won_or_loss is subtracted from each time money is staked, and added to each time money is won. total_staked is added to each time money is staked.
When a study of many sessions is completed, the win_loss list is appended to.
# Multiply by 100 to make it a percentage.
self.win_loss.append(100 * this_table.amount_won_or_lost / this_table.total_staked)
More sophisticated strategies return (on average) a better edge for the player.
Shoes that are replenished at higher penetration levels, and which are replenished with fewer decks of cards, return (on average) a better edge for the player.
Rules of Blackjack https://youtu.be/XYgdLMcPspo
Blackjack terminology, https://en.wikipedia.org/wiki/Blackjack and https://www.blackjackapprenticeship.com/glossary-of-blackjack-terms/