Casino Math Research Paper

1740 Words7 Pages
Mathematical Exploration
Casino Math – Blackjack

Introduction
I have decided to explore the topic of casino math in the mathematical exploration.
Casino games have been gradually growing more popular to the public as time progresses. Blackjack, or “21”, is indeed one of the most popular played games among as it does not require “mind games” between players and that it is certainly a game between no one else but each player and the dealer. Although Blackjack seems like a game that is based completely on luck, there are actually decent mathematical studies behind the game. As one who has been highly interested in card games and especially Blackjack since childhood, this is the perfect opportunity to investigate and evaluate the mathematics
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When two decks of cards are used, there are a total of 104 cards where there is 8 cards for each of the numbers Ace – 9 and 32 cards that represent 10 (10, J, Q, K).
The sample space of the 2 initial cards for players and for dealer in Blackjack can be presented by the following 2-Dimensional Grid:

Through the 2-Dimensional grid, we can see that the probability of getting a card that represents 10 is relatively higher at 0.31 in comparison to cards Ace – 9 at 0.077.
The probability of a certain card drawn from 2 decks of cards can be calculated through the equation: P(A)=(the number of members of event A)/(the total number of possible outcomes)=n(A)/n(U)
Generally, the probability of drawing a certain card from the decks of cards can be shown by the following calculations:
P(10)=32/104=0.30769≅ 0.31
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House advantage, also known as house edge, is the long-term percentage of the wagered money that will be gained by the casino. In the game of Blackjack, if we are to neglect casino math at a higher level such as probabilities and expected values, we can only memorize basic strategies people came up with that may not be the best under differing situations or use general card-counting methods to get an approximate idea of what the rest of the deck of cards are consisted of. These strategies may not be very useful in all situations and can even lead to undesirable
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