Blackjack Probability

Mathematical Studies Project
Probability of Blackjack
Content Page
Page
Statement of task 2
Introduction 3 - 4
Data collection 5 - 6
The four Blackjack strategies 7 - 15
Conclusion 16
Bibliography 17
Statement of Task
This project aims to investigate how mathematics works in one of the most popular card games in the world - Blackjack. It examines the probability in the Blackjack and how the use of mathematics can be…show more content…
Blackjack strategies
Strategy I Hit when the sum of the first two cards is less than the dealer’s upcard
Let x be the player’s sum of card values of the first two cards.
Let D be the dealer’s upcard(the second card).
If x < D, the player should always hit.
When x < D, it is obvious that x must be less than the dealer’s final value (covered card + upcard), given that the sum of the first two cards of the dealer is[pic]- no busting. Therefore, under this situation, the player must hit. Otherwise, his probability of winning is 0.
Strategy II Hit or Stand
If the hard total is 11 or less, the player should always hit. This is because no matter what card the player is getting, the total hand value will not exceed 21. By using the Hit ot Stand strategy, the house edge can be cut to as low as 2%.[1] Fig. 1 is the decision making chart when using this strategy.
Card A 2 3 4 5 6 7 8 9 10 J Q K Real value 1 11 2 3 4 5 6 7 8 9 10 10 10 10 A 1 2 12 3 4 5 6 7 8 9 10 11 11 11 11 11 12 22 13 14 15 16 17 18 19 20 21 21 21 21 2 2 3 13 4 5 6 7 8 9 10 11 12 12 12 12 3 3 4 14 5 6 7 8 9 10 11 12 13 13 13 13 4 4 5 15 6 7 8 9 10 11 12 13 14 14 14 14 5 5 6 16 7 8 9 10 11 12 13 14

The Blackjack Probability Edward games do not offer 'real money gambling' or an opportunity to win real money or prizes. The Blackjack Probability Edward games are intended for an adult audience. Practice or success at social casino gaming does not imply future success at 'real money gambling'.

Blackjack Probability Puzzles

Blackjack Probability To Win

Mathematical Studies Project Probability of Blackjack Content Page Page Statement of task 2 Introduction 3 - 4 Data collection 5 - 6 The four Blackjack strategies 7 - 15 Conclusion 16 Bibliography 17 Statement of Task This project aims to investigate how mathematics works in one of the most popular card games in the world - Blackjack. Probability is calculated on the basis of known data but cannot be used to predict exact outcomes, like the outcome of a hand in the game of blackjack, for example. It simply shows you the likelihood of an event happening, based on the knowledge of the number of desired outcomes and the number of all possible outcomes. The bust probability is calculated by dividing the number of Dealer's busted hands to the total possible blackjack actions. Blackjack actions is a parameter that counts everything: Busted hands, pat hands (17 to 21), blackjack hands, and draws or hits to the first 2-card hands ( incomplete hands ). The probability to get a blackjack (natural): 64 / 1326 =.0483 = 4.83%. 2) Let's do now the calculations for arrangements. (The combinations are also considered boxed arrangements; i.e. The order of the elements does not count). We calculate total arrangements for 52.