Probability Blackjack
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
Probability of Blackjack
2190 Words 9 PagesMathematical 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
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- But I'm not quite sure how to calculate the math behind this and how to calculate the probability for winning a single blackjack hand. I figured with 10,000 credits, I can start my bet at 1, then go to 2, then 4, etc (doubling my bet everytime I lose). This allows me to lose up to 12 hands before I am bankrupt.
- Probability Guide to Gambling: The Mathematics of Dice, Slots, Roulette, Baccarat, Blackjack, Poker, Lottery and Sport Bets Barboianu, Catalin on Amazon.com.FREE. shipping on qualifying offers. Probability Guide to Gambling: The Mathematics of Dice, Slots, Roulette, Baccarat, Blackjack, Poker, Lottery and Sport Bets.
- Probability of obtaining a blackjack from the first two cards is P = 32/663 = 4.82654% in the case of a 1-deck game and P = 64/1339= 4.77968% in the case of a 2-deck game. Similarly, we can calculate the following probabilities.
- 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.
Blackjack Probability Worksheet
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