Blackjack Probability Chart
- According to my blackjack appendix 4, the probability of an overall win in blackjack is 42.22%, a tie is 8.48%, and a loss is 49.10%. I'm going to assume you wish to ignore ties for purposes of the streak. In that case, the probability of a win, given a resolved bet, is 46.36%. The probability of winning n hands is a row is 0.4636 n.
- After accounting for the probability of a dealer blackjack, the 'grand total' return is reported as -0.485 percent, or about one-half of one percent of your original bet for this set of playing rules.
- If you want to learn perfect blackjack strategy, I advise you to learn one chart at a time. Also, if you know you’ll be playing a specific type of blackjack (e.g. 6 decks, dealer hits on soft 17) at a casino, just focus on the charts that are applicable to the game you'll be playing.
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
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
Blackjack Percentage Chart
Blackjack Probability Tables
In the first table you can see your odds according to dealer up card. The second table demonstrates the dealer probability of having a different outcome depending on the first card. You may also try our other blackjack tools created for counting odds, generating strategies and training players.