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
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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
Always choose the opposite of the card you chose. So if it is an O choose X, if it is a X choose O.
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Starting off: Each Player is dealt 7 cards. Before the first hand is dealt, players must shuffle the deck, and choose a random card from the deck. The lowest card chose has to deal. After this, the dealer must deal 7 cards to each player in a clockwise rotation and flip one card face up on the table. A player can have up to 7 cards in their hand at a time.
Narrative Tension - This game determines who gets to deals first, set the full deck of cards in front of players then they cuts out from the same deck. For two players, a dealer deals six cards each; for three players, a dealer deals five cards each and one of the cards off to the side; for four players, a dealer deals five cards each sitting opposite each other.
case presents an excellent example of the application of tight action controls in the table games
Once again, spreading cards in a certain way achieves a specific objective – in this case, to control a selection to the top.
For example, suppose the target number is 20 and the cards in play are 5, 4, 6, 2, and Ace (in the case making the Ace worth 1). One winning combination is: (5 x 2) + (4 + 6) / 1 = 20.
I have decided to focus this math exploration project on the mathematics within the leisure card game Texas Hold’em. On first impression, the outcome of any poker game seems to be entirely arbitrary and based solely on the player’s pure luck. However, after we dismiss the wildy exaggerated poker “legends” we see in myriads of television programs and movies, in reality experts in the game of poker who are just able to have a higher win rate than amateurs do exist. If this game is simple based on random fortune, there would not be the various competitions held worldwide each year and the game would have been a lot less interesting. The strategies within poker games consist of two categories, mathematics and psychology, with the former determining and altering the latter. Therefore, in this investigation I would seek to explore the factors in the first pre-flop that sets the tone for the duration of the round; how would the initial hand determine what would be advantageous in the flop; and what distinguishes experts from the amateurs.
In further exploration of their tactics the security team sends an attractive woman who finds Raymond alone in the casino's bar. She is able to get Raymond to allude to his and Charlie's system of counting of cards. Later, security asks to speak to Charlie privately and suggests that Charlie take his winnings, about $80,000 and leave.
This game of Texas holdem is a new age of poker the basic way the game is played is as follows. First the dealer deals each player two cards and the player then bets on the cards in his or her hand. After each player acts the dealer burry’s the top card then deal the flop which is the first three cards face up in the center. These cards can be used by all the players and each player uses them to make the best five card hand. After a
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Shuffle the entire deck of cards. Deal out the selected number of cards to each player one at a time, faced down and starting with the player on the left of the dealer. After the cards have been dealt, flip over one card from the shuffled deck, facing up. If the face-up card is one of the twenty power cards of Crazy Eights, then return the card into the deck and reshuffle to draw again.
Black Chip Poker is one of the few U.S. facing online poker sites that continues to provide a quality poker experience to Americans even after the infamous Poker Black Friday. In our Black Chip Poker Review for 2016, we’ll go over all of the great features that keep poker players interested and having fun on this unique poker site.
Community cards are cards that the whole "community" can use and there is five of them. Together will your two hole cards whoever makes the best five card hand wins. In regards to the community cards, they are dealt face up in the middle of the table. The first three cards dealt are known as the flop, then the turn and finally the river. The river is your last chance to catch the card you have been waiting for to make your hand a winner. Before and after the flop as well as before and after the river there are rounds of betting. The first two people to the left of the dealer must place a forced bet called the blind. Blinds are to assure there is always money in the pot. In order to see the flop everyone must call the amount of the blind or fold depending on their hole cards. There are four ways to bet, Check, Raise, Fold and Call. Checking means you are betting nothing and passing bet to the next player. Raising is obvious, it means you are putting more money into the pot. Folding is when you do not want to call or your cards are so bad you don't even want to check. And finally, calling is when you match the raise made by another player to see the next card. You have all four options to choose from except when a player has bet before you and then you cannot check.
1. High card – This is based upon the one card of highest value in the players hand.