ContentsRationale: 1Introduction: 2Step 1: Mastering the values assigned to each card in the deck. 4Step 2: The Running Card 5Step 3: Multiple Decks Running Count: “True Count” 8Step 4: The necessity to alter your bets depending on the actual count value. 10Conclusion 10Works Cited 11Figure 1Different cards and their weighted values 5Figure 2 Using Weighted values to calculate a running card. 7Figure 3 Round 2 has a running card sum of 1 7Figure 4 Round 3 has a running card of 1 8Card Counting BlackjackNameInstitutionDateRationale:As part of the semester curriculum, a student must choose a topic that meets the Internal Assessment provisions in line with Mathematics. This paper intends to demonstrate how mathematical principles of probability and statistics correlate with the controversial card counting tricks used in Blackjack gambling. The article is broken down into steps that illustrate how players employ probability and statistics to calculate odds when dealing cards. However, the underlying concepts of card counting are not as simple as many might perceive, it takes a lot of practice, skill and hard work to master the fundamental principles.
This topic is selected for study because it is intriguing to learn how gamblers earn a lot of bucks from blackjack by merely applying simple mathematical skills. No wonder most casinos nowadays prohibit card counting in their Blackjack games (Snyder).This article will illustrate that the mathematical skills used in blackjack marry well with the basics of Statistics and Probability taught in the Math SL course. Moreover, the paper will not only outline the critical steps involved when counting cards and predicting moves but also use images and real-life examples to give a visual impression of the entire process. At the end of the paper, the reader should acknowledge and marvel at the Blackjack skills that players use to calculate probabilities in their heads at high speeds while paying attention to the game.
Introduction:Blackjack is a universal game witnessed in casinos, and people make a living out of it. The game, commonly referred to as ‘twenty- one’ has risen to fame and caught the attention of many gamblers across the globe. Hitherto it is preferred as the most lucrative banking game across Europe and America, and its contagious charm is spreading fast to Asia and Africa. People are trying their luck with this game because it is simple to play and it accommodates many participants. However, the player usually competes against the dealer and not the other competitors. To win, one needs to ensure that his or her cards attain a better value against the dealer amid a particular set of rules. With a total of 52 cards on the deck, the player must beat the dealer at achieving 21 points using the first two cards.
However, the count should not exceed 21 points. Smart players who have learned the art of predicting this game end up collecting vast stacks of cash, and they are not willing to share the secret and math behind it. Thanks to Math IS, you are going to be enlightened.Using Statistics and Probability mingled with a high level of intuition, a player can formulate a mental algorithm that will help them calculate their next moves and judgment on whether to stake more or less.
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Gamblers achieve this by counting the remaining cards on the table and then apply a probability algorithm to predict if the next card will be sufficient enough to beat the opponent (Wattenberg). Some companies have barred gamblers from counting cards in their casinos. Although such practices are legal by law, corporations are justified in denying such services to anyone in a bid to balance tradeoffs. In other words, counting is not by any means a form of cheating but casinos value level grounds that are free of prejudice against the dealers.How does this card counting circus work? Well, a gambler knows that if the number of Aces and Tens dealt are less than those remaining in the deck (commonly referred to as Shoe), he or she will be handled more blackjacks (which earn a profit of 150% depending on your stake). Consequently, the dealer is likely to bust or in other words overshoot the 21 points occasionally target (Burton). Contrariwise, if the number of small cards in the shoe is higher, the contestant gets fewer blackjacks, and the dealer is less prone to busts.
A competitor can use these scientific realities to stake more top gambles when there are more high cards left in the shoe or spread their risks by staking low when there are more low cards left. Nonetheless, applying these principles in real life is an uphill task, it takes a lot of effort and determination to master these concepts and effect than in real life. For a practical card counting ordeal, this paper highlights the four significant steps involved:1. The first step is to master the score values assigned to each card of the deck.
2. Then, one needs to be aware of the “Running Card” which is vital when evaluating the next card to be dealt3. Third, use the information acquired in step 2 to calculate the “true count” of cards in each deck.4. Use the actual count value as feedback in each step to predict your future bets. The article has summarized the primary and most essential steps undertaken to count cards effectively during a Blackjack card game. Now, the subsequent section will elaborate a detailed explanation of what each level means and what it entails in a clear and logical manner.
Step 1: Mastering the values assigned to each card in the deck.Point of Values:1. Low cards: these cards represent a value of +1. They include cards 6, 5, 4, 3, and 2. These tickets are valuable in the hands of dealers, and a score of 17 and below prompts them to take a hit. Furthermore, the dealer is less likely to get a bust (score of more than 21) if they have more low cards in their hands (www.
wikihow.com).2. High cards: these cards represent a value of -1. They include maps Ace, King, Queen, Jack, and 10. These are the cards that mostly favor the player during the game. When the card deck has a higher number of 10s and aces, it will undoubtedly increase the chance of a player getting a “Pat hand” (17 points or over) or the natural 21.
3. Neutral cards: in the Hi/Lo count carding method, these cards represent a null value; they include cards 7, 8, and 9.The Hi/Lo system is the most preferred method of counting cards. It assigns values to every single card such that the resultant value of the 52 cards in the pack is zero.
In other words, the deck has a balanced distribution of high and low cards in the deckFigure 1Different cards and their weighted valuesStep 2: The Running CardAfter learning the values assigned to various high, low and neutral cards and getting acquainted with all card types, it is vital to know how these cards are added or subtracted in every shoe as the game goes along. To make the counting of the cards quick and easier to memorize, the paper proposes an “easy speed tip”: the “plus one” for low cards assumes a value of “one” whereas the “minus one” high cards of are referred to as “M-one.” The neutral cards remain null and represent a zero value. For example. Queen = M-one, 8 = nothing, and 2 = one. Cards are distributed from single card deck and added and subtracted as the following:- 1st card: Ace (+1), total: M-One- 2nd card: King (+1), total: M-two- 3rd card: 8 (0), total: M-two- 4th card: Queen (+1), total: M-three- 5th card: 4 (-1), total: M-two- 6th card: 2 (-1), total: M-one- 7th card: 3 (-1), total: even (say anything)- 8th card: 7 (-1), total: One- 9th card: 9 (0), total: still OneA more complex and illustrated example can be represented belowFigure 2 Using Weighted values to calculate a running card.
For this round, we can see that the running card has a sum of 0 (-2+1+1+0 = 0) Figure 3 Round 2 has a running card sum of 1For our second round, the running card is +1 (0+0+0+1 = +1)Figure 4 Round 3 has a running card of 1In our last round, the running card is also +1 (0+0+0+1 = +1)From these three examples above, it is clear to see that, when it comes to counting cards, the player should count the running card for every single round, and repeat the process until the game is over or shuffled. However, recent blackjack games use two decks of cards, and it becomes a risky affair to start betting using the skills discussed above. Two decks can make it difficult for you to evaluate your assumptions and probabilities when staking your money (Shi). In the past, when the game was played on a single deck, counting cards was an easy task for experts. They could bet with certainty because their probabilities were relatively accurate and safe. Based on a single deck, if the calculated running card has a positive sum throughout the rounds, the player is more advantaged, but if the sum is negative, the advantage goes to the dealer.
Therefore the player should always memorize and keep track of such values when staking to avoid losses and gain profit. Step 3: Multiple Decks Running Count: “True Count”Most casinos use multiple decks in a Blackjack game as a strategy to complicate the card counting process. But some professionals have found a way to maneuver through numerous tiers by employing an additive plan known as the True Count Strategy. This new algorithm is a supplement and works in tandem with the previous concepts to achieve the card counting process in multiple decks (www.blackjackapprenticeship.
com). The professionals borrow the information collected in the initial steps discussed above and translate them into the True Count analogy. Having a counting card sum of +5 in a game with six decks remaining is an entirely different case to when you have an amount of +5 with single layer remaining. For the players, the concentration of high cards compared to the frequency of low tickets matters a lot, but it is not the only factor to consider. For instance, with the counting card value of +5, there will be less than one high card in each of the remaining five decks, meaning that a card counter still will not have the ability to favor them.
In the case of a single pack with a counting sum of +5, the remaining deck will have five other 10s and aces within the 52 cards of the box. This True Count information is precious to the player.To calculate the True Count, we use the following formula:When looking at a scenario of a counting card of +8 and with only two decks remaining, for example, we would substitute this information into the equation:Let’s look at another example: +10 with five decks of cards remainingBonus Tip: How a player can calculate an edgeIn a multiple blackjack game, the true count value is handy since it informs a player their level of an advantage at any point in the game. One can obtain the true count value in multiple decks simply by dividing the existing running count value against the number of decks that are yet to be dealt. For instance, a universal six deck blackjack game will shift the house edge by a half percent in favor of a player for each true count value. A true count value of one would essentially even out the game by erasing the house edge.
A true count value of two will shift the house edge by a margin of a half percent towards the player hence the game plays to his or her advantage. A true count value of three will imply that the player benefits from an upper edge of one percent. However, the rules employed and the number of cards dealt before a reshuffle can alter true count benefits.True Count Deviation:Step 4: The necessity to alter your bets depending on the actual count value.Throughout the game, it’s imperative to when the house edge flips into the player’s favor by establishing a running count and a corresponding actual count. Players who do not align their game concerning the shifting edge values are prone to unnecessary exhaustion with little or no benefits. Capitalizing on the exact count information means raising the stake when edge values flip to your favor and folding hands when the situation is not favorable. In other terms, increase your bets when the actual count values rise and stake low when the costs fall to a neutral or negative.
However, these strategies can somehow get complicated if one lacks sufficient knowledge and underlying principles in betting. Blackjack gambling can indeed cause severe damage to your bankroll if you don’t correctly understand laws of probability and statistics.ConclusionBlackjack is a productive game that has won its place in the hearts of many gamblers. Veteran professionals who have mastered the gambling art hitherto have collected vast sums of money from this game by merely using accrued skills and intuitions. The most intriguing thing about this game is how it applies mathematical concepts: statistics and probability to predict moves and regulate stakes. The paper has outlined the fundamental steps required to achieve this process while highlighting how mathematical concepts blend in. Be warned that irresponsible betting can damage one’s bankroll regardless of the one’s prowess in betting strategies.
This paper recommends a further look at how statistics and probability influence reasoning and decision making in other games.Works CitedBurton, Bill. Blackjack Card Counting.
8 March 2017. Article. 15 January 2018.
Shi, David. What is the mathematics behind card counting in Blackjack? 18 October 2014. Article. 14 January 2018.Snyder, Arnold.
Big Book of Blackjack. Cardoza Publishing, 2013. Book.
Wattenberg, Norm. Modern Blackjack Second Edition. Lulu.com, 2010. Book.www.blackjackapprenticeship.com.
What is Card Counting? 10 September 2000. Article. 14 January 2018.www.wikihow.
com. How to Count Cards. 2 February 2017. Article.
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