Probability in Card Games: Poker and Blackjack - Coursework Example

Your Probability in Card Games: Poker and Blackjack Our world is full of probabilities. We may come across probabilities in some disguise, such as, chance, likelihood, odds, ratios, and percentage. Whether it is our everyday life, card games, natural science, weather, or natural expectancy, probability plays a critical role to make us understand them. Probability is defined as, “… a branch of mathematics that deals with the likelihood that one outcome or another will occur. For instance, a coin flip has two possible outcomes: heads or tails. The probability that a flipped coin will land heads is 50 % (one outcome out of two); the same goes for tails” (Hanks). In poker and blackjack, your knowledge of mathematics plays the key role in determining success. In order to take control of profit and risk and to keep the stress levels low during game, players must know mathematical statistics. Poker and blackjack involve cards with values and a goal, and a player is required to draw as close to a certain value as possible without going bust. Throughout the history, poker and blackjack’s expert players used card counting in one form or the other. However, Edward O. Thorp made it a hit among masses. In today’s gaming scenario, the game is as beatable as it was before, in fact, it’s easier. Probabilities are everywhere in our daily life, from work to sports, board games, medical decisions, weather conditions, and natural expectancy. In this research paper, I’ve explored the idea of probability in poker, blackjack, counting cards and its evolution, and probability in our everyday life. Deterministic and Probabilistic Models It is absolutely critical that we understand the difference between theory and reality. Theory refers to the idea that is proposed in order to explain certain real world phenomenon, for instance, approximations and models of reality. Theories are not always right. Therefore, theories are continuously refined through scientific process. There are deterministic and probabilistic models to deal with it. In order to measure the total area covered by a certain lake, we measure radius and apply it to A = πr2.The formula used here constitute a deterministic model. On the other hand, while tossing a coin, no matter how much measurements we take, we cannot be certain of the outcome. In this situation, we consider a ½ chances or probability of heads as well as tails in a single toss. This is called probabilistic model of reality (Scheaffer and Linda 3). Probability in Poker In poker and blackjack, mathematics and its rules are major underpinning. While psychology plays an important part in every decision you make, mathematics is the key element during that decision making process (Hanks). When we consider probability in deck of cards instead of coin, the number of possible outcomes is much greater. There are 52 cards in each poker deck, each assigned by one of four suits, such as, clubs, hearts, diamonds, spades, and one of the thirteen ranks, i.e., the numbers two through ten, Jack, King, Queen, and Ace. It implies that odds of getting an Ace as first card are 7.7 percent (1 in 13), and odds of getting any spade as first card are 25 percent (1 in 4).It is said that unlike coins, cards have memory. With dealing each card, you change the makeup of the whole deck. For instance, if you get an Ace as your first card, you are left with only three Aces in the remaining 51 cards(5.9 percent) which is far less than the odds were before getting your first Ace. In both poker and blackjack, strong knowledge of math and probabilities assists expert players to adjust their strategies during the game and increases their odds of success and emotional stability for an intelligent game (Hanks). Probability in Blackjack In blackjack, the odds of some specific outcome can be predicted quite correctly because they are studied extensively. Expert players of blackjack prefer to make best move on the basis of probability of certain outcome instead of preferring to win certain hand. It is very simple to calculate the probability of one card, however, it becomes complex as the number of cards increases. In this process, we need to calculate the probability of drawing a card with its worth as 10 in blackjack. One deck includes 16 cards with worth 10, i.e. 4 10’s, 4 jacks, 4 queens, 4 kings. On the next level, you have to calculate the probability of drawing a card worth 11.In this way, simple method to determine probability of drawing blackjack is to multiply simple probabilities, i.e. (16/52)* (4/52)=64/2704 or (the probability is) 2.37 %. On the other hand, if you factor in the cards that have been played, calculations become more complicated. For instance, if you have dealt one card worth 10 in the beginning, probability of drawing an ace marginally changes to 4/51 since one card is already played. Furthermore, it becomes nearly impossible to calculate the probability in the presence of multiple players on the table. Calculation of blackjack on the initial deal is even more complicated since the probability reduces to .048 percent (blackjack-king). Mathematics of Card Counting Without understanding mathematics of card counting, the game of blackjack can be highly stressful since the chances of losing become higher. It is because mathematics is the system of absolutes. It implies that players’ “choice” of hitting or raising a bet does not really involve choice. A great example of smart card counting is computer that goes only for the action that has highest possible mathematical advantage. Therefore, it is critical to understand mathematical statistics to control profit and risk in the game. There are several factors involved, for instance, expected profit, standard deviation, and exponential profit (V.T). Card Counting use of Expected Profit Expected profit is the likelihood of wining from an abstract mathematical point of view. It is about knowing how much you can win if it is only based on the odds you had against the casino. From this point, one can start figuring out his chances of winning through counting cards (V.T).According to V.T (2014) in terms of mathematics, expected profit from any single blackjack hand is considered to be: A×B=P Advantage × Bet = Expected Profit It is logical to take averages of advantage, bet, and expected profit because we can’t exactly predict what cards one will get. avA × avB = avP Avg advantage × Avg bet = Avg expected profit In case of playing more than one hand, we will multiply profit for every hand played. It generates the formula for card counting expected profit. avA × avB × H = avP Avg advantage × Avg bet × Number of Hands = Avg expected profit According to the formula, increase in any one of three numbers on left side can result in increased expected profit. Moreover, due to the fact that they are multiplied, even a fraction of increase will lead to higher profits in the long run. In the beginning, your easiest bet to raise your expected profit is to play more hands, for instance, playing 2000 hands instead of 1000 will double the expected profit. However, with time, other two numbers will have more and more of an effect. After perfect counting, number of hands played is considered to be the most important factor to make more profit (V.T.). History of Counting Cards in Poker and Blackjack Poker and blackjack involve cards with values and a goal, and a player is required to draw as close to a certain value as possible without going bust. Some of the games are played with an ace of fluctuating values from one or eleven. The game of 21 or Blackjack became popular in Europe because of the skill required to win it in compassion to other games that were merely luck based. Europeans loved the feeling of control given to the player by the decision making power to hit or stand. Americans coined the term blackjack, the term may not be as relevant to the game, but they made up for the lack of their naming skills by introducing two new game rules. The idea of making this game beatable stemmed from these rules. In any European version of the game, you were never allowed to see the dealer’s upcard before making decision. Though, dealers had already made their decision on hit or stand option, they started to follow house’s mandatory pattern of hitting on a 16 or standing on 17(Ofton). During 1820, legalized and house-banked games started in New Orleans. In other places, comparatively less-legalized and player-banked games were quite common. In Nevada, house-banked blackjack started in 1931.With its legalization, game standards and controls were started to be enforced. It was the beginning of card counting, and it took over thirty years for card counting to emerge in true sense. During these thirty years, there were several players who came up with ideas to play it the best way. Their predecessors mentioned some of them while exploring the game further. One of them was Jess Marcum who was often kicked out of casinos due to their inability to understand his continuous winning. Some other interesting characters were named as System Smitty and Greasy John. In 1957, four players named Baldwin, Cantey, Maisel, and McDermott wrote a book Playing Blackjack to Win. They gave explicit references to basic strategy of keeping the track of cards in order to keep the odds in your favor. However, this book wasn’t successful enough to capture the attention of casino or public. Another book published in 1962 Beat the Dealer got much more public attention (Ofton). The author of Beat the Dealer, Edward O. Thorp was a man of numbers as he examined the idea of keeping a record of cards and its possibility to give an edge in game. From here started his astonishing discovery that marked the birth of card counting (Ofton). According to his calculations for single-deck only games, Thorp came up with a “ten-count system”. In this system, you think of two numbers, 16 and 36 in which the former represents tens in deck and later represents the other cards in deck .With every card that is drawn, player counts backwards, and divides the count of the left “others” by the number of tens reaching “Thorp Ratio”, that indicates the player’s edge, and serves as an indication to raise bet (Ofton). Thorp’s book made it big and became bestseller on New York Times list. Though the system was difficult for an average player, but the book led everybody and his brother to already overwhelmed casinos. Casinos were hesitant and scared of the information that beats the game. They started implementing changes and single-deck games became two or four-deck. Dealers stopped dealing the cards before reshuffling. On the other hand, dealers were also accommodating the arrival of new blackjack enthusiasts. It turned out that Thorp’s book in fact profited them hugely. It is because floods of players entered casinos equipped with the information that the game could be beaten, however, either they were not prepared, tolerant, brilliant, or skillful enough to beat it in reality. Therefore, casinos kept winning big (Ofton). In the second edition of Thorp’s Beat the Dealer, 1966 computer scientist Harvey Dubner incorporated a counting system known as the Hi-Lo Count and Julian optimized it. With the arrival of computers, blackjack players got the opportunity to attack the game even if it is changed by casino. This modified counting system enabled players to determine their edge in a quick and easy manner even when the number of decks increased. Casino owners kept the game interesting by inviting people to try to beat the game. Pit bosses and dealers started to provide players with the basic strategy cards at the table. They freely offered the information that Thorp’s book recommended when difficult playing decision showed up. By doing so, they created a false sense of comfort for players, however, the information never went far to help average player who eventually ended up becoming a losing player. On the other hand, for dealing those who can actually beat the game, Las Vegas private detective devised a strategy. He compiled a book illustrating the information about known or suspected card counters and made it available at every casino in town. It relieved them from investigating each counter and, apparently, they were able to work together to beat card counters (Ofton). In 1971, Al Francesco started working out ways to avoid defeat in blackjack. He came to casino with his brother who was also a card counter. When his brother sat, Al Francesco stood beside the table apparently engaged in conversation. Every time his brother placed a big bet, Al Francesco offered a $100 bet out. He did that because he was aware of the advantage he had, regardless of not having gained the positive count himself. The Pit Boss flattered all over Francesco and he became the first big player of card counting in history. He also trained other people to count and signal him. These people include Pacific Stock Exchange president Ken Uston. However, Uston published a book about card counting during 1977 which influenced people and led to immediate proliferation of team play, such as, MIT team and Tommy Hyland team. Both of these teams started after one year of the book was published. MIT team received huge appreciation among masses through bestselling books, such as, Bringing Down the House, and in Hollywood with blockbusters, such as, 21.Stanford Wong published Professional Blackjack in 1975.He devised table-hopping and back-counting tables. In today’s gaming scenario, the game is as beatable as it was before. Though, not in the ways it was in Thorp and Francesco’s time, but card counting is far more possible than ever. Recently, Ian Anderson has written about the ways of getting an advantage in modern times (Ofton). The Rules of Card Counting Harvey Dubner developed a simplified version of Thorp’s strategy regarded as “Hi-Lo card counting strategy” or “point count system” (Patterson qtd. in Zimran et al., 7). According to Zimran et al., to start, player has to assign a value to each card which is dealt: Card Value Count 2,3,4,5,6 Count +1 7,8,9 Count 0 10,J,Q,K,A Count -1 A framework for card counting Source: (Zimran et al., 7) According to “Blackjack Strategy” (2009), the table demonstrates: “…cards 2,3,45 and 6 are valued at plus one ;cards 7,8 and 9 are valued at 0; and cards 10, J,Q,K and A are valued at minus one. As the cards are dealt, the player keeps a “count.”The higher the count, the more likely it is that the player will get “Blackjack” (21 points in two cards) or that the dealer will bust, leading the player’s expected value to be positive. When the count is low, on the other hand, there are comparatively more “low” cards in play than “high” cards; the player no longer has an advantage over the dealer, and as a result, his expected value is negative. Thus, when the count is “high” the player will place large bets, whereas when the count is low, the player will place the minimum bet possible” (qtd. in Zimran et al., 7). Probability in our Daily Lives Probabilities influence every big and small decision in our everyday life. In pregnant women, doctors look for the probabilities of having certain genetic disorders. Before a surgery, doctors inform patient about the chances of recovery or complications. Moreover, before you buy a car, you can find out probabilities for almost every aspect of the vehicle, such as, chances of repair, likelihood of car lasting certain number of miles, or your chances of surviving after a crash or overturn, later is another chance on the basis of whether you are wearing a seatbelt or not (Rumsey 11). Similarly, in natural or social sciences, only a few results are considered to be known as absolute. It is more likely that they are presented in term of chances and probabilities. Some examples of everyday life probabilities include: chance of you getting a certain degree; surviving or catching certain disease; chances of getting an annual income of $60,000 in next two years, and chances of winning a certain party in elections. In today’s world, it is critical to understand and be able to make probabilistic inferences for decision making (Scheaffer and Linda 1).In daily life, the concept of probability can be seen at work, in sports, board games, medical decisions, weather conditions, natural expectancy, and many other instances. Probability can be determined for individuals and groups as well. It might be easier to apply it on a larger group than individual, however, it primarily depends on the situation, for instance, playing instant lottery. Let’s suppose that the chances of winning in a lottery is 10 percent or 1/10.It means that in the long run 10 percent of over thousands of tickets will win while other 90 percent won’t win. It does not imply that if you get 10 tickets, you will have a chance of winning one. In some cases when we cannot figure a mathematical formula or model for probability, the approach of relative frequency is used (Ramsey 14). Works Cited “Game of Blackjack-Probability of Getting 21.”Blackjack-King.2007.Web.21 Novermber.2014. Hanks, Gerald. “Poker Math & Probability.”pockerology.pockerology.com, n.d. Web.18 November. 2014. Ofton, Loudon. “The History of Blackjack.” Blackjack apprenticeship.Blackjack Apprenticeship.n.d.Web.19 November.2014. Rumsey, Deborah. Probability for Dummies. Indiana: Wiley Publishing, Inc., 2006.Print. Scheaffer, L. Richard, and Linda, J.Young. Introduction to Probability and its Applications.3rd ed.Boston, MA: Brooks/Cole, engage Learning, 2010.Print. V.T., “Blackjack Card Counting Tricks.”V.T. (2014).eBook. Zimran, Ariell, Anna klis, Alejandra Fuster and Christopher Rivelli. “The Game of Blackjack and Analysis of Counting Cards.”Annaklis.2 December.2009.Web.4 December.2014. Read More