The Application of Probability in the Game of Poker - Coursework Example

Prompt Most who study mathematics never understand how the knowledge acquired can be applied in real life situations. For most this knowledge is only used to write and pass exams. This paper aims at demystifying this myth by focusing on how probability can be used in the world of poker. Writing goals 1) Examine the difference in how poker players and mathematicians approach and understand the game of poker 2) Explore how the study of probability theory helps one to win a poker game 3) Discuss ways in which professional poker players and mathematicians use probability to win a poker game 4) Evaluate whether or not studying probability always makes one win a poker game The Application of Probability in the Game of Poker Introduction Gambling is defined as the staking or pledging of valuable items such as money and property on a result that is partially determined by chance. There are three major categories of gambling, and these include: betting, gaming and lotteries (Rickwood, et al 1). Regardless of the nature of the gambling, players have to expect that they will likely lose a certain fraction of the amount they have gambled with. Because gambling is legalized in many countries, the number of people engaging in these activities has increased. For all gamblers, there is the desire to make profits out of this activity, and this requires that they have a higher chance of that event occurring. One of the common card games people engage in today is poker. It is played with a deck of fifty two cards. The ranks of a player’s cards and the combinations of these cards help determine the winner. In order to win big, players risk larger sums of money, hoping that they do not lose. Therefore, poker, just like any other gambling activity, is purely based on chance. In mathematics, one of the widely covered topics is probability, which is the study of the likelihood of an event occurring. For this reason, poker is directly related to this mathematical concept because outcomes are based on chance. Although most people question the importance of studying mathematics in school, the application of mathematical concepts in the real world are varied. Probability, which is a branch of mathematics, is one of the most used concepts in the world. This research aims at demonstrating how probability is used in gambling by focusing on the game of poker. First, this paper will offer an overview of how poker layers approach the game without the use of probability. This approach will be contrasted to that taken by mathematicians. Secondly, this research will highlight how mathematicians apply probability in a game of poker. Given that poker, like most other gambling activities, is based on chance, the application of probability theory in the game of poker is important in estimating the outcomes of the game. How poker players approach the game of poker The approach taken by most poker players is based on their experiences, with less focus on mathematics and probability. For most poker players, there is strong belief in experience, skill and luck. Most players have an illusion of control in which a person believes s/he has the ability to understand and determine the outcome of uncertain events. In a research conducted by Andrada-Mihaela Istrate (2011), the author attempted to understand the game of poker through the experiences of poker players. Specifically, the author interviewed players from Bucharest who use this game as a means of subsistence. In his research, Istrate (2011) was able to highlight how poker players approach this game. The author notes that psychological poker players are seen as those who have the ability to read their opponents with a high level of accuracy based on tiny or non-existent clues (Istrate 55). Experienced players are those that have the ability to make accurate predictions of their opponents’ moves, thereby increasing their chances of winning. In approaching the game of poker, as Istrate discovered, most players look at their opponents to identify certain flaws or features that will help them to win the game. These flaws will tell them the weaknesses of their opponents, and they therefore capitalize on these weaknesses to win games. For this reason, players look at the position the opponents occupy on the table, their timings and pace, and the way they behave and move their cards. Poker players thus attempt to disguise their feelings and fears from their opponents through facial expressions and body language (Istrate 57). This can be seen as the skills used by these players to win games. In a game of poker, the skills are purely based on the ability of the player to read and understand the actions of others. On the other hand, the player has to hide his or her feelings or expressions that might reveal his or her actions to the opponents. Another important discovery made by Istrate (2011) in his research is the use of experience. These players also rely on experience, which comes as a result of playing many games. Experience in this case is measured by the number of hands one plays. If a person plays more hands, then s/he is more experienced. The more experiences and encounters a player has in the game of poker, the more knowledge the player accumulates. This gives him/her a higher chance of winning; thereby increasing his/her chances of playing the game even more. For most poker players, experience is about having authority (Istrate 60). If a player has had many encounters, then s/he has greater influence on the game, and his/her opinions are likely to be respected. Therefore, it can be seen that poker players rely on skills and knowledge that is obtained through numerous encounters in the game. Poker players argue that hard work and experience are all that makes the difference in this game (Istrate 63). Although most of these players agree that it is a game of chance, they tend to put more emphasis on the experiences, skills and knowledge one has accumulated over the course of his/her playing time. When approaching a poker game, these players will look at the experiences and skills the opponents have, and therefore evaluate their own chances of success. It can be argued that poker players rely on the presence of inexperienced and less talented players to increase their chances of winning. These qualities make one a professional player. For such players, the stakes or earnings in the game increase as one continues to build his/her skills and knowledge. The research by Istrate (2011) demonstrates that Poker players approach the game with less focus on science and mathematics. Although poker is a game of chance, very few players acknowledge the role mathematics plays in predicting or understanding the outcomes of this game. How mathematicians approach the game of Poker In the game of poker, such as the Texas Hold’em, there are a number of unknown factors that need to be predicted with high degree of accuracy. As discussed above, most players use their skills, knowledge and experiences to predict these outcomes. For mathematicians however, the approach is different. In fact, as noted in the article by Jennifer Ouellette (2012), it is argued that the game of poker is 90% math and strategy and only 10% based on the understanding of the table dynamics and the attitudes of other players. Applied mathematicians use the applied probability theory to make such predictions. In a paper by Kenny Brawner (2014), the author delves into the application of mathematics to a game of poker. Brawner (2014) argues that in a game like Texas Hold’em, there are many unknown factors. However, the known factors can be calculated in order to make optimal decisions. Probability basically uses the available known information and factors to predict the unknown outcomes (Brawner 1). For this reason, mathematicians use the available known factors to calculate and predict the unknowns. The decisions made in the game of poker by mathematicians are strategic based on careful calculations and analysis. In the game of poker, mathematicians use probability to assign probabilities to various outcomes such as the drawing of the poker hands, chances of winning with the hands and also in determining the probability of winning the game. Since poker, like any other gambling activity, is mainly based on chance, the application of probability theory is vital in estimating these outcomes. For mathematicians, little focus is given to the psychological aspects of the opponents. Instead, attention is given to the mathematical analysis. The outcomes are largely determined by probability calculations. In the modern game of poker, the players who dominate today and in the future are those who can convert the available knowledge into some useful complete knowledge. This can only be achieved if the right mathematical approaches are used to analyze the various scenarios. Mathematicians thus have the ability to understand the strength of the opponent and his/her likely course of action. In the game of poker, such as the Texas Hold’em, there is the chance that one can either increase or lose his/her chips in one move. This makes the knowledge about the opponents and their behaviors very important in this increasingly competitive game. The only chance of making such accurate predications is through the application of probability to understand the strengths and weaknesses of the opposition. There are many instances in the game of poker where probability finds application. In Texas Hold’em Poker for instance, each of the outcomes of the rounds can be calculated based on the principles of probability. This game is composed of four rounds: the pre-flop, flop, turn and the river (Brawner 4). The participants each play in turn and they have a choice to match the highest bet, increase it or forfeit the game. These are the three main decisions the players have to make when playing poker. In order for a player to win, s/he has to be the last standing player or s/he should have the card with the highest rank after the final round. This shows how the poker players have to engage in critical decisions that help them in winning the game. Therefore, there a number of calculations that can be performed using the principles of probability in understanding the opposition and their actions. In the section below, some of the calculations performed by professional players are discussed. How does the study of probability theory help in winning a poker game? The study of probability and mathematics in general is a vital tool in equipping a player with the right skills to play poker. The knowledge acquired through the study of probability is important in enhancing the understanding of the game and making better predictions. In other words, as noted in the article by Jennifer Ouellette (2012), mathematics skills can be used to replace the intuition and experience that is usually associated with poker. In this case, if a player is new to the game but has acquired enough knowledge in mathematics and probability, s/he has a great chance of beating even the most experienced players. If a player plays many poker games but lacks mathematics knowledge, s/he is likely to find it difficult to make certain decisions. By learning about probability, one can acquire important knowledge that gives him/her an edge over the other players. The mathematical knowledge is based on the probability theory, and this knowledge is used in determining the various combinations of hands in the game of poker. For example, a poker player has to determine the probability that s/he will make money if s/he pays the bet. An inexperienced player will simply make a guess when determining whether or not to call. In most cases, if the bet is large enough, the player is less likely to call but if the bet is small, s/he likely to call. However, for a player with sufficient knowledge in mathematics, s/he is able to work out the pot odds and thus act accordingly. These two examples show that with mathematics knowledge, decisions are well informed. Such crucial decisions can only be arrived at if the player has sufficient mathematics knowledge that helps him/her in analyzing the various situations. Although probability enhances a person’s chances of winning, it is not guaranteed that this knowledge will automatically make someone win. The use of probability does not necessarily make a player win all the poker games; it only gives him/her an edge over the competitors. Although mathematics skills help in enhancing one’s chances of winning, there are other factors that determine whether or not a person wins. For instance, the probability that a person will win is influenced by the number of players in the game. If there are many players, then the probability of wining reduces because there are many ways of getting beaten. On the contrary, if the number of players is small, then the chances of winning increase. This means that although one may use probability in determining his/her chances of winning, it is impossible for one to be certain of the winning. In addition, the behavior of the players greatly determines the outcomes of the game. In the game of poker, one needs to understand when to pay attention to the mathematics and when to look at other factors. It requires a careful balance between table dynamics and experience on one hand and the probability results on the other. How mathematicians use probability in the game of Poker In the game of poker, mathematicians and professional players use probability for two main purposes: to understand the actions of the opposition and to develop a strategy that will help in dominating the opponents. Mathematics is used when determining the combinations for the starting hands. This is the basic application of probability in the game of poker. In the Texas Hold’em, the game starts with two cards being given to all the players. From this information, the amount of unique hands can be calculated using combinatorial probability formula. Mathematically, this is expressed as ;where n represents the total number of elements and r is the number of elements that have to be chosen (Brawner 3). In the case of poker, there are a total of 52 cards, and two cards are given to each player. Therefore, in order to understand the number of distinct hands, the formula above can be applied, giving a total of 1326 hands. Given that each player is deal one of the total 1326 starting hands, mathematicians use probability to calculate the odds and probabilities. In a book by Pat Dittmar (2008) titled Practical Poker Math, the author extensively covers the probability calculations involved the game of poker. Dittmar (2008) notes that in a game of poker, there are various hands and these include one pair, suited cards and the not suited cards (Dittmar 49). The different starting hands can thus be assigned probabilities in order to determine the likelihood that a given player will have a certain combination. For example, the probability that a player will receive suited cards is given as 312/1326 or 0.24 (Dittmar 52). In another example, the probability of receiving unpaired cards is 0.7, which is the most probable event. Using probability formulae, professional players and mathematicians can further determine the specific cards and their odds. Such knowledge can be used by the player to his/her advantage by determining the ranks of the cards the opponents have. After determining the starting hands, mathematicians can use probability to determine a number of uncertainties before the flop (Dittmar 68). Some of the uncertainties to be unveiled include the strength of the hands, the chances that the hand will improve and the estimated cost of continuing in the hand. By using probability, some of these uncertainties can be determined. After the flop, players also want to understand the probability of improving on the next cards. The probability of improvement helps the player understand the chances s/he has for a stronger hand. In other words, the player has to know whether or not s/he should continue based on the future expectations. Probability theory is used in assigning these probabilities, thereby giving the player the chance to decide whether to continue or not. Probability is used in calculating the pot odds versus the odds of winning. For instance, if a person has to bet $20 to call for the opportunity to win $50, then the odds of the player are 2-to-5 against the opponents (Dittmar 93). In order to make such decisions, the player has to understand the ratio between the pot odds and his/her odds of winning. Players thus need to determine whether or not to call or fold, and this requires that they find the outs. The outs refer to the cards that they will reveal to give them a higher chance of winning compared to the opponents. From the above scenarios, it is obvious that probability can be used in the game of poker. The poker environment is one that is characterized by high odds and stakes. For this reason, a player cannot always rely on his/her personal strengths alone to make predictions that will help him win the game. Mathematicians and professional poker players use the concepts from mathematics to aid in their decision making. Through the use of probability, a poker player will know the timings of his/her moves and the chance of his/her moves succeeding. Common information such as the pot-size, the stakes and the board cards are available to all the players, and it is up to the individual players to use such information to their advantage (Dittmar 3). At the end, the use of mathematics and probability makes the player develop good strategies that help him/her in dominating the game or competition. This is what makes the difference between ordinary poker players and the professional players who apply the concepts of mathematics. Conclusion Contrary to the assumptions of some, mathematics is a subject that is applied in different situations in real life. In this research, attempts have been made to show how mathematics, and specifically probability, is used in the game of poker. This is a game with many unknown outcomes, and this calls for the use of probability to determine these outcomes. Since the game involves betting with valuables such as money and property, players have to be certain that they are going to win. Although skill and experience are important in this game, the use mathematics gives the player an edge over the competitors. By having this knowledge, a new player to this game has a higher chance of succeeding compared to the experienced players whom mainly rely on observing the behavior of the opponents. For mathematicians and professional poker players, the use of probability helps in enhancing the accuracy with which certain outcomes are predicted. However, since poker is influenced by other external factors, the use of probability does not guarantee winnings. It only helps increase the chances of one wining. Based on the example of poker, it can be argued that mathematics is a subject that can be used in understanding and dealing with real life problems. Although the present research has focused on the use of probability in the game of poker, there are opportunities for future researchers to expand on this topic by focusing on how probability theory is applied in other fields. One of such applications is weather forecasting. Meteorologists use probability to determine daily weather patterns as well as the possibility of natural disasters occurring. Secondly, in the medical field, probability is applied when understanding the success rate of using a given intervention to a patient, such as the use of surgery. Finally, in the insurance industry, the premiums rate that is decided by insurance companies is also a function of probability. Therefore, in order to fully explore the use of mathematics in real life situations, future researches need to focus on such topics. Works Cited Brawner, Kenny. “Poker: A Game of Mathematics.” 2014. Web Dittmar, Pat. Practical Poker Math. Toronto: ECW Press, 2008. Print Istrate, Andrada-Mihaela. “From pathological to professional: gambling stories.” Journal of Comparative Research in Anthropology and Sociology, 2(2), 2011: 49-67 Ouellette, Jennifer. Poker Science: Math, Game Theory Can Help A Gamblers Strategy, Study Says. The Huffington Post 2012. Web. 30 Mar. 2015. Rickwood, Debra et al., “The Psychology of Gambling.” APS Review Paper, 2010. Web www.psychology.org.au/assets/files/aps-gambling-paper-2010.pdf INDENT SECOND LINES. ITALICIZE JOURNAL NAMES. MAKE ALL CITATIONS FLUSH LEFT, NOT JUSTIFIED. WITHIN THE ESSAY, INTRODUCE YOUR REFERENCES IN THE ESSAY SENTENCES BY NAME RATHER THAN JUST PUTTING THEM IN THE CITATION QUOTATION. Read More