Calculate the Expected Value in Roulette

Calculate the Expected Value in Roulette The concept of expected value can be used to analyze the casino game of roulette.  We can use this idea from probability to determine how much money, in the long run, we will lose by playing roulette.   Background A roulette wheel in the U.S. contains 38 equally sized spaces. The wheel is spun and a ball randomly lands in one of these spaces. Two spaces are green and have numbers 0 and 00 on them. The other spaces are numbered from 1 to 36. Half of these remaining spaces are red and half of them are black. Different wagers can be made on where the ball will end up landing. A common bet is to choose a color, such as red, and wager that the ball will land on any of the 18 red spaces. Probabilities for Roulette Since the spaces are the same size, the ball is equally likely to land in any of the spaces.  This means that a roulette wheel involves a uniform probability distribution. The probabilities that we will need to calculate our expected value are as follows: There are a total of 38 spaces, and so the probability that a ball lands on one particular space is 1/38.There are 18 red spaces, and so the probability that red occurs is 18/38.There are 20 spaces that are black or green, and so the probability that red does not occur is 20/38. Random Variable The net winnings on a roulette wager can be thought of as a discrete random variable. If we bet $1 on red and red occurs, then we win our dollar back and another dollar. This results in net winnings of 1. If we bet $1 on red and green or black occurs, then we lose the dollar that we bet. This results in net winnings of -1. The random variable X defined as the net winnings from betting on red in roulette will take the value of 1 with probability 18/38 and will take the value -1 with probability 20/38. Calculation of Expected Value We use the above information with the formula for expected value. Since we have a discrete random variable X for net winnings, the expected value of betting $1 on red in roulette is: P(Red) x (Value of X for Red) P(Not Red) x (Value of X for Not Red) 18/38 x 1 20/38 x (-1) -0.053. Interpretation of Results It helps to remember the meaning of expected value to interpret the results of this calculation. The expected value is very much a measurement of the center or average. It indicates what will happen in the long run every time that we bet $1 on red. While we might win several times in a row in the short term, in the long run we will lose over 5 cents on average each time that we play. The presence of the 0 and 00 spaces are just enough to give the house a slight advantage. This advantage is so small that it can be difficult to detect, but in the end, the house always wins.

Calculate the Expected Value in Roulette

Calculate the Expected Value in Roulette The concept of expected value can be used to analyze the casino game of roulette.  We can use this idea from probability to determine how much money, in the long run, we will lose by playing roulette.   Background A roulette wheel in the U.S. contains 38 equally sized spaces. The wheel is spun and a ball randomly lands in one of these spaces. Two spaces are green and have numbers 0 and 00 on them. The other spaces are numbered from 1 to 36. Half of these remaining spaces are red and half of them are black. Different wagers can be made on where the ball will end up landing. A common bet is to choose a color, such as red, and wager that the ball will land on any of the 18 red spaces. Probabilities for Roulette Since the spaces are the same size, the ball is equally likely to land in any of the spaces.  This means that a roulette wheel involves a uniform probability distribution. The probabilities that we will need to calculate our expected value are as follows: There are a total of 38 spaces, and so the probability that a ball lands on one particular space is 1/38.There are 18 red spaces, and so the probability that red occurs is 18/38.There are 20 spaces that are black or green, and so the probability that red does not occur is 20/38. Random Variable The net winnings on a roulette wager can be thought of as a discrete random variable. If we bet $1 on red and red occurs, then we win our dollar back and another dollar. This results in net winnings of 1. If we bet $1 on red and green or black occurs, then we lose the dollar that we bet. This results in net winnings of -1. The random variable X defined as the net winnings from betting on red in roulette will take the value of 1 with probability 18/38 and will take the value -1 with probability 20/38. Calculation of Expected Value We use the above information with the formula for expected value. Since we have a discrete random variable X for net winnings, the expected value of betting $1 on red in roulette is: P(Red) x (Value of X for Red) P(Not Red) x (Value of X for Not Red) 18/38 x 1 20/38 x (-1) -0.053. Interpretation of Results It helps to remember the meaning of expected value to interpret the results of this calculation. The expected value is very much a measurement of the center or average. It indicates what will happen in the long run every time that we bet $1 on red. While we might win several times in a row in the short term, in the long run we will lose over 5 cents on average each time that we play. The presence of the 0 and 00 spaces are just enough to give the house a slight advantage. This advantage is so small that it can be difficult to detect, but in the end, the house always wins.

Calculate the Expected Value in Roulette

Calculate the Expected Value in Roulette The concept of expected value can be used to analyze the casino game of roulette.  We can use this idea from probability to determine how much money, in the long run, we will lose by playing roulette.   Background A roulette wheel in the U.S. contains 38 equally sized spaces. The wheel is spun and a ball randomly lands in one of these spaces. Two spaces are green and have numbers 0 and 00 on them. The other spaces are numbered from 1 to 36. Half of these remaining spaces are red and half of them are black. Different wagers can be made on where the ball will end up landing. A common bet is to choose a color, such as red, and wager that the ball will land on any of the 18 red spaces. Probabilities for Roulette Since the spaces are the same size, the ball is equally likely to land in any of the spaces.  This means that a roulette wheel involves a uniform probability distribution. The probabilities that we will need to calculate our expected value are as follows: There are a total of 38 spaces, and so the probability that a ball lands on one particular space is 1/38.There are 18 red spaces, and so the probability that red occurs is 18/38.There are 20 spaces that are black or green, and so the probability that red does not occur is 20/38. Random Variable The net winnings on a roulette wager can be thought of as a discrete random variable. If we bet $1 on red and red occurs, then we win our dollar back and another dollar. This results in net winnings of 1. If we bet $1 on red and green or black occurs, then we lose the dollar that we bet. This results in net winnings of -1. The random variable X defined as the net winnings from betting on red in roulette will take the value of 1 with probability 18/38 and will take the value -1 with probability 20/38. Calculation of Expected Value We use the above information with the formula for expected value. Since we have a discrete random variable X for net winnings, the expected value of betting $1 on red in roulette is: P(Red) x (Value of X for Red) P(Not Red) x (Value of X for Not Red) 18/38 x 1 20/38 x (-1) -0.053. Interpretation of Results It helps to remember the meaning of expected value to interpret the results of this calculation. The expected value is very much a measurement of the center or average. It indicates what will happen in the long run every time that we bet $1 on red. While we might win several times in a row in the short term, in the long run we will lose over 5 cents on average each time that we play. The presence of the 0 and 00 spaces are just enough to give the house a slight advantage. This advantage is so small that it can be difficult to detect, but in the end, the house always wins.

Revisiting Wether, Incidence and Different Than

Revisiting Wether, Incidence and Different Than Revisiting Wether, Incidence and Different Than Revisiting Wether, Incidence and Different Than By Maeve Maddox wether/whether In researching the recent song lyrics post, I came across a comment written by a high school sophomore. (For the information of non-American readers, a high school sophomore is 15 or 16 years of age.) The student said she was writing a research paper on the influence of song lyrics. I certainly hope she looks up the spelling of the conjunction whether before she finishes her assignment; she used it four times in her comment, each time spelling it wether. wether (noun): a castrated ram. whether (conjunction): one use is to introduce an indirect alternative question expressing doubt or choice between alternatives. More at â€Å"Wether, Weather, Whether.† incident/incidence NPR (National Public Radio) announcers are a rich source of nonstandard English. On a recent morning I listened to Sam Sanders report on a pediatrician who prescribes exercise to his overweight patients. One of the doctor’s techniques is to encourage patients to visit local parks. Sanders mentioned that safety is a concern. He said that one of the parks, Kingman Island, â€Å"had 30 incidences of violent crime over the past year.† The erroneous use of incidences for incidents was cleaned up in the transcript, but it can be heard in the audio (3:33). incident (noun): something that occurs. incidence (noun): the range or scope of a thing; the extent of its influence or effects. For example, â€Å"The incidence of poverty among  the aged has consistently been higher than for any other age group in the United States.† More at: †It’s Not the Ox-Bow Incidence† different from/different than/different to A reader asks, â€Å"Is the correct usage ‘different to’ or ‘different from’? Different to seems very common (almost universal), but surely the essence of difference is separation, not convergence, so isn’t ‘different from’ correct?† This question comes up frequently, often with angry attacks on speakers who use the â€Å"wrong† phrase. Of the three, â€Å"different from† is by far the winner on the Ngram Viewer. â€Å"Different to† is heard more frequently in Britain than in the United States. â€Å"Different than† has its American defenders, but the AP Stylebook comes down firmly for â€Å"from, not than.† The Chicago Manual of Style is less dogmatic, but does say, â€Å"The phrasing different from is generally preferable to different than.† More at †Different from, Different to, Different than.† Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Misused Words category, check our popular posts, or choose a related post below:100 Words for Facial ExpressionsThe Possessive ApostropheRite, Write, Right, Wright

Marketing Audit Essay Example | Topics and Well Written Essays - 2500 words

Marketing Audit - Essay Example Market planning can be defined as â€Å"all rational, incremental and intuitive processes that guide a firm’s marketing to its future.† (RAO. 2007) When we talk about marketing planning it may seem as an easy process, however in reality it’s a complicated multifaceted process that involves every aspect of an organization. Marketing planning can be referred to activities that are undertaken by the managers to achieve marketing objectives. In other words it’s a process to identify range of options that are available to the manager in order to achieve marketing objectives and then evaluate those options and plan accordingly. The outcomes of marketing planning process are the marketing strategies to achieve marketing objectives. Marketing planning involves a systematic process of reviewing the situation, assumption formulation, setting objectives about whom to sell and how to, decisions regarding the achievement of objectives and scheduling and costing out act ivities required for implementation. (MCDONALD & WILSON. 2011) The market planning comprises of four basic components, these include marketing objectives, marketing audit, marketing strategies and resource allocation and monitoring. All these components are interlinked and are extremely important for marketing planning. I shall discuss these components in detail further. I’ve been emphasizing that the aim of the marketing planning is to achieve marketing objective, marketing objectives are something that the marketing function strives to achieve as a part of business strategic plan which usually includes increase in sales, awareness about products, creation of brand, increase in market share etc, then these goals are converted to objectives which are measurable, like increasing sales and market share by 15% within one year, this could be measured by analyzing annual sales data and industry data and other publications. (LEVENS. 2012) Marketing Objectives and Strategies In order to achieve these marketing objectives the company has to make marketing strategies. The marketing objectives identified must be in accordance with company’s overall objectives. Marketing objectives can be easily identified on the basis of marketing mix objectives which simplifies the objectives setting process which later on lays basis for marketing strategies to achieve those objectives. A marketing strategy is a series of action statements which are also known as tactics. Effective marketing strategy is critical to successful marketing plan; therefore these would be given extra importance when a marketing plan is being set up. (LANCASTER & MASSINGHAM. 2010) The Integration of Marketing Planning into Objectives and Strategies Planning itself includes goal setting and development of strategies to achieve those goals. The objective or goals and strategies to achieve these will be the outcome of marketing planning process. The marketing strategies tell what should be done and the strategic and operational plans guide how the strategies s hould

Construction of Sports Hall (GYM) in a School in Bahrain Essay

Construction of Sports Hall (GYM) in a School in Bahrain - Essay Example Despite being a country where sports are loved by a majority of the population (especially students), the government of the Kingdom of Bahrain failed to construct adequate sport or gym facilities in the schools largely due to the lack of financial assistance. However, over the last few years, the awareness of sports has increased by an unprecedented level amongst the students in the Kingdom of Bahrain given that the country was due to the host the mini Olympics. As a consequence, the demand for advanced and well-equipped sports hall (Gym) facilities also grew by a drastic margin. In light of these events, the government of the Kingdom of Bahrain felt the urge to make prospective investments behind building sports hall (Gym) in government-sponsored schools. The scope of this project lays in the fact that construction of sports hall (Gym) in the government-sponsored schools will allow students to be engaged in a physical activity of their choice besides being engaged in the academic curriculum. It will also hold students who are obese and are affected by other weakness to regain their physical fitness and strength. This is perhaps the most relevant scope of this project provided that the percentage of students suffering from health issues such obesity, respiratory problems, heart problems, bone density has increased by a considerable margin (Baby, 2006). Therefore the construction of sports hall (Gym) facilities will allow the government of the Kingdom of Bahrain to bring down this ever growing rate of health disorders. Another relevant scope of this project is evident in the fact that it will allow the government schools to build their profile in order to grab the attention of parents and convince to enroll their children to the corres ponding schools (Ministry of Education of Kingdom of Bahrain, 2013).

The Old Man and the Sea :: essays research papers

The book â€Å"The Old Man and the Sea† was written by Hemingway in 1951. Just as Hemingway himself said, the work is the best one he ever wrote in his life. The book was so successful that it enabled Hemingway to win the Nobel Prize for Literature in 1954. The story of is quite simple: an Cuban fisherman finally fished a very big marlin after eighty four days’ taking no fish, but the fish was too big, the old man spent three days conquering the marlin. However, on his way home, he and the big fish were attacked by a lot of sharks. At last, when he came back, only the head, tail and vertebra of the fish remained. I was really moved after reading the book. I regarded the old man as a hero. After eight four days’ taking no fish, he decided to go farther on the eighty-fifth day. When meeting a big marlin, though he knew the fish was much more powerful than he was, he still determined to fight it unless he died. Because he thought he was born a fisherman. He won, for he finally killed the fish. Just as he said: â€Å"Every day is a new day. It is better to be lucky. But I would rather be exact. Then when luck comes you are ready.† The old man had been ready very well. He had caught the chance. However, â€Å"Every day is a new day†, a pack of sharks broke all his hope. He never gave up, he fought with the sharks even after loosing his tools. This proved his bravery again, â€Å"Man is not made for defeat. A man can be destroyed but not defeated.† After the first shark took away about forty pounds of the fish, the old man said like that. I thought it also showed the topic meaning of the book. The old man really gave me a vivid lesson, not only by his heroic behaviors, but by his simple words. Isn’t it the attitude we should take forwards our lives? The old man is also very optimist at the same time. After the first shark’s attack, he said to himself â€Å"Think about something cheerful, old man. Every minute now you are closer to home. You sail lighter for the loss of forty pounds.† Other than complaining about the unfortunate things happened to him, the old man encouraged himself and used an optimist attitude to comfort himself.