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