Casino Games Expected Value Problems And Answers

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You're at a carnival and you see a game. If you're trying to make money, is it in your interest to play the game? To answer a question like this we need the concept of expected value.

The expected value can really be thought of as the mean of a random variable. This means that if you ran a probability experiment over and over, keeping track of the results, the expected value is the average of all the values obtained.

The expected value is what you should anticipate happening in the long run of many trials of a game of chance. The carnival game mentioned above is an example of a discrete random variable. The variable is not continuous and each outcome comes to us in a number that can be separated out from the others.

To find the expected value of a game that has outcomes x 1x 2. Why 8 and not 10? Now plug these values and probabilities into the expected value formula and end up with: This means that over the long run, you should expect to lose on average about 33 cents each time you play this game. Yes, you will win sometimes.

  • If S is the sample space of the experiment then to each i ∈ S the random variable X assigns a certain value α (a real number). The random variable is described Expected value of X: E[X] = ∑ α. αP(X = α). Chuck-a-luck This game (found in fairgrounds) is played by rolling 3 dice and betting on a number between 1 and 6.
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  • we shall discuss two such descriptive quantities: the expected value and the variance. . playing this game. The reader is asked to consider how much he or she would be willing to pay for this privilege. It is unlikely that the reader's answer is more .. The 0 and 00 slots are green, and half of the remaining 36 slots are red.
  • The expected value is a type of calculation in mathematical statistics that measures of the center of a probability distribution. to play the game? To answer a question like this we need the concept of expected value. A ball randomly lands in one of the slots, and bets are placed on where the ball will land.
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But you will lose more often. Now suppose that the carnival game has been modified slightly.

In the long run you won't lose any money, but you won't win any. Don't expect to see a game with these numbers at your local carnival. If in the long run you won't lose any money, then the carnival won't make any. Now turn to the casino.

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In the same way as before we can calculate the expected value of games of chance such as roulette. Half of the are red, half are black. Both 0 and 00 are green. A ball randomly lands in one of the slots, and bets are placed on where the ball will land. One of the simplest bets is to wager on red. If the ball lands on a black or green space in the wheel, then you win nothing. What is the expected value on a bet such as this? Here the house has a slight edge as with all casino games. As another example, consider a lottery.

This gives us an expected value of:. So if you were to play the lottery over and over, in the long run you lose about 92 cents - almost all of your ticket price - each time you play. All of the above examples look at a discrete random variable.

However, it is possible to define the expected value for a continuous random variable as well. All that we must do in this case is to replace the summation in our formula with an integral.

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It is important to remember that the expected value is the average after many trials of a random process. In the short term the average of a random variable can vary significantly from the expected value. Updated March 18, What Is the Expected Value?

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  1. It is impossible to predict the value o a $1 bet, because casino games are random on that scale. What we can do is, say, predict the average return on 10, $1 bets. It takes a large scale and time frame for the house edge to become apparent. Using this method, here are the answers  2 Answers - Why is the expected value in St. Petersburg Paradox.:
    I'm writing a post with 14 gambling probability examples because I think that examples are one of the easiest ways to teach something. Probability is a branch All kinds of probabilities come into play in card games, but they're all based on a handful of qualities that a deck of cards has. A standard deck of. Craps is a gambling game found in most casinos based on rolling two six sided dice. Another way to ask this very same question would be, “how much is the fair price for this game?” (The answer is, of course, $) Another way to answer this question . Solution: Here is the expected value of one dollar bet on the field. A friend offers to play you a game where you pay him $1 if the roll of a 6-sided die comes up as 1,. 2, 3, or 4, and he pays you $2 if the die comes up a 5 or 6. What is the expected value of a round. (for you) if you play the game? What are the odds of your winning? Answer: The probability that you pay $1 is 4/6 since he has 4.
  2. Expected Value. Objectives. 1. Understand the meaning of expected value. 2. Calculate the expected value of lotteries and games of chance. 3. Use expected value to solve applied problems. Life and Health Insurers' Profits Skyrocket %*. How do insurance companies make so much money? When you buy car.:
    The American roulette wheel has 18 red, 18 black, and 2 green slots. These slots are numbered with the green being 0 and 00 and the red and black being numbers from 1 to 36, 18 are red and 18 are green. The European wheel has 18 red, 18 black and 1 green. Problem. Determine your expected winnings if $1 is bet on. Expected Values: learn how to calculate the expected value of a game. We study games not only to learn about common games, like poker or some other casino game. Playing games and consequently understanding their does it favor the house? To answer questions like that, we can use this formula for 'n' outcomes.
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Save your draft before refreshing this page. Submit any pending changes before refreshing this page. Ask New Question Sign In. To answer your question more fully It takes a large scale and time frame for the house edge to become apparent. No game guarantees you'll win that casino would go out of business pretty quick!

But if you were to gamble your money on a chance based game, what type of gambling would be the best in Can the current Bitcoin casinos survive? Can a negative expectation casino game be beaten?

Is the money earned in a casino via gambling taxable? What casino games have the best odds for the player? This house edge is represented in a percentage. You can use that percentage to determine your expected loss over time on any particular game. You can find more house edge percentages at www. To best be able to demonstrate how this formula works, we can calculate a table of expected values. We have to match an expected value with the probability of attaining that value.

A blank table would look like this. The size of a table the number of columns depends upon the game we are studying. Look at the examples that follow to understand how to fill the table. Sally has a spinner game. Here are the rules of the game: If the spinner lands on red, the player wins nothing. To determine who this game favors, we must fill an expected values table.

This requires us to know a little bit about probability, too. If all the spaces on the spinner are the same size, which is a safe assumption based upon the spinner presented here, there is a 1 in 8 chance of landing on any one space. We will use that fact to fill the table.

To land on purple, there are two spaces. We will fill in the rest of the information into the expected values table. The table is almost complete. It is incomplete because we have yet to account for one crucial piece of information: This will be the last entry into the table, like so. Now that we have our table of values, we are going to multiply values times their respective probabilities, like so.

Once we gain these products, we add them together. Here is the resulting calculation: Cleaning up the expression gives us this. So that we can easily combine this expression, transform the -2 into eighths. We now need to add the fractions. Since they are all in eighths, add the numerators. Next, reduce the fraction.

Sure, a player can land on yellow many times in a row. However, over the long haul, a player will lose a quarter per game. This example had a long explanation because it was necessary to explain all the details of the process. For the following examples, less steps will be shown. Here is a game that involves a marble bag. The payout depends on what color marble the player pulls, according to this chart. To construct a table of expected values, we need to know the probabilities of pulling various marbles.

First, we count up the marbles. Placing them in another chart will be the easiest way to organize our information. This information will now be placed within a table of expected values. So, this will be entered within the last column.

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What is the expected value on a bet such as this? Here the house has a slight edge as with all casino games. As another example, consider a lottery. This gives us an expected value of:. So if you were to play the lottery over and over, in the long run you lose about 92 cents - almost all of your ticket price - each time you play. All of the above examples look at a discrete random variable.

However, it is possible to define the expected value for a continuous random variable as well. All that we must do in this case is to replace the summation in our formula with an integral. It is important to remember that the expected value is the average after many trials of a random process.

In the short term the average of a random variable can vary significantly from the expected value. Updated March 18, What Is the Expected Value?

What casino games have the best odds for the player? This house edge is represented in a percentage. You can use that percentage to determine your expected loss over time on any particular game. You can find more house edge percentages at www. Every game at every casino is different. A few specifics and we can probably help. Related Questions What casino game gives the lowest expected loss per average bet, and the longest expected playtime?

What are some examples of game protection in casinos? What are casino gambling tricks? With that in mind, we will take a look at a few games that involve money to determine which are favorable to the player, favorable to the house, or are fair games that favor neither the player nor the house.

If you are not yet familiar with probability, examine our lesson on probability before continuing. Some games are difficult to determine who they favor. If a game favors the house the person running the game , how much does it favor the house?

To best be able to demonstrate how this formula works, we can calculate a table of expected values. We have to match an expected value with the probability of attaining that value. A blank table would look like this. The size of a table the number of columns depends upon the game we are studying. Look at the examples that follow to understand how to fill the table.

Sally has a spinner game. Here are the rules of the game: If the spinner lands on red, the player wins nothing. To determine who this game favors, we must fill an expected values table. This requires us to know a little bit about probability, too. If all the spaces on the spinner are the same size, which is a safe assumption based upon the spinner presented here, there is a 1 in 8 chance of landing on any one space.

We will use that fact to fill the table. To land on purple, there are two spaces. We will fill in the rest of the information into the expected values table. The table is almost complete. It is incomplete because we have yet to account for one crucial piece of information: This will be the last entry into the table, like so.

Now that we have our table of values, we are going to multiply values times their respective probabilities, like so. Once we gain these products, we add them together. Here is the resulting calculation:

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Practice with Expected Value 1. Answers: 1. Let X be the You should expect to lose $ after one-hundred games. 4. Expected Values: learn how to calculate the expected value of a game. We study games not only to learn about common games, like poker or some other casino game. Practice Problems Hypothesis Tests What is the expected value on a bet such as this? Here the house has a slight edge (as with all casino games). Expected.

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Expected Value