# What is the expected value of playing the lottery?

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In summary, the expected value of each ticket is simply the number of distinct tickets sold multiplied by P / (kN), where k is the number of tickets sold so far. More formally, let Yk denote the number of distinct tickets given k ticket sales and Xk denote the value of a ticket given k ticket sales.

## What is the expected value of the Powerball?

For example, the odds of having a single matching number and the Powerball number correct on a single ticket is 1 in 92. One divided by 92 equals approximately 1.09%. Multiplying 1.09% by the fixed \$4.00 payout results in an expected value of \$0.04.

## What is the expected value of a Mega Millions ticket?

Typically, with an average-sized jackpot, the “expected value” of a Mega Millions ticket is about a quarter; it’s 32 cents for Powerball. Expected value is a financial concept that projects what something is worth based on the probability of certain predictable outcomes.

## Which lottery has the best expected value?

Jeremy Elson calculated for the Mega Millions lottery, the best expected value is an advertised jackpot around \$385 million, which gives a return of about \$0.57 per \$1 ticket. For Powerball, that is about \$890 million, which gives a roughly \$0.80 return per \$2 ticket.

Buying two Powerball tickets does increase your chance of winning but I do not think it doubles your expected value. Yes, buying more lottery tickets does improve your chance of winning. Let’s say you buy a single \$1 ticket out of 100 that have been sold. Your chance of winning is 1 in 100.

## How much is 1 number and the Mega Ball worth?

Here’s How Much You Win for Matching One Number

If you matched one yellow ball (which is the last number drawn), then you’ll win \$2. You can put that money into buying one more Mega Millions ticket!

## How much is the Mega Millions?

The Mega Millions® jackpot has surpassed the magical half-billion mark, and the next drawing on Friday, May 21, will feature an estimated \$515 million prize (\$346.3 million cash)!

\$515 Million Jackpot Set for Friday Night.

Amount Date Winning Tickets
\$515 million (est) 5/21//2021 ?
\$451 million 1/5/2018 1-FL

## What are the big lotteries?

10 largest US jackpots

• \$1.586 billion, Powerball, Jan. …
• \$1.537 billion, Mega Millions, Oct. …
• \$768.4 million, Powerball, March 27, 2019 (one ticket, Wisconsin)
• \$758.7 million, Powerball, Aug. …
• \$731.1 million, Powerball, Jan. …
• \$687.8 million, Powerball, Oct.

## How do you calculate an ex?

To find the expected value, E(X), or mean μ of a discrete random variable X, simply multiply each value of the random variable by its probability and add the products. The formula is given as E(X)=μ=∑xP(x).

## What is expected value of a random variable?

The expected value of a random variable is denoted by E[X]. The expected value can be thought of as the “average” value attained by the random variable; in fact, the expected value of a random variable is also called its mean, in which case we use the notation µX. (µ is the Greek letter mu.) xP(X = x).

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## What is the mean or the expected value of a person who buys a ticket?

The expected value of the ticket is the sum of the value for all event probabilities. If you buy 1 ticket, you have a 1/1000 chance obtaining a \$1200 dollar item and a 999/1000 chance of obtaining a nothing (a \$0 item).

## Do Mega Millions tickets carry over?

Unlike other lotteries, the US Powerball does not have a rollover limit or a jackpot cap. (We discuss limits and caps in more detail below.) As long as no one wins the jackpot, the prize money will keep on getting bigger! 