Expected Value in Lotteries: Exposing Its Significance and Impact


Last updated on January 2, 2024

So you tell everyone in your lottery syndicate team – “OK folks, let’s buy more tickets because this strategy increases our chances of winning.” Not so fast. You haven’t heard the aspect of expected value or EV yet.

What is the Expected Value?

The EV is the gauge that tells you when the lottery is profitable and not.

For illustration, let me use the U.S. Powerball as an example.

When writing this article, the U.S. Powerball was at an estimated jackpot of $384 million.

Therefore, at $2 per ticket, my calculation for EV is a negative $0.37.

The U.S. Powerball Expected Value at $384 Million Jackpot

The Powerball 5/69 showing a negative expected value of -0.37

The table shows that EV is negative, so it tells me that it will not be profitable when you play the U.S. Powerball at a $384 Million jackpot prize.

Compare that to when the U.S. Powerball reached the $1.5 billion mark in January 2016. We can see a huge improvement in EVs.

The U.S. Powerball Expected Value at $1.5 billion Jackpot

The Powerball 5/69 showing a positive expected value of $3.45 at 1.5 billion jackpot prize level

The table above shows that playing Powerball in January 2016 is “probably” a good idea.

EV provides an overall idea of how profitable a game will be in the long run.

So, in theory:

A positive EV means a profitable game. A negative EV means a losing endeavor.

But wait a minute.

You’ll probably think that the time you get into a ticket-buying frenzy is when the lottery is at its positive EV.1 Right?

Wrong …

A Positive EV Doesn’t Always End Up a Positive One

While theoretically, a positive EV is a good signal for buying lotto tickets, in practice, a positive EV doesn’t always give you positive returns.

You add other factors such as taxes, the annuity, the cash option, and the possibility of splitting the jackpot prize, and you’ll end up with a negative value.

An analysis by the Business Insiders team of the Powerball $1.5 Billion jackpot shows a negative expected value of -$0.25 after the tax is taken out.2

In short, a positive EV in the lottery rarely happens. Realistically, the lottery always yields a negative value.

Therefore, playing the lottery can never be a substitute for a real job to earn a full-time income.3 If you’re looking for tips on winning the lottery, remember that winning takes a long streak of losses.4 The lottery is a gambling activity and must be considered only for fun and excitement.5

EV calculation differs from one lottery to another, depending on the payout.

So the next time you play, ask yourself: “Do I have a positive EV?” Get some pen and paper and get your math done.6

See related post: How to Win the Lottery According to Math.

How to win the lottery #5: Accept that the lottery is not a profitable exercise. A lottery game is just for fun. This hypothetical monsters are setting aside money for their lottery entertainment.
Since the expected value of the lottery is always negative, play only the money you can afford to lose.

Questions and Answers

What does “expected value” mean in lottery games?

The expected value in lotteries represents the average amount one might expect to win per ticket. It is calculated by multiplying the prize amounts by their respective probabilities and summing these products. This calculation is crucial for understanding the long-term financial prospects of playing the lottery, as it offers insight into whether a game is statistically worth playing.

When can a lottery game have a positive expected value?

In rare circumstances, a lottery game can have a positive expected value, typically when the jackpot has rolled over multiple times and grown significantly. However, such situations are infrequent, and the odds of winning remain extremely low. The expected value is usually negative, especially if the payout doesn’t roll down to the lower-tier prizes.

Why doesn’t a positive expected value ensure profit in lotteries?

A positive expected value doesn’t guarantee profit due to the low probability of winning the top prize. Lotteries are designed to be profitable for the organizer, not the player. Even with a positive expected value, most players will lose money.

Additional Resources

  1. Why Buying Hundreds of Lotto Tickets Can Be Useless    []
  2. According to math, it’s not worth risking $2 to play for the $1.5 billion Powerball jackpot    []
  3. Lottery Addiction – Signs, Dangers and Where To Get Help    []
  4. The Winning Lottery Formula Using Math    []
  5. Play The Lottery Responsibly    []
  6. Lottery Calculator: A Mathematical Guide Beyond Number Selection    []

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