What it means
Most lotteries are run by governments or licensed operators. Players pay a small price per ticket, and a portion of total sales is paid out as prizes, with the rest going to operating costs, taxes and, in many places, good causes.
Because the operator keeps a share, the total prizes paid are always lower than the total ticket sales. Expected value is the average result if the game were repeated many times.
It is calculated by multiplying each possible prize by its probability and adding the results. For nearly every lottery the expected value of a ticket is lower than its price, which means players lose money on average.
The attraction is psychological. People weigh a tiny chance of a life-changing sum more heavily than its true probability suggests, and the cost of each ticket feels trivial.
Behavioural economists use this to explain why people buy lottery tickets while also buying insurance, which are opposite attitudes to risk. Winners face financial questions of their own.
Prizes are often offered as a lump sum or as payments over many years, and the lump sum is smaller because the annuity version includes future interest. Tax treatment varies by country, and sudden wealth calls for good advice on investing, spending and estate planning.
For an individual, a lottery ticket is entertainment and not a savings plan. Money spent regularly on tickets could instead be invested, where it would on average earn a positive return over time.
Regulation focuses on fairness and protection. Operators must publish odds and payout rules, and many jurisdictions restrict sales to minors and promote responsible play.
Because lotteries raise money for governments or good causes, critics sometimes describe them as a voluntary tax that falls most heavily on lower-income households.
In practice
Real-world examples.
Example
A shop worker spends $5 a week on lottery tickets. Over a year that is $260, and with an average return of 60 cents per dollar she can expect to get back around $156, losing about $104. She treats this as the price of a weekly bit of excitement and keeps it in her entertainment budget.
Example
A financial planner shows a client that investing $260 a year at a 6% annual return for 30 years would grow to a meaningful sum, whereas lottery spending is gone each time. He notes that the invested sum would be about $20,000 after 30 years, assuming the return held.
Example
A winner of a $5,000,000 prize has to decide between a lump sum and annual instalments. His adviser compares the after-tax value of each, taking into account his needs, his tax position and the interest that could be earned. She advises him to place the money in a separate account while he decides.
Formula
Calculation
Expected value of a ticket = Sum of (Prize x Probability of winning that prize)
Net expected value = Expected value - Ticket price
Suppose a $2 ticket has a single jackpot of $10,000,000 with a probability of 1 in 20,000,000, plus a $10 prize with probability 1 in 50.
Jackpot contribution = $10,000,000 x (1 / 20,000,000) = $0.50.
Small prize contribution = $10 x (1 / 50) = $0.20.
Expected value = $0.50 + $0.20 = $0.70.
Net expected value = $0.70 - $2.00 = -$1.30, so on average the player loses 65% of the ticket price.Case study
Seen in the real world.
Hartley Street Social Club is an illustrative, fictional group of twelve colleagues who pool $5 each week for lottery tickets. Over a ten-year period they spent a total of $31,200 and won a series of small prizes worth $11,400.
One member, who works in accounts, calculated that the group had returned about 37% of the money spent. She proposed that they continue the club for fun but cap spending at $2 each, and put the saved $3 a week per person into a shared savings plan.
After ten more years the savings plan, earning a modest return, was worth more than the lottery winnings of the previous decade. In this fictional story the club kept its Friday ritual, but the members stopped regarding it as a financial strategy.
Watch out
Common mistakes.
- Treating a lottery ticket as an investment, when its expected return is negative.
- Believing numbers are due to come up because they have not been drawn lately, when each draw is independent.
- Counting the headline jackpot as the likely prize, when taxes, shared wins and the lump sum discount reduce it.
Questions
People also ask.
Is a lottery ever a good bet?
Almost never in financial terms, because the operator keeps a share of sales, though a jackpot that has rolled over many times can occasionally have a higher expected value before prize splitting.
Why do people play despite the odds?
Many value the excitement and the small chance of a dramatic change, and treat the cost as entertainment.
What should a big winner do first?
Seek professional tax and financial advice, keep the win private where possible, and avoid hasty spending or lending.
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