How Much Are Mega Millions And Powerball Lottery Tickets Worth?

Given the current (as of the time of writing) $640 million jackpot for the Powerball and the $750 million jackpot for the Mega Millions lotteries, I thought I’d share an updated version of an Investor Update commentary I wrote three years ago. Its focus was determining how much a lottery ticket is worth.

Ask most people how much a lottery ticket is worth and the most probable answers will be the price of the ticket, the value of the jackpot or simply: “Is it a winning ticket?” The value of a ticket for a forthcoming drawing is none of these. The reason for this is related to a concept of risk and reward many people often fail to grasp, aren’t aware of or ignore at their own peril.

The concept is expected value. This is the projected value based on the probability of a given set of outcomes occurring. If it is possible to assign odds to a set of monetary outcomes, an expected value can be calculated. Expected value is a concept that works in a variety of situations. Investors, for instance, can use historical data to determine the likelihood of being able to fund retirement with a certain savings rate or allocation strategy.

The two multi-state jackpot lottery games provide great examples of how the concept of expected value works. Both Mega Millions and Powerball have specific and published odds for the possible winning outcomes. They also have published prize amounts. This allows anybody with a calculator—though a spreadsheet makes the calculations easier—to determine when the expected value of a lottery ticket exceeds the $2.00 cost.

The calculation is simply each potential payout times the odds of having a ticket with the right combination of numbers. 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. Put another way, if you adjust the value of the prize by the probability of actually winning the prize, you end up with an expected value of $0.04. Running this math for all of the fixed payouts gives us cumulative expected values of $0.25 for a Mega Millions ticket and $0.32 for a Powerball ticket.

The big prize in both games is, of course, the jackpots. Both the sheer size and the variable nature of a jackpot have great influence on the expected value of a lottery ticket. Not surprisingly, the larger the jackpot, the higher expected value. The current estimated $750 million Mega Millions jackpot equates to an expected pretax value of $2.73 for a single ticket. The jackpot single-handedly adds $2.48 to the expected value of a single ticket purchased for the drawing. The math is $750 million times the 0.0000003% odds of matching all five primary numbers plus the sixth Mega Ball number.

The expected value of a Powerball ticket is different not only because the jackpot is different, but also because there are differences in the odds for the various payouts as well. The jackpot prize accounts for $2.19 ($640 million times 0.0000003%) of the total $2.51 expected value of a single ticket.

The impact that the size of the jackpot has should be very apparent. This has significance for investing as well. The riskier the investment is, the higher the required return must be to justify the excess risk. And the higher the required return is, the greater the likelihood of not realizing that return. This is why so-called “lottery stocks” and similar types of securities are risky. For every Facebook, Apple, Netflix, Alphabet (aka Google) and Tesla, there is a very large number of companies that flounder.

While it may be hard to assign exact odds, a person can use historical data to judge when a projected rate of growth is unusually high. Adding basic industry and economic research can add to the scenario analysis (e.g., is it realistic for the company to sell $X dollars of its product or service). Even when you lack the data necessary to calculate an expected value, you should be able to gather enough information to place some odds on whether an “everything goes right” scenario will or will not occur. For returns large enough to justify the risks, the “everything goes right” scenario is often necessary.

When doing such analysis, be aware of the element of luck. Just as every lottery jackpot has an eventual winner, the odds of losing everything spent on a lottery ticket always remain steady at 96%. The same principle applies to investing in high-risk stocks and securities: While a few will realize huge returns, many will end up losing most of their value.

(Note: The calculation used to determine the expected value of the Mega Millions and Powerball tickets does not factor in taxes on the winnings, how the jackpot will be claimed—lump sum or a series of payments—or what will be done with the winnings afterward. Nor do they consider how sharing the jackpot with one or more other winning ticket holders will impact the expected value. I avoided going down this rabbit hole in order to focus on the concept of expected value. In a real-world environment, all three have a significant impact.