How Much Is a Mega Millions Lottery Ticket Worth?

The Mega Millions jackpot is currently an estimated $1.25 billion. It is the fourth-largest Mega Millions jackpot and the sixth-largest U.S. lottery jackpot ever. So, it’s good time to revisit a question I’ve addressed in previous Investor Updates, how much is a lottery ticket worth?

Ask most people and the most probable answers will be the price of the ticket, the value of the jackpot or simply: “Is it a winning ticket?” When one simply considers the likelihood of winning anything, the value following Friday’s drawing for most people will be zero, zilch, nothing.

For possibly one (or even more than one) ticket holder, the gross value will be an estimated $1.25 billion. In between, there will be a small percentage of ticket holders who will have tickets with a gross value of between $4.00 and $1 million.

None of these reflect the expected value of the ticket prior to Friday night’s drawing. There is a concept of risk and reward that 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.

Multistate jackpot lottery games like Mega Millions provide great examples of how the concept of expected value works. 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. The odds of having just the gold Mega Ball correct on a single ticket are 1 in 37. One divided by 37 is 2.7%. Multiplying 2.7% by the fixed $2.00 payout results in an expected value of $0.05. Put another way, if you adjust the $2.00 prize by the probability of having the right Mega Ball number on your ticket, you end up with an expected value of $0.05.

The expected value of having one other number correct in addition to the Mega Ball is actually lower ($0.04) even though the prize is double the amount at $4.00. This is because the odds of getting both numbers right are less than half at 1 in 89, or 1.1%.

Running this math for all the fixed payouts gives us a cumulative expected value of $0.25 for a Mega Millions lottery ticket. This value is inflated because taxes will be owed on the winnings and the larger prize amounts will be reported to the Internal Revenue Service (IRS).

The big prize in the Mega Millions, of course, is the jackpot. 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 the expected value. The current estimated $1.25 billion Mega Millions jackpot equates to an expected pretax value of $4.38 for a single ticket. The jackpot single-handedly adds $4.13 to the expected value of a single ticket purchased for the drawing.

This is based on a sole winner taking the annual payout. If there is a single winner and they opt for the current estimated cash payout of $625.3 million, the expected value falls to $2.31 per share.

In response to previous requests, I factored federal taxes into the analysis. Assuming the 37% federal tax bracket holds, taking the annual payout results in a current expected value of $2.72. Opting for the cash payout instead results in an expected aftertax value of $1.46. Neither calculation factors in what the winner might do with the money (spend it, invest it, etc.) or adjusts it for future inflation. The analysis simply determines whether the expected value based on the estimated payout amounts is above or below the $2.00 cost of the ticket.

The impact that the size of the jackpot has on the expected value 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 risking dollars on companies in or headed to bankruptcy, like Yellow Corp. (YELL), is not a good idea. The probable—not just likely, but probable—outcome is a complete loss of the dollars invested. (Speculated may be a better word than “invested.”)

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 necessary data 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. To determine whether expected returns are 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 Mega Millions jackpot has an eventual winner, the odds of losing everything spent on a lottery ticket remain steady at 94.5%. 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.