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. 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. Multiplying 1.09% by the fixed $4.00 payout results in an expected value of $0.04. One divided by 92 equals approximately 1.09%. For example, the odds of having a single matching number and the Powerball number correct on a single ticket is 1 in 92. The calculation is simply each potential payout times the odds of having a ticket with the right combination of numbers. 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. Both Mega Millions and Powerball have specific and published odds for the possible winning outcomes. The two multi-state jackpot lottery games provide great examples of how the concept of expected value works. 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.

Expected value is a concept that works in a variety of situations. If it is possible to assign odds to a set of monetary outcomes, an expected value can be calculated. This is the projected value based on the probability of a given set of outcomes occurring.

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. Its focus was determining how much a lottery ticket is worth.Īsk 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. 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.

Current mega and powerball jackpot