What Is the Expected Value of a Lottery Game?

The expected value of a lottery game is calculated by dividing its odds-of-winning by payout and is used to understand how much risk you are taking when participating in a game, and to help determine if playing it is worthwhile or not. We will use an example lottery game with a $5 million jackpot to examine how expected value changes as jackpot size increases.

Lotteries are games of chance, so their expected values tend to be negative. A jackpot with enough value could theoretically offset this expected value; however, such scenarios are extremely unlikely and most lottery tickets usually have an expected value of less than two dollars because chances of winning are so minimal; therefore your money spent purchasing tickets won’t even return if you win the jackpot prize!

As a rule, the higher the jackpot is, the lower its expected value is. This is due to odds being proportional to prize value – so if your chances of winning are one in two instead of three, your expected return would be half what it would otherwise be.

Many lottery gamers may think the expected value of lottery games changes dramatically when the jackpot grows, but this is simply not true; jackpots only have a minor effect on expected ticket values and should never exceed $0.25 per play.

Expected value is a concept applicable to any probabilistic process and used to compare opportunities across fields. When applied to gambling, expected value of casino games is determined by their house edge – for instance if playing a game with 40% house edge will cause actual losses to approach expected losses after about 100 rounds.

Lotteries operate along similar principles to casinos; however, with one key difference: house edges in lottery games tend to be less steep; yet their expected values still come out negative.

Expected value does not provide as accurate an analysis for lotteries as other forms of gambling, for several reasons. Expected value fails to account for how the satisfaction with money declines with additional income and treats each dollar as equal, which does not correspond with real life situations.

Expected value does not consider how the cost of lottery tickets affects overall odds of winning. This factor is essential, since ticket price can either increase or decrease chances of success; to decrease odds even further it is often best to buy multiple tickets; but this may not always be feasible or affordable.