What Expected Value Means for Powerball and Mega Millions

Expected value is the average amount a ticket returns over many plays, and for both Powerball and Mega Millions that number is negative. A $2 Powerball ticket and a $5 Mega Millions ticket each return less than they cost, even when the jackpot looks enormous. Understanding why is the single most useful thing you can learn about big-draw games, because it explains when a jackpot is at least less of a bad deal and when the headline number is mostly an illusion. The figures below are current as of this writing, and jackpots move constantly, so treat the dollar amounts as a snapshot rather than a fixed truth.

What Expected Value Actually Is

Expected value (EV) is a weighted average. You take every possible outcome, multiply each prize by the probability of winning it, add all of those products together, and then subtract the cost of the ticket. The formula is simply EV = sum of (prize x probability) minus ticket cost. If the result is positive, the bet pays more than it costs on average. If it is negative, you lose money on average. Lottery tickets are designed to be negative EV, because the games have to fund prizes, retailers, administration, and state programs out of ticket sales. The question is never whether a ticket is a good investment. It is how negative the EV is, and whether a swollen jackpot narrows that gap enough to matter.

A quick example makes the math concrete. Imagine a single prize of $300 million with a 1 in 292,201,338 chance of winning it. The jackpot contribution to EV is roughly $300,000,000 divided by 292,201,338, which is about $1.03 per ticket from the jackpot alone. That already sounds close to the $2 ticket price, and it is the reason people convince themselves a giant jackpot is a fair bet. The rest of this article is about why that $1.03 is badly overstated.

Use the Cash Value, Not the Annuity Headline

The advertised jackpot is an annuity, paid out over roughly three decades in growing installments. The lump sum you can actually take today, the cash value, is much smaller because it is the present value of that annuity. For Powerball right now, the advertised jackpot is about $302 million but the cash value is about $135.3 million. For Mega Millions, the advertised jackpot is about $452 million while the cash value is about $201 million. Almost everyone who wins takes the cash, so the cash value is the honest number to drop into an EV calculation. Using the annuity headline roughly doubles the jackpot in your math and makes the bet look far better than it is.

Redo the Powerball jackpot term with the cash value: $135,300,000 divided by 292,201,338 is about $0.46 per ticket, not $1.03. That single correction cuts the jackpot contribution by more than half before a dollar of tax is considered.

Taxes Take Another Large Cut

Lottery winnings are ordinary income. A jackpot drops you into the top federal bracket of 37%, and the IRS withholds 24% up front with the rest due at filing. Many states add their own income tax on top, commonly in the 3% to 10% range, though a handful of states tax lottery prizes at zero. After federal tax alone, that $135.3 million Powerball cash value is worth closer to $85 million in the winner's pocket, and a typical state tax trims it further. Plugging the after-tax figure back into the EV math pushes the jackpot contribution down to roughly $0.29 per ticket on Powerball. The ticket still costs $2.

Jackpot Splitting Gets Worse as Jackpots Grow

There is a counterintuitive trap built into large jackpots. When the prize climbs, ticket sales spike, which means more numbers in play and a higher chance that two or more people hit the jackpot and split it. A split jackpot pays each winner a fraction of the total, so the prize you are actually buying a chance at is smaller than the posted number. This is why EV does not simply rise forever as the jackpot grows. Past a certain point, the extra ticket sales that pump up the jackpot also raise the odds you would share it, and the two effects partly cancel. The biggest, most heavily advertised jackpots are often the ones most exposed to splitting.

The Non-Jackpot Prizes Barely Move the Needle

Both games advertise good overall odds of winning something. Powerball lists overall odds of 1 in 24.87 and Mega Millions about 1 in 24, meaning you win some prize on roughly 1 in every 24 to 25 tickets. That sounds encouraging until you see what those prizes are. The vast majority are small, often just the cost of the ticket or a few dollars, and stepping up the tiers gets rare fast at 1 in 292,201,338 for the Powerball jackpot and 1 in 290,472,336 for the Mega Millions jackpot. Add up every non-jackpot tier weighted by its probability and you get only a few cents of EV per ticket. They soften the loss a little. They do not change the conclusion.

Mega Millions After the 2025 Redesign

Back in April 2025 Mega Millions raised its ticket price from $2 to $5. The increase was not purely a price hike. The redesign improved the jackpot odds and built a random multiplier into every ticket, so the prize structure changed alongside the cost. The higher price still has to clear a higher bar to be worthwhile, and at $5 a play the EV gap in raw dollars is wider than Powerball's even though the structure is richer. The redesign is a useful reminder that ticket price, odds, and prize structure are three separate levers, and you have to look at all three together rather than reacting to any one number.

The Summary

Even a bet framed as 1 in 292 million for $300 million is negative EV once you swap the annuity headline for the cash value, subtract federal and state taxes, and account for the real chance of splitting the prize. That is not a reason to feel foolish for buying a ticket now and then. It is a reason to buy with clear eyes: the entertainment is real, the expected return is not, and no jackpot size flips the math fully positive in practice. If you want to think about where each dollar goes more carefully across all lottery products, our ValueScore explainer covers how we rank the scratch-off side of the market using the same logic. The takeaway is short: use cash value, subtract taxes, respect split risk, and treat the small prizes as pennies, not as a reason to play.

Sources

Powerball: Prize Chart and Odds (jackpot odds 1 in 292,201,338; overall 1 in 24.87 on a $2 play)

Mega Millions: Mega Millions to Get MEGA Enhancements in April 2025 ($5 ticket; jackpot odds improved to 1 in 290,472,336; built-in multiplier)

Internal Revenue Service: Topic No. 419, Gambling Income and Losses (24% federal withholding on winnings of $5,000 or more; remainder due at filing)