Is a Lottery Ticket Ever Worth Buying? The Expected Value of Powerball and Mega Millions

What does "expected value" mean for a lottery ticket?

Expected value is the average amount a ticket pays back if you could play the same drawing an enormous number of times. You take each prize, multiply it by the chance of winning it, and add the results. If the total is below the ticket price, the ticket loses money on average. If it is above, the ticket has positive expected value, which is the textbook definition of a bet worth taking.

It is a long-run average, not a prediction. Nobody wins 32 cents on a Powerball ticket. Almost everyone wins nothing, about 1 player in 25 wins a small prize, and a tiny number win a lot. Expected value folds all of those outcomes into one number so you can compare games, add-ons and jackpot sizes on equal terms.

The inputs come straight from the official prize charts. Every figure below uses the odds published by Powerball and Mega Millions, and the arithmetic was checked by computing each game's odds from scratch (5 of 69 plus 1 of 26 for Powerball, 5 of 70 plus 1 of 24 for Mega Millions). For how those odds are derived, see our guide to how lottery odds work.

How much is a Powerball ticket worth without the jackpot?

Start with the prizes that don't change from drawing to drawing. Powerball pays $1 million for matching five white balls, $50,000 for four plus the Powerball, $100 for four or for three plus the Powerball, $7 for three or for two plus the Powerball, and $4 for one plus the Powerball or the Powerball alone.

So the fixed prizes hand back about 16 cents of every dollar spent. The remaining value has to come from the jackpot, which is why the size of the jackpot matters so much to this calculation and so little to your odds. The odds of the top prize stay at 1 in 292,201,338 whether the jackpot is $20 million or $2 billion.

How much is a Mega Millions ticket worth?

Mega Millions works differently since its April 2025 overhaul. A play costs $5 and every ticket carries a built-in multiplier of 2X, 3X, 4X, 5X or 10X that applies to all non-jackpot prizes. The official chart lists the 2X amounts as the lowest prizes: $2 million for five white balls, $20,000 for four plus the Mega Ball, $1,000 for four, $400 for three plus the Mega Ball, $20 for three or two plus the Mega Ball, $14 for one plus the Mega Ball and $10 for the Mega Ball alone.

The multiplier odds Mega Millions publishes (1 in 2.13 for 2X, 3.2 for 3X, 8 for 4X, 16 for 5X and 32 for 10X) work out to an average multiplier of 3. Multiply the base prizes by 1.5 to get their expected size, weight each by its odds, and the fixed prizes are worth about $1.12 per $5 play, or 22 cents per dollar.

That is a better return on the fixed prizes than Powerball's 16 cents, but you are spending $5 instead of $2 for one shot at a jackpot with very similar odds (1 in 290,472,336). The higher price buys bigger small prizes, not a better chance at the big one. Our Powerball vs Mega Millions comparison covers the rule differences in more detail.

Why the advertised jackpot overstates what a ticket is worth

The jackpot figure on the billboard is the annuity: 30 graduated payments over 29 years, each 5% larger than the last. The lump sum you can take instead is much smaller, because it is roughly what the lottery would need to invest today to fund those payments.

Two recent examples from powerball.com show the gap. When two tickets split the $1.787 billion jackpot of September 6, 2025, each winner's share was $893.5 million as an annuity or $410.3 million in cash, a cash value of about 46% of the headline. On November 8, 2026 the site listed a $30 million estimated jackpot with a $12.9 million cash value, about 43%. The ratio moves with interest rates; the calculations here assume 45%.

Most big winners take the cash, and for expected-value purposes the cash figure is the honest one: it is what the prize is worth today. Using the advertised annuity roughly doubles the jackpot's apparent contribution. Our guide to lump sum vs annuity explains when the annuity can still make sense for a winner.

How do taxes change the math?

The IRS requires the lottery to withhold 24% of any prize where the winnings minus the wager exceed $5,000, according to the instructions for Form W-2G. That withholding is a down payment, not the final bill. A jackpot pushes the winner into the top bracket, which for tax year 2026 is 37% on income above $640,600 for a single filer and $768,700 for a married couple filing jointly, per the IRS 2026 inflation adjustments. Nearly all of a large jackpot is taxed at that rate, so the calculations below apply 37% to the cash value.

State tax comes on top. A handful of states don't tax lottery winnings at all, while New York can take more than 10% before city tax. The tables below leave state tax out, so they show the best case. Our breakdown of tax on big jackpot wins has the state-by-state figures.

What is a Powerball ticket worth at different jackpot sizes?

The table assumes a cash value of 45% of the advertised jackpot, the 37% top federal rate on the jackpot, no state tax, no splitting, and the 32 cents of fixed prizes counted before tax. The splitting problem comes in the next section; for now, imagine you are guaranteed to be the only winner.

The "headline" column is the one that circulates on social media when a jackpot gets big, and it suggests a $2 ticket becomes worth more than $2 at around $490 million. That figure ignores the cash option and taxes. Using the cash value alone, before tax, the crossover is near $1.09 billion. After federal tax, it is about $1.73 billion, a level reached only a few times in the game's history.

The same table for Mega Millions is starker. At a $1 billion jackpot a $5 ticket is worth about $2.09 after federal tax, and at $1.5 billion about $2.58. The after-tax break-even point works out to roughly $4 billion, about twice the largest jackpot any US lottery has ever offered.

What are the chances of splitting the jackpot?

This is the factor most break-even claims leave out. Big jackpots sell far more tickets, and every extra ticket is another chance that someone else matches the same six numbers. If they do, you share the prize.

Powerball doesn't publish the number of plays sold per drawing, but its winner counts allow a rough estimate. For the September 6, 2025 drawing, Powerball reported more than 9.9 million prize-winning tickets, 20 Match 5 winners and 322 Match 4 plus Powerball winners. Dividing those counts by each tier's odds gives estimates between about 234 million and 294 million plays, so roughly 250 million is a fair round number. That drawing produced two jackpot winners, in Missouri and Texas.

With a known number of plays, the expected share of a winning ticket can be calculated. Assuming numbers are spread randomly (quick picks are, and hand-picked numbers cluster, which makes splitting more likely):

At 250 million plays, a winning ticket keeps about two thirds of the jackpot on average. That one adjustment pushes the after-tax Powerball break-even from about $1.73 billion to roughly $2.6 billion, above the record $2.04 billion jackpot won in California in 2022. Sales and jackpot size rise together, so the bigger the jackpot gets, the harder the splitting factor pulls back. For what happens when a jackpot is shared, see what happens if two people win.

Was the $1.787 billion Powerball jackpot worth playing?

It is the closest real test available. The total cash value of that jackpot was $820.6 million (two shares of $410.3 million). Run it through the steps above:

• Fixed prizes plus the full cash jackpot, before tax and with no splitting: about $3.13 per $2 ticket.
• After 37% federal tax on the jackpot: about $2.09.
• After also allowing for an estimated 250 million plays and the chance of sharing: about $1.51.
• Adding a 5% state tax: about $1.41.

Even at one of the three largest jackpots in Powerball history, a ticket was worth around 70 cents on the dollar for a single winner in a typical taxing state. That is better than the 16 cents of an ordinary drawing, but it is still a losing bet.

Do Power Play and Double Play improve the value?

Both are $1 add-ons, so the question is whether that extra dollar returns a dollar.

Power Play multiplies non-jackpot prizes by 2, 3, 4, 5 or, when the advertised jackpot is $150 million or less, 10. Match 5 becomes a flat $2 million with any multiplier. Using Powerball's published multiplier odds (24, 13, 3 and 2 in 43 for 2X to 5X, and 1 in 43 for 10X), the average multiplier is about 2.77 when 10X is in play and 2.60 when it isn't. The extra dollar buys about 50 cents of expected value with 10X available and about 46 cents without it. Our Power Play guide covers the full multiplier chart.

Double Play, sold in 30 lotteries, enters your same numbers into a second drawing with a $10 million top cash prize, $500,000 for Match 5 and smaller fixed prizes. Using the odds on the Double Play prize chart, the extra dollar is worth about 53 cents, of which 3 cents comes from the top prize. Because that top prize is fixed, the value never rises with the main jackpot.

On these numbers, neither add-on rescues the ticket, but each returns about half its cost, which is a much higher rate than the 16 cents per dollar of the base Powerball play in a normal drawing. For a player who has already decided to spend a set amount, a Power Play dollar loses less on average than a second base ticket.

Which lottery games give the best return?

Daily number games are a useful comparison. In fixed-prize states such as Florida, Georgia and Texas, a $1 Pick 3 straight bet pays $500 at odds of 1 in 1,000. That is an expected value of exactly 50 cents per dollar, with no jackpot and no tax drama on a $500 win. Our Pick 3 and Pick 4 payout guide lists the box and combo figures.

The pattern is consistent: the closer a game is to a fixed payout, the steadier its return, and the bigger the jackpot, the more of your dollar is tied up in a prize you will almost certainly not win. The jackpot games make up for the low base return only in rare drawings, and even then taxes and sharing cancel most of the gain.

Is the lottery worth it as entertainment?

Expected value measures money, and money isn't the only reason people play. For a lot of players, a ticket buys a few days of thinking about what they would do with a fortune, a conversation at work, or a small ritual with family. Those are real, and it is reasonable to pay for them the way people pay for a movie ticket, knowing the money doesn't come back.

The arithmetic is still useful for setting limits. If a $2 Powerball ticket returns 32 cents on average, the true cost of playing is about $1.68 per ticket. Someone who buys five tickets a week is spending roughly $437 a year on the experience after typical small wins. Deciding in advance whether that is worth it to you is a better approach than chasing the moment a jackpot "becomes worth it", because on the numbers above, that moment almost never comes.

A few practical rules follow from the math:

• Set a fixed amount you would be comfortable spending on any other hobby, and stop there, whatever the jackpot.
• Buying more tickets for a bigger jackpot raises your spending in a straight line while barely changing your chance of winning. Five tickets at 1 in 292 million is still about 1 in 58 million.
• No strategy changes the expected value. Systems, "due" numbers and lucky stores don't alter the odds of a random drawing.
• If you are playing to win back losses, or spending more than you planned, that is a sign to step away.

If gambling has stopped being fun, the National Council on Problem Gambling's helpline is free and confidential: call or text 1-800-MY-RESET. Current numbers and jackpots for both national games are on our Powerball results page and Mega Millions results page.

Sources: the Powerball prize chart and Power Play odds; the Double Play prize chart; Powerball's announcement of the $1.787 billion Missouri and Texas jackpot; the Powerball home page for the November 2026 jackpot and cash value; the Mega Millions How to Play page; the IRS Form W-2G instructions and 2026 tax brackets. Expected values are our own calculations from those published prizes and odds.

Lottery expected value FAQ

Is buying a lottery ticket ever a good investment?

Not in practice. A $2 Powerball ticket is worth about 32 cents from its fixed prizes, and even at a $1.787 billion jackpot it was worth roughly $1.41 to $1.51 after the cash option, federal and state tax, and the chance of splitting. Mega Millions has never reached break-even after tax.

At what jackpot is Powerball worth buying?

Using the advertised annuity, the math crosses $2 near $490 million, but that ignores the cash option and taxes. Using the cash value after 37% federal tax, the break-even is about $1.73 billion, and once the chance of sharing with other winners is included it rises to roughly $2.6 billion, above the $2.04 billion record.

What is the expected value of a Mega Millions ticket?

About $1.12 per $5 play from the fixed prizes, using the official chart and the built-in multiplier's average of 3. The jackpot adds to that, but after the cash option and 37% federal tax the after-tax break-even is around $4 billion.

Is Power Play worth the extra dollar?

It returns about 46 to 50 cents per dollar on average, depending on whether the 10X multiplier is in play. That is still a loss, but a smaller one per dollar than the base Powerball play, which returns about 16 cents per dollar in an ordinary drawing.

Which lottery game has the best odds of a return?

Fixed-prize daily games return more per dollar than jackpot games. A $1 Pick 3 straight bet pays $500 at odds of 1 in 1,000 in states such as Florida, Georgia and Texas, an expected value of 50 cents per dollar.