Lottery Expected Value Calculator

The fundamental theorem of lotteries

Expected value (EV) is the long-run average outcome of a bet:

EV = Σ (probability of outcome × value of outcome) − ticket cost

For lotteries, this is almost always negative. The lottery is designed to return 50-60% of ticket revenue as prizes, with the rest going to government programs, retailer commissions, operator profit, and marketing.

A typical $2 lottery ticket is worth somewhere between 85 cents and a dollar, so you lose 50 to 58 percent of what you spend. That is not an accident, it is the business model, and the number is printed on the annual report.

The major US lotteries and their odds

The “1 in 292,201,338” odds for a Powerball jackpot are nearly impossible to grasp. Some reference points:

• Your annual odds of being struck by lightning are about 1 in 1.2 million, so a single ticket is roughly 240 times longer odds than getting hit by lightning this year.
• Over a lifetime, lightning is about 1 in 15,300, which makes the jackpot nearly 20,000 times longer.
• An asteroid impact killing you is put at about 1 in 75 million over a lifetime, so the jackpot is about 4 times less likely than that.
• Picking one specific person at random out of everyone in the United States, about 340 million people, is roughly the same shot.

That third one is the useful one. Most people will happily agree that they are never going to be killed by an asteroid, and then buy a ticket at four times worse odds.

Powerball EV breakdown

For a $2 Powerball ticket at a $300M advertised jackpot:

So a $2 ticket is worth about 75 cents at a $300M jackpot. Push the jackpot to $1 billion and the jackpot line rises to about $1.19 after the lump-sum cut and tax, which takes the ticket to roughly $1.51 in value against a $2 price: still a loss of about 49 cents, and that is before anyone else wins a share of it.

Why “the jackpot is so high I should buy a ticket” is wrong

When jackpots get extreme ($500M+), ticket sales spike. When ticket sales spike:

• More winners possible, so the jackpot gets split two or three ways
• The lump sum is about half the advertised figure
• After federal tax (37%)
• After state tax (0-13%)
• The “real” value often returns to negative EV

A $1.5 billion Powerball jackpot announced in 2016 sold so many tickets that the actual expected value of a single ticket fell back to about -$0.80, even at that record size.

Lump sum vs annuity, and the number that keeps moving

Almost all winners take the lump sum. The share it represents is not fixed: it is whatever the advertised annuity is worth today at current interest rates, which is why it drifted from roughly 62% in the near-zero-rate years to about 50% today. Check the cash value the lottery publishes rather than assuming a percentage.

At 50%, on a $300M advertised jackpot:

• Lump sum: $150M
• After federal tax (37%): $94.5M
• After state tax (0 to 13%): $82M to $94.5M net

The “advertised jackpot” is the present value of an annuity stream paid over 29 or 30 years. Taking the lump sum effectively gives you the present value at the lottery’s assumed discount rate (~3-5%). Investing the lump sum yourself in a diversified portfolio could match or beat the annuity, but…

Why the annuity might be better

Despite the math favoring lump sum, the annuity offers:

• Protection from bad financial decisions (~30% of jackpot winners go bankrupt within 5 years per some studies)
• Protection from family/friend pressure (you “can’t” give it all away if it comes in 30 annual payments)
• Tax bracket smoothing: each year is taxed on $10M to $15M rather than the whole lump sum at once
• Estate planning simplification

For winners with poor financial discipline (statistically most), the annuity is genuinely better.

The 30% bankruptcy myth

You’ll hear “30% of lottery winners go bankrupt within 5 years.” The original source is a 1996 NORC study and some 2008 economic research, but the numbers are heavily disputed. More careful research suggests:

• Roughly 10-20% of lottery winners file bankruptcy within 5 years
• This is higher than the general population (~1-2% per year) but not “30%”
• Most bankruptcies are by small-prize winners ($50k-$200k) who already had financial problems
• Mega-jackpot winners (over $10M) actually have lower bankruptcy rates if they get financial advice

The narrative is more cautionary than statistical.

The diminishing marginal utility of money

A $1 marginal increase in wealth doesn’t have the same psychological/practical value at every level. For someone earning $40k/year:

• First $50k: huge, because it pays off debt and builds savings
• Next $200k: very valuable, covering a house and a college fund
• Next $1M: somewhat valuable, invested for retirement
• Next $10M: significant lifestyle change
• Next $100M: marginal additional benefit
• Beyond $1B: largely indistinguishable from $100M for living standards

This is why some economists argue lottery tickets can be “rational” at low spending levels even with negative EV. The small monetary loss buys real entertainment value, while the tiny chance at life-changing money has high subjective value. Buying $5 of tickets occasionally as entertainment is one thing; buying $100/week is gambling addiction.

Lottery participation by income (regressive)

Studies consistently show lottery participation as a percentage of income decreases with income:

This makes lotteries one of the most regressive forms of taxation (low-income people pay a far higher proportion of income). Defenders note the lottery is voluntary; critics call it a “tax on the poor.”

Smaller games can have better EV than mega-lotteries

Often-overlooked: small state lotto games with jackpots under $10M sometimes have better EV than Powerball. Lower jackpots mean fewer ticket buyers, fewer shared prizes, and proportionally better odds. Cash 5 or Lucky for Life sometimes offers ~70% of revenue back to players vs Powerball’s ~50%.

Scratch tickets are unique:

• Some scratch games have 65-75% return-to-player (better than mega-lotteries)
• Specific game odds are published by state lottery agencies
• The “trick” is buying tickets after the major prizes have been won (the remaining odds get better)
• Some serious enthusiasts track which games still have unclaimed prizes

The “rational” lottery buyer

If you must buy lottery tickets, the framework that minimizes loss:

1. Limit spending to small entertainment budget ($5-$20/month)
2. Buy when jackpots are at “psychological maximum” (when entertainment value peaks)
3. Take lump sum if you win and have basic financial discipline
4. Take annuity if you’d be tempted to give it all away
5. Don’t play scratch tickets repeatedly, because the entertainment fades fast
6. Don’t buy with the intent of winning; buy with the intent of dreaming briefly

What a lifetime of playing actually buys

Buy one Powerball ticket every week for fifty years and that is 2,600 tickets. Against 1 in 292,201,338 the chance of ever hitting the jackpot works out to 0.00089%, which is about 1 in 112,000. You will see much friendlier figures than that quoted; they are wrong, and they are usually wrong by a factor of ten or twenty because somebody dropped a zero.

Put the other way round: 99.999% of lifelong weekly players never see a jackpot. Not 95%. Doubling to two tickets a week doubles the chance to 1 in 56,000, which is roughly eleven times more likely than being dealt a royal flush pat in five cards, and nobody has ever built a retirement plan around that either.

The 2,600 tickets cost $5,200. At the numbers this calculator returns for a $300M jackpot, the expected loss over those fifty years is about $3,500, which comes to under $6 a month. As a monthly entertainment cost that is entirely defensible, and it is roughly what one coffee a month buys. As a plan it is not a plan.