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 has an expected value of -$0.85 to -$1.00, meaning over many plays you lose 40-50% of what you spend. This isn’t an accident — it’s the business model.

The major US lotteries and their odds

The “1 in 292,201,338” odds for Powerball jackpot are nearly impossible to grasp. Reference points for that probability:

• About 100x less likely than being killed by a lightning strike (1 in 28,500/year)
• 4x less likely than being killed by an asteroid impact (1 in 75M lifetime)
• Less likely than dying on the way to buy the ticket
• Roughly equal to picking one specific person at random among everyone in the US

Powerball EV breakdown

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

So you lose ~$1.25 per $2 ticket on average. Increase the jackpot to $1 billion and the EV improves to roughly -$0.25/ticket — still negative.

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 (jackpot might be split 2-3 ways)
• After lump sum reduction (~60% of advertised)
• 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 — the typical confusion

Almost all winners take the lump sum, which is about 60-65% of the advertised jackpot.

• $300M advertised → ~$190M lump sum
• After federal tax (37%): $120M
• After state tax (varies 0-13%): $105-$120M 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’s tax is on $10-$15M, not the full $190M)
• 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 — pays off debt, builds savings
• Next $200k: very valuable — pays off house, college fund
• Next $1M: somewhat valuable — invests 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 — the entertainment fades fast
6. Don’t buy with the intent of winning; buy with the intent of dreaming briefly

The 0.0000034% probability

At 1 in 292M for Powerball, the chance of winning is so low that:

• A regular weekly player has 0.018% chance of winning in their lifetime (50 years × 52 weeks)
• 95% of regular players will never see a major Powerball prize
• The expected number of lifetime jackpot wins for the average American: 0.00001
• Most lottery winners are first-time or rare players (statistical luck)

Bottom line

Lottery EV is negative — typically -$0.75 to -$1.25 per $2 Powerball ticket. Lotteries return 50-60% of revenue as prizes. Jackpot odds (1 in 292M for Powerball) are so low they’re essentially zero. Lump sums after taxes are about 35% of advertised jackpots. Lottery participation is heavily regressive (low-income people spend disproportionately more). If you must play, treat it as entertainment with a known cost, not as an investment. The math always wins long-term — that’s why governments and corporations run lotteries.