Analysis
When is a lottery ticket "worth" it? The expected-value math
There is a jackpot size at which a ticket's expected value passes its price. It is much higher than most people assume, and reaching it still does not make the bet a good one.
Expected value is the average result of a bet repeated forever: each outcome's value multiplied by its probability, all added together. For a lottery ticket it is the cleanest way to see what you are buying — and the calculation has a genuinely surprising middle section.
Step 1: the fixed prizes
Everything below the jackpot is a known amount at known odds, so it can be summed directly.
| Match | Prize | Probability | Contribution to EV |
|---|---|---|---|
| 5 white | $1,000,000 | 1 in 11,688,054 | $0.0856 |
| 4 white + PB | $50,000 | 1 in 913,129 | $0.0548 |
| 4 white | $100 | 1 in 36,525 | $0.0027 |
| 3 white + PB | $100 | 1 in 14,494 | $0.0069 |
| 3 white | $7 | 1 in 579.76 | $0.0121 |
| 2 white + PB | $7 | 1 in 701.33 | $0.0100 |
| 1 white + PB | $4 | 1 in 91.98 | $0.0435 |
| 0 white + PB | $4 | 1 in 38.32 | $0.1044 |
| Total fixed prizes | $0.3199 |
A $2 Powerball ticket therefore returns $0.32 — 16.0% of its price — from the fixed tiers alone. The equivalent figure for a $5 Mega Millions play is $0.37, or 7.5%, before its built-in 2X–10X multiplier is applied. Roughly a fifth of your money, in other words, is buying small prizes; the rest is buying jackpot probability.
Step 2: the naive break-even jackpot
For the whole ticket to break even, the jackpot term has to cover the remaining $2 − $0.32 = $1.68. Divide by the jackpot probability and you get the required prize:
Break-even jackpot = (ticket price − fixed EV) × 292,201,338 ≈ $491 million
That is the number people usually stop at, and on its own it makes billion-dollar jackpots look like a bargain. It is also wrong, because it treats the advertised jackpot as money received.
Step 3: what the jackpot is actually worth
The advertised figure is an annuity spread over 29 years. Take the cash instead and you get roughly half. Then the entire amount is taxed as ordinary income at the top federal rate.
| Adjustment | Multiplier | Running value of an advertised $1 billion |
|---|---|---|
| Advertised annuity | 1.00 | $1,000 million |
| Cash option (≈50%) | 0.50 | $500 million |
| Federal tax at 37% | 0.63 | $315 million |
| Kept, best case | 0.32 | $315 million |
Only about 32% of the advertised prize reaches the winner in a no-state-tax jurisdiction, so the break-even jackpot has to be scaled up by the inverse of that fraction:
| Game | Naive break-even | After cash discount and 37% federal tax |
|---|---|---|
| Powerball | $491 million | $1.56 billion |
| Mega Millions | $1.13 billion | $3.58 billion |
Powerball has reached that territory a handful of times in its history. Mega Millions, at $5 a play, essentially never has.
Step 4: the killer — sharing
The calculation above assumes you would be the only winner. At exactly the jackpot levels where expected value looks attractive, that assumption collapses: enormous jackpots sell enormous numbers of tickets, and the chance that somebody else holds your combination rises with every one of them.
The record board is blunt about it. The January 13, 2016 Powerball jackpot, the first over a billion dollars, was split 3 ways. The September 6, 2025 jackpot of $1.787 billion was split 2 ways. Sharing does not reduce the jackpot term a little; it halves or thirds it, and it does so precisely when the prize is large enough to have tempted you in.
Why positive expected value still wouldn't make it a good bet
Suppose the arithmetic did tip over. A ticket would still be a terrible financial instrument, for reasons that have nothing to do with the mean:
- The variance is absurd. The expected value is carried almost entirely by an outcome with probability 1/292,201,338. You would need to buy tickets for far longer than the age of the universe for the average to have any predictive power over your own results.
- Money is not linear. Losing $2 a week for decades costs real utility; the millionth dollar of a jackpot adds far less happiness than the first. Under any concave utility function the bet gets worse, not better.
- You cannot scale into it. Buying every combination would cost hundreds of millions of dollars, take longer than the sales window allows, and still expose you to sharing.
The historical exceptions
Beatable lotteries have existed, and none of them were jackpot games. In 1992 a syndicate bought a large share of all possible combinations in the Virginia state lottery when a rolled jackpot made the maths favourable. Between 2005 and 2012, groups in Massachusetts exploited Cash WinFall, a game whose jackpot "rolled down" into the lower tiers when it was not won, briefly giving high-volume buyers a genuine edge. Both loopholes were structural design flaws in small games with cheap coverage, and both were closed. Neither has an analogue in a 1 in 292,201,338 national jackpot.
Treat a ticket as an entertainment purchase with a known price and a known, tiny payoff probability. That framing is honest and it never leads anywhere expensive. Our responsible play page has the warning signs worth knowing.