Alternatives
This is not an argument that one is good and the other is bad. It is a description of two probability distributions, with the same money put through each for ten years.
People compare these two things badly, in both directions. "The lottery is a tax on people who can't do maths" is smug and skips the entertainment value. "Stocks are a gamble too" is technically true and hides a difference of several orders of magnitude.
The useful comparison is not moral. It is distributional. Put the same money through both for the same length of time and describe what comes out — mean, median, spread, and the shape of the tails.
$20 a week for 10 years. That is $10,400 of contributions, either way.
Powerball's prize structure is fully published, so the distribution is exactly computable rather than estimated.
Probability any given ticket wins anything. Sum the reciprocals of the published odds across all nine divisions:
1/38.32 + 1/92 + 1/701 + 1/580 + 1/14,494 + 1/36,525 + 1/913,129 + 1/11,688,054 + 1/292,201,338 = 0.04021
which is 1 in 24.87 — the game's published overall odds, recovered from the divisions. Over 5,200 tickets you expect about 209 winning tickets, and the overwhelming majority of those pay $4.
Expected value from the fixed divisions. Everything below the jackpot has a fixed prize, so it sums exactly to $0.32 per ticket (the full working is here). Over 5,200 tickets: $1,664.
Probability of a jackpot. 1 − (1 − 1/292,201,338)^5,200 = 1.78 × 10⁻⁵, or 1 in 56,193.
Probability of any prize of $50,000 or more. Combining the three divisions at that level or above: 1 − (1 − 1.1839 × 10⁻⁶)^5,200 = 0.61%.
So the ten-year lottery distribution is:
| Outcome | Probability | Value |
|---|---|---|
| No prize above $50,000 (the overwhelming case) | 99.39% | about $884 returned on $10,400 spent |
| At least one prize of $50,000 to $1,000,000 | ~0.6% | life-improving, not life-changing |
| Jackpot | 0.0018% | life-changing, before cash value, tax and sharing |
The $884 is worth deriving, because it is the number a player actually experiences. Of the $0.32 of fixed-prize expected value per ticket, $0.14 sits in the two divisions paying $50,000 and $1,000,000 — money you will almost certainly never collect. Strip those out and the reachable divisions give:
Mean: about −$5,200 across the whole distribution (Powerball's prize pool is 50% of sales). Median: about −$9,516, or −91.5% of stake. The gap between those two numbers is entirely jackpot expectation you will not sample.
Here we cannot compute; we can only look at history and state assumptions. The reference series is Damodaran's NYU Stern dataset, 1928 to 2025, in which $100 in the S&P 500 with dividends reinvested became $1,157,598.95 — a geometric mean of 10.02% a year, nominal.
At an assumed 7% (a deliberately conservative figure allowing for fees and a margin against the historical rate), $20 a week for ten years compounds to $15,047 against $10,400 contributed. At 4% it is $12,781. At 0% it is $10,400.
And the downside is real, which is the part the smug version of this comparison leaves out. From the same dataset:
| Period | Cumulative S&P 500 total return |
|---|---|
| 1929–1932 | −64.8% |
| 1974 (single year) | −25.9% |
| 2000–2002 | −37.4% |
| 2008 (single year) | −36.6% |
A ten-year window can end inside one of those. Contributing steadily softens it — you buy more units when prices are low — but does not remove it. Anyone who tells you equities cannot lose money over a decade is selling something.
| Property | 5,200 Powerball tickets | $20/week index fund, 10 years |
|---|---|---|
| Expected return on stake | negative, about −50% | positive under any historically-grounded assumption |
| Median outcome | about −91.5% of stake | modestly positive |
| Best realistic case | jackpot, probability 1 in 56,193 | roughly double the money in a strong decade |
| Worst case | lose it all | a drawdown of a third to two thirds, recovered historically but not guaranteed |
| Skew | extreme right skew; mean far above median | mild right skew; mean near median |
| Can you lose 100%? | Yes, and it is the modal outcome | Only if the fund's entire holdings go to zero |
| Is the variance diversifiable? | No. Buying more tickets buys more of the same bet | Yes. That is what an index fund is |
The last row is the one that does the most work and gets discussed least. An index fund is a variance-reduction device. Owning 500 companies rather than one does not raise your expected return; it collapses the spread around it. Buying 5,200 lottery tickets instead of one raises your chance of a jackpot from 1 in 292 million to 1 in 56,193 — a 5,200-fold improvement on a number that started at essentially zero and remains essentially zero. The arithmetic of that is in how many tickets you would need to be favourite.
Everything above assumes the two are competing as ways to turn money into more money. For most ticket buyers they are not.
A lottery ticket buys a few days of specific, vivid daydream about a life you do not currently have. An index fund buys a slow, boring, statistically superior outcome that will not change your circumstances in kind, only in degree — which is a genuine limitation, not a rhetorical concession. If your honest goal is "become rich enough that my life is different", a fund receiving $20 a week is not a route to it, and saying so is not an argument for tickets; it is an argument for reading realistic paths to a windfall.
The defensible position is boring. The two things are not substitutes. Compare the ticket with other entertainment spending, decide what the daydream is worth, cap it, and put whatever else you were going to gamble somewhere with a positive expectation. Setting a lottery budget does the first part; invest instead of tickets and the invest-instead calculator do the second.
Last verified: 2026-08-29