Understanding the math behind the lottery draws a sharp line between two activities people sometimes lump together: gambling, where the expected value is negative by design, and investing, where money is put to work with a reasonable expectation of long-run growth. They are not the same kind of financial decision, and the numbers show why.
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What “expected value” actually means
Expected value is a way of asking what an outcome is worth on average if you repeated it many times. For a lottery ticket, you multiply each possible prize by its probability and add those up. Because a lottery pays out less in total prizes than it collects in ticket sales, that average always comes out below the price of the ticket. A longer walkthrough of the math, with worked examples, is available at the Lotterycodex expected value page.
Investing works on a different structure. Returns come from the performance of real, underlying assets, businesses generating profits, paying dividends, and growing over time. Average outcomes are positive over long horizons, though returns are never guaranteed and can be negative in any given year.
What the lottery actually returns
The Motley Fool’s research team found that Americans spent $104.7 billion on lottery tickets in 2024, a record high. Of that, $70.2 billion went back out as prizes, and states kept $29.7 billion after administrative costs. In no state does the lottery pay out more in prizes than it collects in sales. The share states keep has actually shrunk over time, from 32.8 cents of every dollar in 2012 down to 28.3 cents by 2024, as prize payouts have grown faster than ticket sales.1
For an individual player, that translates into long odds and small returns. The odds of winning a Powerball jackpot sit at 1 in 292,201,338. The odds of winning any prize at all, including the smallest ones, are closer to 1 in 24.9.
The picture looks similar outside the US. AJ Bell, a UK investment platform, calculated that the National Lottery’s expected value works out to about 45 pence for every £1 spent, once you account for the chance of smaller wins alongside the near-impossible jackpot.2 British households spend an average of around £420 a year on lottery tickets and scratchcards combined, or about £35 a month, according to the National Lottery’s own figures cited by AJ Bell. Frequent players who also join subscription draws often spend closer to £50 a month.
Running the same money through an investment account instead
AJ Bell modeled what that £50 a month would look like over 20 years under both paths. Spent on lottery tickets, £12,000 in contributions carries a theoretical value of about £5,400, based on the 45p-per-£1 expected return. Invested instead in a fund tracking a broad global stock index, using a conservative 7% average annual return, that same £12,000 would grow to roughly £24,000 over the same 20 years, even after accounting for fees. That is a difference of about £18,600 between the two paths, run through identical monthly contributions.
The gap comes down to compounding. A lottery ticket is a one-shot bet that resets to zero the moment it doesn’t win. An index fund holds a stake in companies that, in aggregate, tend to generate more cash than they need and pass some of that back to shareholders through dividends and buybacks, which can then be reinvested to buy more shares. Over enough years, that reinvestment compounds. A lottery ticket has no equivalent mechanism.
Here’s the computation laid out step by step, using the same figures and assumptions AJ Bell used:
| Step | Lottery path | Investing path |
|---|---|---|
| Monthly amount | £50 | £50 |
| Time horizon | 20 years (240 months) | 20 years (240 months) |
| Total contributed | £12,000 | £12,000 |
| Assumed return basis | 45p expected value per £1 spent | 7% average annual return (global equity index, e.g. FTSE All-World) |
| Calculation | £12,000 × 0.45 | £12,000 compounded monthly at 7%/year, minus a small deduction for charges |
| Resulting value after 20 years | ≈ £5,400 | ≈ £24,000 |
| Difference | — | ≈ £18,600 more than the lottery path |
Why people still spend more on lottery tickets than stocks
Despite the math, lottery tickets remain the most common speculative purchase in the US. A national SSRS poll from 2025 found that 76% of American adults have ever bought a lottery ticket, more than any other type of speculative asset the survey asked about.3 By comparison, 49% have ever invested in individual stocks. Looking only at the past year, 53% of adults had bought a lottery ticket recently, compared with 30% who had invested in stocks over the same period.
The gap is not just about awareness. Investing in individual stocks requires an account, some upfront knowledge, and, in many cases, a larger commitment of time and money than walking into a convenience store. A lottery ticket is available at the register for a couple of dollars. That accessibility gap likely explains part of why lottery spending remains so widespread even though its expected return is lower.
What consistent lottery spending costs over a lifetime
Economists Victor Haghani and James White at Elm Wealth estimated that Americans were on track to spend about $125 billion on lottery tickets in 2024, more than they spend on music, sports tickets, movies, and books combined. Within that total, they estimate roughly 40 million households are habitual players, spending around $2,500 a year each, and that these households are concentrated in the lowest income quartile, where $2,500 often represents a meaningful share of discretionary income.4
Elm Wealth’s modeling shows what that same $2,500 a year could do if redirected. Put into a retirement account for 35 years and invested at a 4.25% real annual return, it could support a real annual retirement annuity of about $15,000 starting at age 65. That is not a claim about what any individual will earn. It is a projection based on a fixed contribution, a fixed time horizon, and a fixed assumed return, and real-world results will vary with market performance and personal circumstances.
The core difference, in one line
A lottery ticket is a single, independent draw with a fixed, negative expected value baked into the game’s structure. An investment in a diversified portfolio is a claim on the long-run output of real businesses, with a return that is variable and never guaranteed, but that has historically trended positive over long periods. Both involve risk. Only one of them is built so that the total paid out is mathematically less than the total collected.
None of the figures above are predictions about what any specific person will earn from either activity, and past results in either the market or the lottery are not a guarantee of future outcomes. This article is for general information and does not constitute financial advice.
References
- The Motley Fool, Lottery Statistics and Revenue by State [↩]
- AJ Bell, Lottery Spending Versus Investing [↩]
- SSRS, From Lottery Tickets to Stocks: The Public and Investments in Speculative Assets [↩]
- Haghani, V. and White, J., Elm Wealth, Buying a Dream, Losing a Future: The Financial Fallacy of Lottery Tickets for Low-Income Households [↩]