The mathematics of odds
Every lottery publishes, somewhere, what proportion of sales it returns as prizes. We collect the designed figures from game rules and the realised ones from audited accounts, and explain why they differ.
"Return to player" is prize money divided by ticket sales. It is the single most informative number about a gambling product, and — unusually for this industry — it is genuinely published. You just have to know that there are two versions of it and that they are not the same number.
The designed rate lives in the game rules: the percentage of sales a game is obliged to allocate to prizes. The realised rate lives in the audited accounts: what actually got paid out over a financial year. Rules-based figures are exact and forward-looking; accounts-based figures are exact and backward-looking, and include product mix, unclaimed prizes and jackpot luck.
| Game | Prize allocation | Source wording |
|---|---|---|
| UK Lotto | 50% of sales | "On average, 50% of Lotto sales will be available to be paid out in Lotto Prizes, with 9.34% of that 50% being put into a reserve fund." |
| EuroMillions (UK share) | 50% of the entry price | "Allwyn will calculate 50% of the price paid for a EuroMillions Entry and this will be the fund Allwyn uses to pay Prizes." |
| US Powerball | 50% of sales | "The Prize Pool contribution for all Prize Categories shall consist of fifty percent (50%) of each Drawing period sales." |
| Mega Millions | 55% of sales | "The prize pool for all prize categories is estimated to be fifty-five percent (55%) of Mega Millions sales." |
| Saturday Lotto, Oz Lotto, Powerball (Australia) | 60% of subscriptions (55% prize pool + 5% reserve) | "The Prize Allocation in a Game shall be not less than sixty percent (60%) of Subscriptions… not less than fifty five percent (55%) of Subscriptions… The Prize Reserve Fund… five percent (5%)." |
| Lotto (New Zealand) | 60% of turnover | "The prize pool for a game of standard lotto must be determined by the Commission, but must be an amount of not less than 60% of the turnover for the game." |
The UK figures come from the Lotto and EuroMillions Game Procedures; Powerball's from the Colorado Lottery's codified Rule 14.A; Mega Millions' from the Iowa Lottery's game rules. Note that Mega Millions moved to 55% when it restructured to a $5 ticket in April 2025 — the two flagship US games are no longer on the same setting.
The same Colorado rule also fixes how the 50% is carved up: "The maximum contribution rate to the Grand Prize Pool shall be 68.0131% of the Prize Pool" — which is 34.0066% of sales going to the jackpot and about 16% of sales to everything below it. That second figure is exactly the $0.32 of fixed-prize expected value we derive from the prize chart, arriving from the opposite direction.
UK Lotto is more explicit still: "8.88% of sales for a Lotto Draw are allocated to the Jackpot", with the remaining prize fund covering the fixed tiers.
The Australian figures deserve their own note, because two different numbers circulate and both are correct. The NSW/ACT Lotto Game Rules, gazetted under the Public Lotteries Act 1996, set a Prize Allocation of at least 60% of subscriptions, which splits into a Prize Pool of at least 55% — distributed in that draw — and a Prize Reserve Fund of 5%, which funds guaranteed jackpots in later draws. Queensland's Lotteries Rule, a statutory instrument effective 3 February 2026, states the same thing from the other side: "net prize pool, for a drawing of Saturday gold lotto, means 60% of the total subscriptions for the drawing less any amount put aside as a bonus prize reserve." Western Australia's Lotteries Commission (Saturday Lotto) Rules 1996 carry an identical 60/55/5 table. Australia's draw games are set ten points above the UK's and US Powerball's 50%.
| Operator | Financial year | Sales | Prizes | Payout |
|---|---|---|---|---|
| Massachusetts State Lottery | FY2025 (to 30 Jun) | ~$5.96bn | — | 74.07% |
| Texas Lottery | FY2025 (to 31 Aug) | $7,912.4m | $5,381.1m | 68.01% |
| Florida Lottery | FY2025 (to 30 Jun) | $9,132.9m | $6,206.5m | 67.96% |
| California Lottery | FY2023-24 (to 30 Jun) | $9,275.1m | $6,031.6m | 65.0% |
| Michigan Lottery | FY2025 (to 30 Sep) | $4,572.0m | $2,925.6m | 63.99% |
| New York Lottery (traditional games) | FY2025 (to 31 Mar) | $7,812m | $4,751.6m | 60.82% |
| Allwyn UK (National Lottery) | Calendar 2025 | £8,061.2m | £4,555.4m | 56.51% |
| UK National Lottery (Gambling Commission) | FY2024-25 (to 31 Mar) | £7,886.3m | £4,351.1m | 55.17% |
Sources in order: Massachusetts Lottery Commission minutes ("The estimated prize payout reached 74.07 percent… setting a new record"), the Texas audited financial report, the Florida annual financial report (which states its own 67.96%), the California ACFR, the Michigan ACFR, the New York Lottery financial statements, the Allwyn UK Annual Report 2025 and the Gambling Commission's pence-per-pound breakdown.
Read that table carefully: the fiscal years end on four different dates and the product mixes are wildly different, so it is not a like-for-like league table. It is eight honest measurements of eight different things.
Australia cannot be added to it cleanly. The Lottery Corporation reports revenue net of prizes, so there is no prize expense line to divide — its FY2026 Annual Report records $5.1 billion of lotteries and keno prize money against turnover of $8,206 million, a derived payout near 62% (higher once the prize figure's exclusion of Western Australia is allowed for). That exceeds the 55–60% statutory floor, as it should, because reserve funds built up in earlier years pay out later. The same report notes that "27 cents in every dollar spent on a typical lottery ticket is returned to state and territory governments" — Australia's counterpart to Britain's 23p of good causes plus 12p of duty.
Because "the lottery" is not one game. The designed 50% applies to draw games. Scratch tickets pay back far more, and in most US states scratch tickets are the majority of sales.
Michigan is the only one of these operators that publishes sales and prizes per game, which makes it the decisive evidence:
| Game (Michigan, FY2025) | Sales | Prizes | Payout |
|---|---|---|---|
| Retail instant (scratch) tickets | $2,265,049,278 | $1,722,936,453 | 76.07% |
| Pull-tab tickets | $55,987,978 | $40,555,494 | 72.44% |
| Club Keno (all variants) | $502,678,424 | $324,502,660 | 64.55% |
| Lotto 47 (with Double Play) | $62,346,182 | $34,553,523 | 55.42% |
| Powerball (all) | $185,096,148 | $95,125,792 | 51.39% |
| Daily 4 | $510,818,037 | $258,592,722 | 50.62% |
| Daily 3 | $440,117,340 | $217,281,671 | 49.37% |
| Mega Millions (with Megaplier) | $144,987,917 | $70,681,104 | 48.75% |
There it is in one table: scratch cards return three quarters, draw games return about half. A state's headline payout is simply the weighted average, so it mostly measures how much scratch the state sells. Texas reports that "scratch tickets sales reached $6.434 billion in FY 2025, accounting for more than 81% of total sales" — which is the whole explanation for its 68.01%. Massachusetts, even more scratch-heavy, reaches 74.07%.
Two further wrinkles worth stating rather than hiding. Michigan's online instant games enter "sales" as net win rather than gross handle; note 8 of the same report gives the gross figures — $1,594,359,704 staked against $1,425,902,791 returned, an 89.43% payout, because online instants behave like casino products. And realised figures always differ from designed ones because jackpots are lumpy: Michigan's Mega Millions realised 48.75% against a 55% design target in a year that spanned the game's restructuring.
The UK publishes the cleanest decomposition in the world. For the financial year ended 31 March 2025, the Gambling Commission's pence-per-pound release breaks £7,886.3m of sales down as:
| Destination | £m | Pence per £1 |
|---|---|---|
| Prizes paid out | 4,351.1 | 55 |
| Good causes | 1,808.3 | 23 |
| Lottery Duty | 944.1 | 12 |
| Operator costs and profit | 542.4 | 7 |
| Retailer commission | 240.5 | 3 |
| Total sales | 7,886.3 | 100 |
The DCMS states the Fourth Licence expectation slightly differently, splitting the operator's share: "56p on prizes to players, 23p on good causes, 12p on Lottery Duty to HM Treasury, 3p on retailer commission, 5p on operating costs and 1p on operator profit." Lottery Duty is levied by HMRC at "12% of all stake money paid in the accounting period", and — importantly for the arithmetic — "you can't make any deductions from the amount you're due to pay duty on" (HMRC guidance).
Allwyn's own framing of the same money: "Including prizes paid, we returned around 94.0% of all total sales to our winners and to society, even before paying for operating costs."
Return to player is a per-stake figure, not a per-player one. A 55% lottery returns 55p of every pound staked — and only if you never restake winnings is that also 55p of every pound you brought. Products where winnings are naturally recycled post far higher RTPs while extracting more. That comparison, and the structural reasons draw games sit at 50% while slots sit above 90%, is in the payout ratio league table.
Last verified: 2026-08-29