The industry and where the money goes
Lengthening the odds is not a way of keeping more money. It is the only lever an operator has that reliably makes the advertised jackpot bigger.
Every few years a big lottery game announces a redesign, and the jackpot odds get longer. Powerball in 2015, Mega Millions in 2017 and again in 2025, Oz Lotto in 2022, UK Lotto in 2015 — the direction of travel is consistent, and it is not an accident.
The industry term is jackpot fatigue: a jackpot of a given size sells fewer tickets than the same jackpot did a few years earlier, because players have recalibrated what counts as big. The operator response is to engineer bigger jackpots. The only reliable way to do that is to make them harder to win.
This is worth deriving because the result is more surprising than the argument.
Let:
The probability that a single draw produces no jackpot winner is:
(1 − 1/N)^T ≈ e^(−T/N)
When T is much smaller than N — which it always is for a game with hundred-million odds — the expected number of draws until somebody wins is approximately:
Expected draws to a win ≈ N ÷ T
Each of those draws adds r × T to the jackpot. So the expected size of the jackpot at the moment it is finally won is:
(r × T) × (N ÷ T) = r × N
The T cancels.
The expected winning jackpot depends on the odds and the jackpot contribution rate — and not at all on how many tickets are sold.
Selling more tickets makes the jackpot grow faster, but it also makes it get hit sooner, and the two effects exactly offset. If you want a bigger headline number, growing the player base will not do it. Only two levers work: put more of each ticket into the jackpot (which means paying less in the lower divisions, or raising the price), or lengthen N.
Take Powerball's October 2015 redesign, which moved the matrix from 5 of 59 plus 1 of 35 to 5 of 69 plus 1 of 26:
| Before | After | |
|---|---|---|
| Combinations N | 5,006,386 × 35 = 175,223,510 | 11,238,513 × 26 = 292,201,338 |
| Ratio | — | 1.67× |
If r were, say, 30¢ of each $2 ticket — an illustrative figure; the real allocations are set out in how prize pools are split — then the expected winning jackpot moves from 0.30 × 175,223,510 = $52.6m to 0.30 × 292,201,338 = $87.7m. Whatever r actually is, the ratio is the same 1.67×, because it is just the ratio of the odds.
That is the entire trick. Lengthening the odds by two-thirds raises the typical advertised jackpot by two-thirds, and it does so without the operator taking a single extra cent per ticket.
This is not an inference. When the 2015 Powerball change was announced, the Louisiana Lottery's president explained the reasoning directly:
"The last time Powerball's game matrix changed was in 2012. Since then, the game's playing population has grown to include 47 lottery jurisdictions, and jackpots are consequently hit faster. This change will help produce those eye-popping jackpots that players have come to expect with Powerball."
(Louisiana Lottery — Powerball's matrix changes to build bigger jackpots)
Read that against the derivation. More jurisdictions means larger T. Larger T does not raise the expected jackpot — it just gets it hit sooner, which is exactly what "jackpots are consequently hit faster" says. Raising N is the correction.
The obvious objection is that players should see the odds getting worse and buy less. The research says they mostly do not, and there is a specific reason.
Philip Cook and Charles Clotfelter examined why lotto games sell better per head in larger states, in The Peculiar Scale Economies of Lotto, American Economic Review, volume 83, issue 3 (1993), pages 634–643. Bigger states had bigger jackpots but worse odds. Their explanation is the key sentence in this whole subject:
Players tend to judge the likelihood of winning based on the frequency with which someone wins, rather than on the actual mathematical odds.
Someone wins Powerball every few weeks either way. The visible signal — a winner on the news — is roughly unchanged by the redesign, while the jackpot on the sign is visibly larger. From the player's side the game looks better, not worse. The full account of why the odds are effectively unimaginable is in how lottery odds are calculated and the odds visualiser.
Operators do not usually lengthen the jackpot odds alone. They pair it with a change that makes the overall odds of winning something look better, and then advertise that.
Powerball 2015 is the model. Enlarging the white-ball pool from 59 to 69 lengthened the jackpot; shrinking the Powerball pool from 35 to 26 shortened the bottom tier. The lowest division — matching the Powerball only — moved like this:
The Louisiana Lottery's announcement gives the resulting headline: overall odds of any prize improved from about 1 in 32 to 1 in 25. Both statements — "harder to win the jackpot" and "easier to win a prize" — are true, and only one of them tends to appear in the marketing.
The same pairing shows up elsewhere. Oz Lotto's May 2022 change added a third supplementary number alongside the longer matrix; Mega Millions' April 2025 change built a 2×–10× multiplier into every ticket. The pattern is consistent enough to be a design convention.
There is good evidence that sales respond strongly to jackpot size. Emily Oster's Are All Lotteries Regressive? Evidence From the Powerball, National Tax Journal, volume 57, issue 2 (2004), pages 179–187, found that the composition of Powerball buyers shifts with the jackpot: the game is "significantly less regressive at higher jackpot sizes", because larger jackpots pull in players who do not otherwise buy.
That is the demand curve operators are working with. Big jackpots do not merely sell more tickets to existing players — they recruit occasional ones. A game whose peak jackpot stops growing loses that recruitment channel, and the peak jackpot only grows if N grows.
Whether the fatigue is genuine habituation or simply inflation is harder to settle, and we have not found a published study that isolates it. What is documented is the operator behaviour and its arithmetic consequence.
The redesigns are not neutral for a player. The jackpot chance you buy for a fixed stake falls in direct proportion to N, so the cost per chance at the top division rises by exactly the odds ratio.
The full timeline of matrix changes, with the before-and-after odds derived from each matrix, is in the history of jackpot inflation, and the operator-versus-player accounting of each change is in why lotteries changed their matrices. To compare what a given game currently charges per unit of jackpot chance, use the cost-per-chance calculator.
Last verified: 2026-08-29