The industry and where the money goes
A dated record of the redesigns that lengthened the world's biggest lottery odds, with every odds figure derived from the published matrix rather than repeated.
The jackpot odds on the world's largest lottery games have been lengthened repeatedly and deliberately. This is the record, with dates, and with every odds figure derived from the matrix rather than copied from a press release.
The method throughout is the standard combination count, set out in how lottery odds are calculated. For a game where you pick k numbers from a pool of n plus one supplementary from a separate pool of s:
Combinations = C(n, k) × s, where C(n, k) = n! ÷ (k! × (n − k)!)
Tickets for the new game went on sale Sunday 4 October 2015, with the first draw on Wednesday 7 October (NC Education Lottery). The white-ball pool went from 59 to 69; the Powerball pool from 35 to 26.
| Before | After | |
|---|---|---|
| Matrix | 5 of 59 + 1 of 35 | 5 of 69 + 1 of 26 |
| C(n, 5) | 5,006,386 | 11,238,513 |
| × supplementary pool | × 35 | × 26 |
| Jackpot odds | 1 in 175,223,510 | 1 in 292,201,338 |
| Overall odds of any prize | 1 in 32 | 1 in 25 |
Longer by a factor of 292,201,338 ÷ 175,223,510 = 1.668. Cost of covering every combination at $2 a line: $350.4m before, $584.4m after.
The price doubled from $1 to $2, the main pool shrank from 75 to 70, and the Mega Ball pool grew from 15 to 25, from the draw of 28 October 2017 (Lottery.net).
| Before | After | |
|---|---|---|
| Matrix | 5 of 75 + 1 of 15 | 5 of 70 + 1 of 25 |
| C(n, 5) | 17,259,390 | 12,103,014 |
| × supplementary pool | × 15 | × 25 |
| Jackpot odds | 1 in 258,890,850 | 1 in 302,575,350 |
| Ticket price | $1 | $2 |
Odds longer by 1.169×, price doubled. Cost to cover the matrix: $258.9m before, $605.2m after — 2.34× more expensive for one guaranteed jackpot.
The most interesting entry in the list, because it goes the other way on odds and much further on price. From 5 April 2025 the Mega Ball pool shrank from 25 to 24 and the price rose from $2 to $5 (Louisiana Lottery).
| Before | After | |
|---|---|---|
| Matrix | 5 of 70 + 1 of 25 | 5 of 70 + 1 of 24 |
| Jackpot odds | 1 in 302,575,350 | 1 in 290,472,336 |
| Overall odds | 1 in 24 | 1 in 23 |
| Ticket price | $2 | $5 |
| Starting jackpot | $20m | $50m |
The odds got 4% shorter. The price rose 150%. Multiply the two and the cost of covering the matrix goes from 302,575,350 × $2 = $605.2m to 290,472,336 × $5 = $1,452.4m — 2.40× more. Every ticket also carries a built-in 2×–10× multiplier on non-jackpot prizes, which is where a good part of the extra $3 goes.
This is the same manoeuvre as a matrix lengthening, executed through price instead of combinatorics. The result on the jackpot side is identical: more money per unit of jackpot chance, therefore a faster-growing and larger headline number.
The UK ran the two levers separately, two years apart.
Lotto launched on 19 November 1994 as 6 from 49 at £1 a line. The price doubled to £2 from 3 October 2013 with the matrix untouched. Then from 10 October 2015 the pool went from 49 to 59.
| 1994–2013 | 2013–2015 | From Oct 2015 | |
|---|---|---|---|
| Matrix | 6 of 49 | 6 of 49 | 6 of 59 |
| Combinations | C(49,6) = 13,983,816 | 13,983,816 | C(59,6) = 45,057,474 |
| Ticket price | £1 | £2 | £2 |
| Cost to cover the matrix | £13.98m | £27.97m | £90.11m |
Odds longer by 45,057,474 ÷ 13,983,816 = 3.222×. Combined with the price doubling, the cost of buying one guaranteed jackpot rose 6.44× in 21 years. (National Lottery history; current rules on the UK Lotto odds page.)
EuroMillions has never changed its main matrix. It has changed the Lucky Star pool twice, which is enough.
| Era | Matrix | C(50,5) × C(s,2) | Jackpot odds |
|---|---|---|---|
| From launch (2004) | 5 of 50 + 2 of 9 | 2,118,760 × 36 | 1 in 76,275,360 |
| From May 2011 | 5 of 50 + 2 of 11 | 2,118,760 × 55 | 1 in 116,531,800 |
| From September 2016 | 5 of 50 + 2 of 12 | 2,118,760 × 66 | 1 in 139,838,160 |
Two extra Lucky Stars, added twelve years apart, lengthened the odds by 1.833× in total — from adding three balls to a pool of nine. That is the leverage a small secondary pool gives an operator: C(11,2)/C(9,2) = 55/36 = 1.528, and C(12,2)/C(11,2) = 66/55 = 1.200.
The May 2011 change also added a second weekly draw and a new lowest tier; the September 2016 change raised the ticket price and the minimum jackpot (EuroMillions changes timeline). Current rules: EuroMillions odds.
| Era | Matrix | Calculation | Jackpot odds |
|---|---|---|---|
| From 1996 | 5 of 45 + 1 of 45 | 1,221,759 × 45 | 1 in 54,979,155 |
| From 1 March 2013 | 6 of 40 + 1 of 20 | 3,838,380 × 20 | 1 in 76,767,600 |
| From 19 April 2018 | 7 of 35 + 1 of 20 | 6,724,520 × 20 | 1 in 134,490,400 |
Longer by 2.446× across the two changes. The 2018 figure matches the Division 1 odds The Lott publishes exactly, which is the cross-check we apply to every game record — see Australian Powerball odds.
From draw 1474 on 17 May 2022, Oz Lotto moved from seven numbers drawn from 45 with two supplementaries to seven from 47 with three.
| Before | After | |
|---|---|---|
| Matrix | 7 of 45 + 2 supps | 7 of 47 + 3 supps |
| Division 1 combinations | C(45,7) = 45,379,620 | C(47,7) = 62,891,499 |
| Overall odds of any prize | 1 in 55 | 1 in 51 |
Two extra balls, and the top division becomes 1.386× harder. The third supplementary is what pays for it: adding a supplementary ball creates additional ways to win the lower divisions without touching Division 1, which is why the overall odds improved at the same time (Lotterywest — Oz Lotto update FAQs). Current rules: Oz Lotto odds.
Lotto Max now draws seven numbers plus a bonus from a pool of 52. C(52,7) = 133,784,560, and because a $6 play buys four selections the operators quote the jackpot as 1 in 33,446,140 — which is 133,784,560 ÷ 4 exactly (WCLC — Lotto Max). The pool has been enlarged since the game launched; we have not found an operator source dating each step, so those dates are left out. See Lotto Max odds.
Nine dated changes across six games. Eight lengthened the odds or raised the price per unit of jackpot chance; the ninth — Mega Millions 2025 — shortened the odds by 4% while raising the price by 150%.
Every one of them produced a larger typical advertised jackpot, and the reason that works is short enough to state in a sentence: the expected jackpot at the moment it is won is proportional to the number of combinations, and independent of how many tickets are sold. That derivation is in jackpot fatigue, and the operator-versus-player accounting of each redesign is in why lotteries changed their matrices.
To compare what any current game charges per unit of jackpot chance, use the cost-per-chance calculator or the odds calculator.
Last verified: 2026-08-29