The mathematics of odds
A roll-down injects money accumulated in earlier draws into a single draw's prize pool. It is the one mechanism that can push a draw's return to player far above its designed level — and once made a US game genuinely +EV.
Almost every lottery jackpot rolls: no winner, the pool carries forward. A few games put a stop on the rolling, and what happens at the stop is the most mathematically interesting event in the whole industry. Money collected from earlier draws gets injected into one draw, and for that draw only, the arithmetic of a ticket changes.
The Lotto Game Procedures (Edition 22, effective 7 June 2026) say it plainly:
"If the Jackpot is not won in either Round in a Lotto Draw, it can roll over five times. If the Jackpot is not won in either Round in the fifth Rollover Lotto Draw (being the sixth consecutive Lotto Draw, and known as the 'Must Be Won Draw'), it will be distributed in the following way…"
"each Winning Lotto Entry in the Match 2 Prize category will receive £5 instead of the usual fixed £1 Prize. If the Jackpot is insufficient to pay £5 to each Winning Lotto Entry in the Match 2 Prize category, Allwyn may use up to a maximum of £8million from the Reserve Fund to top up the Jackpot…"
"If only the Jackpot fund is used… and there is money left over after paying these Prizes, the remaining Jackpot monies will be distributed equally amongst all Winning Lotto Entries in the Match 3 Prize category."
Note what that does not say. Under the current rules the roll-down does not flow into Match 4, Match 5 or Match 5+Bonus, which are fixed prizes. It flows to Match 2 first, then whatever remains goes to Match 3. The rules also let Allwyn "designate any Lotto Draw a Must Be Won Draw for promotional purposes", so they are not purely mechanical.
EuroMillions Game Procedures work differently — a hard cap plus a countdown:
"The EuroMillions Jackpot is not allowed to exceed €250million… Any prize money that would have increased the Jackpot above the level of the Jackpot cap will roll down to the next Prize category in that EuroMillions Draw where there is at least one winner… Once the Jackpot has reached the cap, it can roll four times before it must be won… If the Jackpot is not won in that fourth EuroMillions Draw (which will be the fifth successive EuroMillions Draw at the Jackpot cap), the Jackpot Prize Fund will roll down to the next Prize category where there is at least one winner."
The Irish operator's EuroMillions Rules state the same thing from the other side: "a maximum of five successive Draws are permitted at the Flow-down Cap." The precise count matters — it is five draws at the cap, not five rollovers after it.
Two structural differences are worth naming. EuroMillions starts leaking money downward the moment the cap binds, because everything above €250 million flows to the next tier with a winner in that very draw. And when the countdown expires, the whole €250 million lands on one tier — typically Match 5 + 1 Lucky Star, whose odds are 1 in 6,991,908 — rather than being spread across millions of small winners the way UK Lotto spreads it.
Other games with a stop: Lotto Max in Canada caps its jackpot at $90 million and diverts the excess into separate $1 million MaxPlus draws rather than rolling it down, and South Africa's Daily Lotto guarantees its Division 1 pool is either won or rolled down to the next division every single day. US Powerball and Mega Millions have no cap at all, which is why their jackpots reach ten figures.
The general result is simple enough to state in one line:
A roll-down adds (rolled-down pool ÷ lines sold in that draw) to every ticket's expected value.
That is because the pool is exhausted in that draw. Nothing carries forward, so every pound of it is divided among that draw's players.
Worked example — a UK Must Be Won draw. Suppose the draw sells £40,000,000 and the displayed jackpot is £20,000,000. From the rules, this draw's own prize fund is 50% of sales = £20,000,000, and its own jackpot allocation is 8.88% of sales = £3,552,000. So the money carried in from the five earlier draws is:
£20,000,000 − £3,552,000 = £16,448,000
Total prize money leaving the operator in that draw:
£20,000,000 (this draw's prize fund) + £16,448,000 (carried in) = £36,448,000
Against £40,000,000 of sales, that is a return to player of 91.1% for that draw — against a designed 50%. A single draw briefly pays out like a slot machine.
Per ticket. The Match 2 uplift alone is worth computing. Match 2 has probability 1/10.26 per round, and a £2 line plays two rounds, so the £1 → £5 uplift is worth:
2 rounds × £4 × (1/10.26) = £0.7797 per ticket
added to the £0.7290 of fixed-prize expected value a normal draw carries — before the jackpot term and before whatever spills into Match 3. This is a real, computable improvement, and it is the only routine circumstance in which a UK Lotto ticket's expected value approaches its price.
It still is not a licence to print money. Two forces push back. Must Be Won draws are heavily advertised, so lines sold rise sharply, which both dilutes the per-ticket share of the carried-in pool and raises the chance the jackpot is simply won outright — in which case there is no roll-down at all. Second, the pool is finite: if enough Match 2 winners turn up, the £5 has to be funded from a Reserve Fund capped at £8 million, and the leftover for Match 3 disappears.
The definitive example is Cash WinFall, run by the Massachusetts State Lottery from 2004 to 2012. It was a 6-from-46 game with a jackpot capped at about $2 million; when the cap was reached and nobody matched six, the jackpot did not carry forward — it rolled down into the Match 5, Match 4 and Match 3 tiers, multiplying those prizes.
Because the roll-down was announced in advance, players could compute the added expected value before deciding whether to buy — the pool was known, and only the sales volume was uncertain. On roll-down draws, a $2 ticket's expected value could exceed $2. High-volume syndicates, including groups of MIT students, bought at industrial scale. The Massachusetts Inspector General's July 2012 letter report to the State Treasurer examined the episode; contemporaneous reporting on that report put syndicate spending at roughly $40 million and returns at roughly $48 million over seven years, and found the Lottery had been aware of the activity for years (Boston Globe). The game was discontinued in 2012.
Two lessons survive from it. First, the +EV came entirely from the roll-down design and the advance notice — no prediction, no pattern, no system, just a published pool divided by a forecastable number of tickets. Second, it required scale: at a few percent edge, a handful of tickets is still a lottery ticket. The general conditions under which a draw genuinely turns positive are the subject of our whole +EV cluster, and you can test any draw yourself in the EV calculator and track rollovers with the jackpot tracker.
If you are going to buy a ticket anyway, a roll-down or Must Be Won draw is measurably the best draw of the cycle to buy it in — not because your odds improve (they do not; the matrix never changes) but because money from draws you did not enter is being distributed in a draw you did. That is a genuine, computable, one-directional effect, and it is the only one in this entire cluster.
Last verified: 2026-08-29