The mathematics of odds

Cheapest cost per chance: what a jackpot shot really costs

Dividing the ticket price by the jackpot probability gives one honest number per game — what you would spend to buy a certainty. It ranges from a few million to over a billion, and it exposes which games are quietly expensive.

Jackpot odds alone cannot tell you whether a game is expensive, because games charge wildly different prices for a line. The fix is one division:

cost per chance = ticket price ÷ P(jackpot) = ticket price × jackpot odds

Read it as: this is what one guaranteed jackpot would cost you if you could buy every combination once at the advertised price. It is also, exactly, the jackpot size at which the jackpot component alone would return your stake — which makes it the natural companion to the break-even jackpot tool. Every figure below is computed by our cost-per-chance tool from the operator's own matrix and price.

One rule before the tables: we never convert currencies. Exchange rates move, and a comparison whose conclusion depends on this morning's rate is not a durable fact. So the games are grouped by the currency they are actually sold in, which is also how a player experiences them.

US dollar games

Game Line price Jackpot odds (1 in) Cost per chance
Pick 3 $1 1,000 $1,000
Fantasy 5 (Florida) $1 376,992 $376,992
Fantasy 5 (California) $1 575,757 $575,757
Lotto 47 (Michigan) $1 10,737,573 $10,737,573
New York Lotto $1 buys two plays 45,057,474 $22,528,737
Lotto Texas $1 25,827,165 $25,827,165
Lotto America $1 25,989,600 $25,989,600
Illinois Lotto $2 15,890,700 $31,781,400
SuperLotto Plus $1 41,416,353 $41,416,353
Florida Lotto $2 22,957,480 $45,914,960
Millionaire for Life $5 22,910,580 $114,552,900
Powerball $2 292,201,338 $584,402,676
Mega Millions $5 290,472,336 $1,452,361,680

Mega Millions is the standout. Its jackpot odds are shorter than Powerball's — 290.5 million against 292.2 million — but at $5 a line versus $2, a jackpot chance costs 2.49 times as much. The $5 price and built-in multiplier buy larger secondary prizes, not a better shot at the top.

Sterling games

Game Line price Jackpot odds (1 in) Cost per chance
Lotto HotPicks (Pick 5) £1 834,398 £834,398
Thunderball £1 8,060,598 £8,060,598
Set For Life £1.50 15,339,390 £23,009,085
Lotto £2 for two rounds = £1 per round 45,057,474 per round £45,057,474
EuroMillions £2.50 139,838,160 £349,595,400

UK Lotto needs the footnote. Since 10 June 2026 a single £2 line is entered into two independent rounds each draw night, each with its own 1-in-45,057,474 jackpot chance. So the line costs £2 and buys two chances: £1 per chance. Quoting "£2 × 45,057,474 = £90 million" would double-count.

Euro games

Game Line price Jackpot odds (1 in) Cost per chance
Daily Million (Ireland) €1 3,262,623 €3,262,623
Bonoloto (Spain) €0.50 13,983,816 €6,991,908
Lotto 6 aus 45 (Austria) €1.50 8,145,060 €12,217,590
Tzoker (Greece) €0.50 24,435,180 €12,217,590
Lotto (Finland) €1 18,643,560 €18,643,560
Lotto (Ireland) €2 10,737,573 €21,475,146
Loto (France) €2.20 19,068,840 €41,951,448
El Gordo de la Primitiva €1.50 31,625,100 €47,437,650
La Primitiva €1 139,838,160 €139,838,160
LOTTO 6aus49 (Germany) €1.20 139,838,160 €167,805,792
Eurojackpot €2 139,838,160 €279,676,320
SuperEnalotto (Italy) €1 622,614,630 €622,614,630

Austria's Lotto and Greece's Tzoker land on exactly the same €12,217,590 by different routes — €1.50 against 1-in-8.1 million, and €0.50 against 1-in-24.4 million. Identical jackpot exposure per euro, entirely different games to play.

Australian dollar games

Game Line price Jackpot odds (1 in) Cost per chance
Saturday Lotto $0.90 8,145,060 $7,330,554
Weekday Windfall $1.00 8,145,060 $8,145,060
Keno 10 Spot $1.00 8,911,711 $8,911,711
Set for Life $1.15 38,320,568 $44,068,653
Oz Lotto $1.55 62,891,499 $97,481,823
Powerball $1.35 134,490,400 $181,562,040

Australian per-game prices are approximate because agent commission varies by state, so treat the ordering as robust and the last digits as indicative.

What the number means — and what it does not

It is a break-even benchmark. Ignore the lower divisions for a moment. If a Powerball jackpot ever advertised $584,402,676 in cash, in a draw you alone entered and with no tax, then the jackpot alone would exactly return your $2. Everything below that figure means the jackpot component is losing money on its own. Counting the eight fixed-cash tiers, whose combined expected value is $0.3199 per ticket, drops the real crossover to about $490.9 million — the working is in lower-division prizes are the real returns.

It is not "which game to play". Pick 3's cost per chance is $1,000, which sounds gloriously cheap until you note the top prize is typically $500 on a $1 straight play. Cost per chance measures exposure, not value. Divide by the prize and you get the real ratio: Pick 3 returns roughly $500 per $1,000 of exposure; Powerball at a $500 million cash jackpot returns roughly $500 million per $584 million.

It assumes you can buy the combinations. You cannot, practically — the logistics of covering a matrix are examined in buying every combination, and the answer is that printing capacity, not money, is usually the binding constraint.

It ignores sharing and tax. A cost-per-chance figure treats the jackpot as yours alone and untaxed. Neither is safe in a large draw: see how prize pools are split and what you actually get from an advertised jackpot.

The single most useful habit this number encourages is checking the price against the matrix rather than against the billboard. Two games with the same headline can differ by a factor of two and a half in what a jackpot chance costs you, and the billboard never says so.

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Last verified: 2026-08-29