Lottery Odds Explained

The math behind lottery odds isn't complicated once you see it laid out. This page covers the formulas, the actual numbers, and what those numbers mean in practice.

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Jackpot Odds - 12 Major Lotteries

All odds calculated using the combinations formula C(n,r) = n! / (r! × (n-r)!).

Lottery	Jackpot Odds	Format
🇺🇸 Powerball	1 in 292,201,338	5 from 1–69 + 1 Powerball from 1–26
🇺🇸 Mega Millions	1 in 302,575,350	5 from 1–70 + 1 Mega Ball from 1–25
🇪🇺 EuroMillions	1 in 139,838,160	5 from 1–50 + 2 Lucky Stars from 1–12
🇪🇺 EuroJackpot	1 in 95,344,200	5 from 1–50 + 2 Euro Numbers from 1–10
🇬🇧 UK Lotto	1 in 45,057,474	6 from 1–59
🇮🇹 SuperEnalotto	1 in 622,614,630	6 from 1–90 (no bonus ball)
🇦🇺 Australia Powerball	1 in 134,490,400	7 from 1–35 + 1 Powerball from 1–20
🇨🇦 Lotto Max	1 in 33,294,800	7 from 1–50 (per $5 play = 3 lines)
🇮🇪 Irish Lotto	1 in 10,737,573	6 from 1–47 + 1 Bonus Ball
🇳🇿 New Zealand Lotto	1 in 3,838,380	6 from 1–40
🇬🇧 UK Set For Life	1 in 15,339,390	5 from 1–47 + 1 Life Ball from 1–10
🇬🇧 Thunderball	1 in 8,060,598	5 from 1–39 + 1 Thunderball from 1–14

Formula Breakdown

🇺🇸

Powerball

1 in 292,201,338

Formula: C(69,5) × C(26,1)

Format: 5 from 1–69 + 1 Powerball from 1–26

🇺🇸

Mega Millions

1 in 302,575,350

Formula: C(70,5) × C(25,1)

Format: 5 from 1–70 + 1 Mega Ball from 1–25

🇪🇺

EuroMillions

1 in 139,838,160

Formula: C(50,5) × C(12,2)

Format: 5 from 1–50 + 2 Lucky Stars from 1–12

🇪🇺

EuroJackpot

1 in 95,344,200

Formula: C(50,5) × C(10,2)

Format: 5 from 1–50 + 2 Euro Numbers from 1–10

🇬🇧

UK Lotto

1 in 45,057,474

Formula: C(59,6)

Format: 6 from 1–59

🇮🇹

SuperEnalotto

1 in 622,614,630

Formula: C(90,6)

Format: 6 from 1–90 (no bonus ball)

🇦🇺

Australia Powerball

1 in 134,490,400

Formula: C(35,7) × C(20,1)

Format: 7 from 1–35 + 1 Powerball from 1–20

🇨🇦

Lotto Max

1 in 33,294,800

Formula: C(50,7) ÷ 3

Format: 7 from 1–50 (per $5 play = 3 lines)

🇮🇪

Irish Lotto

1 in 10,737,573

Formula: C(47,6)

Format: 6 from 1–47 + 1 Bonus Ball

🇳🇿

New Zealand Lotto

1 in 3,838,380

Formula: C(40,6)

Format: 6 from 1–40

🇬🇧

UK Set For Life

1 in 15,339,390

Formula: C(47,5) × C(10,1)

Format: 5 from 1–47 + 1 Life Ball from 1–10

🇬🇧

Thunderball

1 in 8,060,598

Formula: C(39,5) × C(14,1)

Format: 5 from 1–39 + 1 Thunderball from 1–14

Probability Concepts

Combination Formula

Formula:

C(n,r) = n! / (r! × (n-r)!)

Example:

C(69,5) = 69! / (5! × 64!) = 11,238,513

Explanation:

Calculates the number of ways to choose r items from n items without regard to order

Independent Events

Formula:

P(A and B) = P(A) × P(B)

Example:

Drawing main numbers and Powerball are independent events

Explanation:

The probability of two independent events both occurring

Mutually Exclusive Events

Formula:

P(A or B) = P(A) + P(B)

Example:

Winning different prize levels are mutually exclusive

Explanation:

The probability of either of two mutually exclusive events occurring

Odds in Context

Putting lottery odds alongside other probabilities helps illustrate the scale. All figures are mathematically derived from published game formats.

Event	Odds	Context
Winning Powerball Jackpot	1 in 292,201,338	About 19× less likely than being struck by lightning in your lifetime
Winning Mega Millions Jackpot	1 in 302,575,350	About 20× less likely than being struck by lightning in your lifetime
Being struck by lightning (lifetime, US)	1 in 15,300	19× more likely than winning Powerball
Being struck by lightning (in a given year, US)	1 in 1,222,000	239× more likely than winning Powerball in a single year
Winning UK Lotto jackpot	1 in 45,057,474	6.5× better odds than Powerball - the best jackpot odds of any major lottery
Winning New Zealand Lotto jackpot	1 in 3,838,380	76× better jackpot odds than Powerball

Prize Level Odds

Game	Match	Prize	Odds
Powerball	5 + Powerball	Jackpot	1 in 292,201,338
Powerball	5 numbers	$1,000,000	1 in 11,688,053
Powerball	4 + Powerball	$50,000	1 in 913,129
Mega Millions	5 + Mega Ball	Jackpot	1 in 302,575,350
Mega Millions	5 numbers	$1,000,000	1 in 12,607,306
Mega Millions	4 + Mega Ball	$10,000	1 in 931,001