Things More Likely Than Winning the Jackpot — Only the Ones We Can Prove

Lists of "things more likely than winning the lottery" are the junk food of statistics writing. Most of the entries trace back to nothing: a number appears in one article, gets copied, and after twenty years of citation laundering it reads like a fact.

This list has one rule. Every entry is either derived from first principles on this page, or linked to a published statistic from an authority. Everything else was dropped, and the last section says what and why.

The baselines

Those combination counts are computed, not quoted — the method is in how lottery odds are actually calculated. Powerball is the benchmark below because it is the longest odds of the three.

Computed exactly

Flipping 28 heads in a row

Each flip is independent with probability 1/2, so 28 in a row is:

2^28 = 268,435,456, or 1 in 268,435,456

292,201,338 ÷ 268,435,456 = 1.09

Twenty-eight consecutive heads is 9% more likely than a Powerball jackpot. It takes 29 flips (1 in 536,870,912) for the coin to become the longer shot.

Rolling ten sixes in a row

6^10 = 60,466,176, or 1 in 60,466,176

292,201,338 ÷ 60,466,176 = 4.83

Ten consecutive sixes on a fair die is nearly five times more likely than the jackpot. Eleven sixes is 6^11 = 362,797,056, which overtakes Powerball — so the crossover sits between ten and eleven.

Being dealt a royal flush in five cards

There are four royal flushes among all five-card hands:

C(52,5) = 2,598,960 hands, so P(royal flush) = 4 ÷ 2,598,960 = 1 in 649,740

292,201,338 ÷ 649,740 = 450

A royal flush off the deal is 450 times more likely than a Powerball jackpot. And a specific named five-card hand — the exact five cards you nominate in advance — is 1 in 2,598,960, still 112 times more likely.

Two people in a room of 23 sharing a birthday

The classic result, computed properly. The probability that 23 people all have different birthdays (ignoring leap years and seasonal clustering) is:

(365/365) × (364/365) × (363/365) × … × (343/365) = 0.4927

So P(at least one shared birthday) = 1 − 0.4927 = 50.73%

That is not "more likely than the jackpot" in any interesting sense — it is more likely by a factor of about 148 million — but it earns its place because it is the standard demonstration that human intuition about coincidence is badly calibrated, which is the same failure that makes 1 in 292 million feel imaginable. The odds visualiser exists to attack the same intuition from the other direction.

Guessing a stranger's phone number

Guess the last eight digits of a randomly chosen phone number: 10^8 = 1 in 100,000,000. Nearly three times more likely than the jackpot, and it feels impossible, which is the point.

Every ticket bought this week, and still nothing

The complement is the number most worth internalising. With one ticket, P(not winning) = 1 − 1/292,201,338 = 0.9999999966. Buy one a week for fifty years — 2,600 tickets — and the probability of never hitting the jackpot is:

(1 − 1/292,201,338)^2,600 = 0.9999911

A lifetime of weekly play leaves you with about a 1 in 112,000 chance of ever winning. That is the honest summary of the game, and it is worked in more detail in how many tickets you would need to be favourite.

Sourced to an authority

Being struck by lightning

This is the folklore entry, and it turns out there is a real source, so it stays — with the actual figures rather than the invented ones.

The US National Weather Service publishes lightning odds computed from ten years of data (2009 to 2018) against a US population of 330 million:

• Odds of being struck in a given year: 1 in 1,222,000
• Odds of being struck in an 80-year lifetime: 1 in 15,300

The NWS notes that about 27 people a year were killed and 243 to 270 injured over that period, and that "only about 10% of people who are struck by lightning are killed, leaving 90% with various degrees of disability."

Against Powerball:

• 292,201,338 ÷ 1,222,000 = 239 times more likely to be struck this year than to win a jackpot with one ticket
• 292,201,338 ÷ 15,300 = 19,098 times more likely to be struck in your lifetime

Note what this does not say. It is not a claim about dying, it is US-specific, and it is a population average, not your personal risk — the NWS figure treats a Florida golfer and a Manhattan office worker identically. That kind of qualification is exactly what gets stripped when a statistic is copied.

What we dropped, and why

Every one of these appears in the standard list. None of them survived.

If any of these acquires a citable source, it goes in. Until then it is not evidence, it is decoration.

Why the comparisons work at all

The reason a lightning strike feels less likely than a jackpot, when it is 239 times more likely, is not innumeracy about the numbers. It is availability. Jackpot winners appear on television holding a novelty cheque, every week, by design. Lightning-strike survivors do not have a marketing department.

That asymmetry — vivid, promoted evidence of the rare good outcome versus invisible evidence of the more common one — is the actual mechanism, and it is the subject of the psychology cluster. The arithmetic on this page is only useful to the extent it interrupts it. The odds visualiser tries to do the same job with pictures instead of ratios, and picturing one in 292 million with physical analogies.