Real probabilities for the things people actually wonder about — from card hands to lightning strikes.
Cards & Games
Drawing all four aces as your first four cards
1 in 270,725
There is exactly one way to draw all four aces, out of 270,725 possible combinations of four cards from a standard deck.
Being dealt a royal flush in five-card poker
1 in 649,740
Four possible royal flushes (one per suit), out of nearly 2.6 million five-card hands.
Being dealt any flush in five-card poker
1 in 508
Flushes are rare enough to celebrate, common enough to actually happen in a long session.
Rolling the same number six times in a row
1 in 7,776
The first roll doesn't need to match anything. After that, each roll has a 1 in 6 chance of repeating.
Flipping heads ten times in a row
1 in 1,024
Each flip is independent. The probability halves with every additional flip required.
Flips in a row: 10
Everyday Life
Being struck by lightning in your lifetime (UK)
1 in 300,000
Rare, but not as rare as most people assume. Around 30–60 people are struck by lightning in the UK each year.
Source: UK Met Office estimates. US figure is approximately 1 in 15,300 over 80 years.
Being involved in a fatal plane crash as a passenger
1 in 11,000,000 per flight
Flying is extraordinarily safe. You'd need to fly every day for 30,000 years to make a fatal crash statistically likely.
Source: Aviation safety data — approximately 1 fatal accident per 16 million flights.
Dying in a car accident in your lifetime (UK)
1 in 240
The mundane risks are the real ones. This is why seatbelts matter far more than shark repellent.
Source: UK road fatality statistics, lifetime risk estimate.
Being attacked by a shark in your lifetime
1 in 3,748,067
You are roughly 15,000 times more likely to be killed in a road accident than by a shark.
Source: Florida Museum of Natural History.
Finding a four-leaf clover on your first try
1 in 10,000
There are approximately 10,000 three-leaf clovers for every four-leaf one. Some people find them regularly — which says more about their patience than their luck.
Approximately one meteorite falls per 500,000 km² per year. A house is about 100m². The maths is humbling. (Approximate estimate.)
Source: Derived from known meteorite fall rates and average house footprint.
Solving a scrambled Rubik's Cube by random moves
1 in 43,252,003,274,489,856,000
There are 43 quintillion possible Rubik's Cube states. Solving one by random moves is so unlikely it has never happened and almost certainly never will.
The Birthday Paradox
How many people until two share a birthday?
The answer surprises almost everyone.
People in the room: 23
50.7%
chance of a shared birthday
In a room of 23 people, there's a 50.7% chance two share a birthday. In a room of 70, it's 99.9%.
This works because you're not asking "does anyone share my birthday?" — you're asking "does any pair share a birthday?" With 23 people there are 253 possible pairs. Each pair has a 1 in 365 chance of matching. The combinations add up fast.
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How are these odds calculated?
Every figure on this page comes from real combinatorics or published incident data — nothing here is a rounded guess dressed up as a statistic.
The maths behind the card and dice odds
Card and dice odds are pure combinatorics — counting how many ways an outcome can happen against how many outcomes are possible overall. A royal flush can happen in exactly 4 ways (one per suit) out of 2,598,960 possible five-card hands from a 52-card deck, giving odds of roughly 1 in 649,740. Dice odds work the same way: the chance of rolling the same number five times in a row is 1/6 multiplied by itself five times, since each roll is independent of the last.
Where do the lightning, shark and plane crash figures come from?
Real-world risk figures like lightning strikes, shark attacks and plane crashes aren't derived from first principles — they come from published incident data (aviation safety records, the Florida Museum of Natural History's shark attack file, UK Met Office lightning estimates) divided across an estimated population or number of trips. The specific source is noted beneath each figure where one applies.
The birthday paradox, explained
Move the slider on the interactive above and the odds update instantly — but the reason they climb so fast surprises almost everyone.
Why does it only take 23 people?
The trick is that you're not asking whether anyone shares your birthday — you're asking whether any two people in the room share a birthday with each other. With 23 people there are 253 possible pairs, and each pair only needs a 1 in 365 chance of matching. It's the number of pairs that grows quickly, not the number of people, which is why the odds cross 50% far sooner than intuition expects.
Is it really a "paradox"?
Not in the logical sense — there's no contradiction, just a result that clashes with most people's gut instinct. It's called a paradox the way a magic trick is called impossible: because it feels that way until you see how it works. The underlying maths — multiplying the chance of no match across every added person, then subtracting from 1 — is straightforward once written out, and is exactly what the calculator above runs on every move of the slider.