Pharmacies check your name and birth date. Is that enough to tell you apart from everyone else?

Two people with the same name and the same birthday sounds like a one-in-a-million fluke. In a big enough system, it's close to guaranteed.

One health system in Houston, Texas

Patients named Maria Garcia
2,833
in Harris Health System's records
Share a birth date
528
of those Maria Garcias have the same date of birth as another
Same name and birth date
138,000
cases across the whole system, counting every name

How many people with the same name before two probably share a birth date?

Chance that at least two share an exact date of birth, if their birthdays are spread evenly across 80 years

Curve showing the chance that at least two people with the same name share an exact date of birth: about 4% with 50 people, 16% with 100, 50% with about 200, 79% with 300, and nearly 99% with 500. Harris Health's 2,833 Maria Garcias are far past the point where a shared birth date is certain. 0% 25% 50% 75% 100% 0100200 300400500600 People who share one name About 200 people: a coin flip 2,833 Maria Garcias: far off this chart →

A match that's rare for any two people becomes certain in a big enough crowd. The chance that two particular Maria Garcias share a birth date is tiny, about 1 in 29,000. But with thousands of them, there are millions of possible pairs, and some pairs are bound to match. It's the birthday paradox with full birth dates instead of just birthdays.

The same thing happens with any check built from a few common details: a name and a zip code, the last four digits of a card, a short password. Something that seems unique for one person can be shared by many once enough people are in the system. That's why the two-detail check exists, and why it isn't foolproof.

What detail do you think of as uniquely yours that thousands of other people might share?

How the curve is calculated
People with one namePossible pairsChance two share a birth date
501,2254%
1004,95016%
20019,90049%
30044,85079%
500124,75099%
2,833about 4 millionCertain: about 137 matching pairs expected

The curve assumes birth dates are spread evenly over 80 years, about 29,200 possible dates. Real birth dates bunch up by age group and season, which makes matches even more likely than the curve shows. Some matches in real records are also the same person entered twice, another problem that name and birth date checks struggle to catch.

Related exhibits

Sources: Harris Health System figures reported by its chief information officer, Tim Tindle, in Advisory Board, "Daily Briefing," February 20, 2019; probabilities calculated with the standard birthday-problem approximation.