When a shared birthday becomes likely
birthday is one function. Everything below came out of it during this
build, at parameters taken from the essays rather than invented for this page — so a figure
here is the same figure a reader meets in an essay, and if the generator changes, this page
changes with it.
At its defaults
show: "pairs"
What it checks while it draws
Collected by running the family and recording what it asserted, not written here. The count is how many separate times the claim was put to the test while these drawings were made.
- 22 is still under a half ×1
- 23 is over it ×1
- one person shares with nobody ×1
- the half-way point is 23 people ×1
- the pair count is k choose 2 ×1
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.
How long until every one turns up
Draw at random from six equally likely kinds until all six have appeared. The wait is not six draws, and it is not sixty; it is fourteen point seven, and the number is a harmonic sum wearing a hat.
ProbabilityNobody gets their own hat
Hand back a pile of hats at random and ask for the chance that not one person gets their own. The answer barely moves as the crowd grows — it is a third and a bit at four people, and a third and a bit at four thousand.
ProbabilityTwenty-three people
A room needs 253 people before someone probably shares a birthday with you. It needs 23 before two of them probably share one with each other. The gap between those numbers is the whole problem.