The Math Engine
// 1. Comparisons (Pairs)
Pairs = n à (n - 1) / 2
// 2. Probability of a Match
P(Match) = 1 - (365! / (365âŋ Ã (365 - n)!))
// 3. Expected Matches (Mean)
Mean = n à (n - 1) / 730
Why is this happening?
It feels like you need 183 people (50% of 365) to get a match, but that's wrong.Explained here!
You aren't comparing everyone to you. You are comparing everyone to everyone.
The Formula:
With 23 people, there are 253 lines connecting them.
With 50 people, there are 1,225 connections!
That spiderweb in the background? That represents the explosive growth of possible matching pairs.