Ask AI: Cousin Count - Anglo-Celtic Connections

In the latest Family History AI Show episode, Mark Thompson said “these (AI) tools are no longer bad at math.”

Here’s a consistency check. Each AI was prompted exactly with. “In a family tree where each person has two siblings how many siblings, first, second and third cousins of the same generation does each person have?”

Gemini and Claude returned that each person has 2 siblings, 12 first cousins, 72 second cousins, and 432 third cousins.

ChatGPT initially counted only one side of the family when calculating first cousins. Asked to check its calculation it apologized and gave the same answer as the other two.

Gemini provided a formula. For any degree of cousin $n$ where each person has $s$ siblings family size $k = s + 1$ children:

\text{Count of } n\text{-th cousins} = 2^n \times s \times k^n

Please don’t take this as the correct answer, and especially don’t take it as representative. All families don’t have three children who lived to have three children, and so on. Families are getting smaller. There’s a geographical and cultural bias in family size. The calculation assumes no pedigree collapse.

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