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@oblomov @mcc @grumpygamer
After reading up on this a bit I can semi-confidently say that this branching process with d6s will continue infinitely. The highest chance of it terminating is of course in the first or second roll, but after that chances of terminating become infinitesimally small.

@oblomov @mcc @grumpygamer hi! It seems like you've stumbled upon the lovely mathematical genre of problem called 'branching processes' and 'extinction probabilities'. I don't know how to calculate this, but I can show you where to look.

Tbis Reddit post had a similar idea to you: https://www.reddit.com/r/askscience/s/jH1LzTXROe

This is the wiki page on branching processes: https://en.wikipedia.org/wiki/Branching_process?wprov=sfla1