How long should you wait to harvest your crops in Minecraft? -- Optimizing periodic farms

This video summarizes my work on optimizing periodic farms in the video game Minecraft. The lambda function introduced in this video appears in many other disciplines, as the Poisson Distribution is pretty fundamental.

This video was inspired by Ilmangos video on amethyst crystals:    • 1.17 Shard Farming: Doing The Crystal Math  

I would like to thank Professor Iddo Ben-Ari for his support on this project.

This work is only relevant for certain crops in the game. Sugar cane and cacti have more complicated behavior, as they are composed of more than a single block. This work is only relevant for single block plants. Also note that this video's results will not work for copper oxidization in the game, as oxidation, though random ticked based, follows different update rules than other random tick based events. cubicmetre shows some numerical results for copper in this video:    • A Viewer made my Copper Factory Obsolete  

The links for the mathematics topics discussed in this video can be found below:
https://en.wikipedia.org/wiki/Lagrang...
https://en.wikipedia.org/wiki/Fa%C3%A...
https://en.wikipedia.org/wiki/General...
https://core.ac.uk/download/pdf/15760...
https://core.ac.uk/download/pdf/82146...
https://en.wikipedia.org/wiki/Bell_po...[3l%22]_on_p._136-5