After being inspired by a video by ‪@SeaJayPlays‬, I embarked on my own journey to learn some new math and how it can be used to optimize a sugarcane farm's harvest interval.

‪@SeaJayPlays‬' video:
   • I Simulated Minecraft to Find the Bes...  

‪@ilmango‬'s Crystal Math:
   • 1.17 Shard Farming: Doing The Crystal...  

Rigorous proof by Nukelawe:
github.com/Nukelawe/sugarcane/blob/master/main.pdf

Rigorous proof by Yiyan Shou:
www.dropbox.com/s/ankdmjqat5p2mke/sugarcane.pdf?dl…

Building ilmango's sugarcane harvester in survival (includes testing world download!!!)
   • Survival Tutorial: ilmango's Bamboo Farm  

My Mathematica notebook file (version 12.1):
1drv.ms/u/c/49d9f3bb01877138/ETBEhZCAlQFNktZYUwaKk…

My Powerpoint slideshow:
1drv.ms/p/c/49d9f3bb01877138/Ee-dIpoMVA1IolNlQmKi_…

Chapters
0:00 Intro and sugarcane mechanics
3:27 Binomial distribution
7:12 PDF and CDF
11:58 Applying PDF and CDF to sugarcane
20:49 Calculating drops from one harvest
23:58 Calculating drops per hour (multiple harvests)
25:57 Got the chart! But something's wrong...
28:19 The solution? Markov chains
32:26 Stationary distribution
34:17 Creating a transition matrix
41:12 Using a Markov process to get the stationary distribution
44:15 Plotting the final result!
46:12 Plotting a non-stationary distribution
49:49 Another problem?! Running numbers in-game
50:40 Demonstrating ilmango's sugarcane machine
52:37 Discovering the harvest delay and correcting for it
1:00:34 Outro