I recently watched a great 16 minute YouTube video on the basics of information theory: https://www.youtube.com/watch?v=bkLHszLlH34. The video shows the link between probability and information entropy and a great takeaway from it is that you can use these concepts to decide what kind of experiments to do, to get as much information as possible. This…

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Information entropy can guide experimental design by quantifying how much information different choices provide. Using probability theory, you can calculate expected bits of information from various outcomes and select experiments that maximize information gain. The classic 12-ball weighing problem demonstrates this: weighing 4 balls per side yields the highest expected entropy (1.58 bits) because it creates three equally probable outcomes. The key heuristic is choosing experiments where all possible outcomes have similar probabilities, as uniform distributions maximize information entropy.

Using Information Entropy To Make Choices / Choose Experiments

Using Expected Information Entropy To Choose Experiments