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I am reading about consistent hashing for system design and I understand the application of consistent hashing and the use of virtual nodes. I want to understand how to calculate the optimum number of virtual nodes and how to place them on the unit circle.

https://youtu.be/zaRkONvyGr8?t=433

in the above video the author explains that k hash functions are required, pass the key through each hash function to have k points for each server and the optimum number of hash functions k = log(M).

where M is number of servers (not sure if I completely understand this portion, feel free to correct me). The presenter in the video says "search space", but imo I think he means he means # of

How / Why does this work ?

Other resources I have gone through are:

but this portion isn't explained

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