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Collections are a way for you to organize kata so that you can create your own training routines. Every collection you create is public and automatically sharable with other warriors. After you have added a few kata to a collection you and others can train on the kata contained within the collection.
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This is a fun introduction to what's called "Monte Carlo integration". I like to describe it as "the drunkard's dartboard".
It's also even slower at converging than the 4/1 - 4/3 + 4/5 - 4/7 + ... arctangent series. The error in an average of n random values is proportional to 1/sqrt(n), while the arctangent series error is proportional to 1/n.
So, if averaging N trials gives you 2 decimal places of pi, you'll need 100N trials to get 3 decimal places.