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Random Walk Watershed Point

This experiment is based on a question posed on this Reddit post.

Start with a random number between 0 and 5. Then, pick a number between 0 and that number, and multiply them together. Now, pick a number beneath that number, and multiply them together, and so on.

The question is: what number is the watershed point in which the random numbers have an equal chance of going towards zero or infinity.

I ran a simulation and found that 2.4 is the watershed value.

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