Answer by user479885 for Understanding "randomness"

Consider you have a simple coin flip problem where even is considered heads and odd is considered tails. The logical implementation is:

rand() mod 2

Over a large enough distribution, the number of even numbers should equal the number of odd numbers.

Now consider a slight tweak:

rand() * rand() mod 2

If one of the results is even, then the entire result should be even. Consider the 4 possible outcomes (even * even = even, even * odd = even, odd * even = even, odd * odd = odd). Now, over a large enough distribution, the answer should be even 75% of the time.

I'd bet heads if I were you.

This comment is really more of an explanation of why you shouldn't implement a custom random function based on your method than a discussion on the mathematical properties of randomness.