why am i obsessed with random numbers?

Question

i invented this simple program that randomly generates 0 or 1 with equal probability. i have to guess a number between 0..1, for example,0.6, to predict this number. then the covariance between my guess and the randomly generated data is calculated. it turns out that i cannot get the covariance over 0.1, which is statistcally right. but i cannot for a moment stop to think that i cannot do it. why is that? it's only one idea fails, i go with another. i also sometimes have two guess, like, i knew it all along. can someone explain to me, why this happens?

Answer 1

I believe that you would increase the covariance if you picked the same number several times in a row.

Answer 2

This is all much simpler than you imagine.

You just need a girlfriend.