Why is it hard for a program to generate random numbers?

Question

My kids asked me this question and I couldn\'t really give a concise, understandable explanation.

So I\'m hoping someone on SO can.

Answer 1

It's easy to come up with an algorithm that generates unexpected numbers, that appear random in some sense. But to design an algorithm that generates true random numbers, well, that's hard.

Imagine designing an algorithm to simulate a dice roll. You can easily formulate some procedure to generate different numbers on each iteration. But can you guarantee that, in the long run (I mean, up to the infinity), the amount of times that 6 came out will be the same as any other number? When designing a good random number generator, that's the kind of commitment that you have to assume. You have to provide strong guarantees (i.e. mathematical proofs) about the randomness, if the application (e.g. lottery) requires it.