In fact, it can be further generalized for any random (allegedly) distribution

For example, we may assume that the rolls (if we are talking about dice here) are independent of each other. So far, so good. But if we apply this presumably flawless logic, we necessarily arrive at an impossible inference that there should be endless losing or winning streaks. And this is where things get complicated

Since we can safely assume as well that at some point in the future our repetitive streak is going to end, we can also claim that with each roll this point comes closer and closer. But by deduction, we can then easily reach a conclusion that rolls are not really as independent as they seem to be, or future is not as unpredictable as it appears, either