Are you a mathematician or just spitting out fancy words to confuse us amateurs?Wait, what? The probability of X-long losing streak depends on your sample size and that's not present anywhere from what I see. The problem is not as easy as it seems
PS. if you assume that you actually living in a Bernoulli distribution world, you can use the de Moivre formula (originally developed for gambling with unfair coin). If you had a statistical sample, you can use bootstrapping (of limited value if your distribution is strongly skewed).
I need to take more online classes to understand Bernoulli distribution.

