HOW MANY PICS

i go to this site, and they show me a random pic so i say LOL GIMME MOAR and i click click click. after only 7 clicks, i see a picture i already saw... how can i guesstimate the amount pictures on the website?

If you go to Gelbooru and search any series-unspecific term, there's a high probability at least one picture on every page or at least every two pages is Touhou related.

im so disappointed, isn't there any mathfag here willing to teach me something?

Let X be a random variable with probability mass function f_X(x;n)={}probability of taking x draws until a repetition when drawing from n items with replacement.

In your case, you drew 8 times until a repetition, so your problem is to maximize the likelihood function L(n)=f_X(8;n).

Now, there are n^8 ways to draw 8 items with replacement, and if we are to have our first repetition on the eighth draw there are n possibilities for the first draw, n-1 for the second, ..., n-6 for the seventh, and 7 for the eighth.  Thus f_X(8;n)=\frac{7n!}{(n-7)!n^8}=7\cdot7!{n\choose7}/n^8.

Note {n\choose7}/n^8 has a maximum at n=25, so your estimator is \hat n=\mathop{\rm argmax}_{n\in\mathbb{N}}L(n)=25.