ok you kind of have a point, first of all I'm not sure what you mean by gibberish, if you mean, no english words, or no strings of english words that are sentences, etc.

However getting hamlet is even harder than I proposed

Here is why:

if we only had to produce one letter, say "a", instead of all of hamlet, it would not take 26 random hits as I purport my little story. This is because its possible to repeat letters and completely miss the letter "a". The probability that we get it on the first try is 1/26. If we were trying to generate the word "and" then the probability we get that with the first 3 keypresses is (1/26)*(1/26)*(1/26) = 1/(26^3). The more attempts we make the higher the probability that we get the word "and" but it is never guaranteed.

this follows standard equations from probability that I can't remember off-hand.

basically all this means is that it would take a lot longer than previously thought (now maybe hundreds of thousands or millions of universe-lifetimes) for the probability of having Hamlet in our hands was above 75%. And we will never definitely have it. but then again, we could get lucky and get it on the first try, or in the first say, hundred thousand years. but that probability is probably much smaller than 1%.