Why does l'Ecuyer reject p-values close to 1?
So, what's wrong with a p-value close to 1?

Because random sequences don't look 'perfectly random' (or, rather, they have a low probability of doing so).  We're checking if this sequence quacks [1] like a perfectly random sequence; acting 'too uniform' is evidence that it is not.

[1]: from the proverb &quot;if it acts like a duck, and it quacks like a duck, then it is a duck&quot;.  Fairly common where I am; however you never know how regional sayings like this are..