A common mistake is to assert that the digits of pi are random. This is wrong by definition. Pi's digits are fixed and may be computed formulaically and hence are instantly distinguishable from a random sequence. The question people really want to know is whether or not the digits of pi are distinguishable by inspection in any obvious way from a random sequence, such as whether there are biases or recurring patterns in the digits. None have yet been found.

The most common formal term called into play is whether or not pi is normal. This conjecture is widely believed to be true and has held true for the billions of digits found so far. However no component of this conjecture has been formally proven for any base.

Even if a number is normal, this does not mean there are no obvious trends in it. It is easily shown that the number 0.12345678910111213141516171819202122 ... is normal. But just because that pattern is more obvious to your tiny human mind than the Bailey-Borwein-Plouffe algorithm for computing decimals of pi, doesn't mean it is any less random. In fact, neither is random at all, both are perfectly deterministic.