Pi can be as it's (thought to be) normal (all digits appear with uniform frequency), but like anything, it's how you use it. Imagine you selected a digit from pie and used it to decide rock, paper, or scissors (3 options, so let's take a digit and mod 3)

    0: 0 Rock
    1: 1 Paper
    2: 2 Scissors
    3: 0 Rock
    4: 1 Paper
    5: 2 Scissors
    6: 0 Rock
    7: 1 Paper
    8: 2 Scissors
    9: 0 Rock

Now, let's check the frequency of each option:

    0/Rock: 4
    1/Paper: 3
    2/Scissors: 3

Your RNG is biased towards 0 here. The same thing happens, and is very common, when people just take the system random number generator and mod it by the number of values they want. They always end up biasing the bottom section of their distribution.

The common way of dealing with this is to "ignore" any number that would make the set biased. Here you would ignore 9 and you have an even distribution. So, you're playing 7 rounds of RPS and you go

    3/R
    1/P
    4/P
    1/P
    5/S
    9! SKIP! 2/S
    6/R

The simple reason is because a pseudorandom number generator is a complexity theoretic thing, but an information theoretic thing. In order for it to be robust, it must be indistinguishable from true random for any polynomial time algorithm. Since we have algorithms which can calculate Pi in polynomial time, as long as the computer recognized the sequence (or the deterministic seed of the sequence as Pi), it could with certainty predict the next digit of the sequence.

As for why converting digits in this way matters - a lot of randomness is expressed by the entropy. It's harder for you to correctly guess the sequence {1,7,9,3,6,8,2,4} than it is to guess the sequence {1,1,1,1,0,0,0,0}.

If I ask you to guess a decimal digit I've chosen "randomly", you have a 1/10 chance of being correct. If I ask you to do the same for binary digits, you have a 1/2 chance of being correct.

Basically you want to think of these as subsequences, not individual numbers. If Pi is normal (which is a big if), then Pi is normal in every single base, including decimal or binary. But it's not generally true that a normal number generates another normal number by mapping each digit to the digit's parity.

> it could with certainty predict the next digit of the sequence //

If pi is [absolutely] normal though all sequences exist in it at equal frequency. Meaning that for any given sequence there is an infinite number of positions in pi to find it and that all the possible following digit sequences are equally likely.

So the computer could never know the next digit.

Aside: guessing a D16 roll seems way more likely than guessing a nibble of binary, and perhaps a little less likely than guessing 4 coin flips!??