Why can't pi be used as a PRNG, and why does converting each digit to its parity lose a possible PRNG property? Sure it removes a lot of entropy, but it does so by destroying information, not from creating/overwriting memory.
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
0/Rock: 4
1/Paper: 3
2/Scissors: 3
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/RAs 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.
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!??