I'm having trouble parsing your questions. You have some sentences that end in question marks. Are you asking whether I agree with those sentences? I'm having trouble understanding the assertions made by those sentences, so I can't tell whether I agree with them (if that was what you were asking).

The claim that I was making could be summed up as follows. I described an agent using a PRNG to solve a problem involving painting marbles. The usual way to view such a solution is as

deterministic amnesiac agent PLUS randomness.

My suggestion was instead to view the solution as

deterministic amnesiac agent

PLUS

a particular kind of especially limited memory

PLUS

an algorithm that takes the contents of that memory as input and produces an output that is almost guaranteed to have a certain property.

The especially limited memory is the part of the PRNG that remembers what the next seed should be. If there weren't some kind of memory involved in the PRNG's operation, the PRNG would keep using the same seed over and over again, producing the same "random" number again and again.

The algorithm is the algorithm that the PRNG uses to turn the first seed into a sequence of pseudo-random numbers.

The certain property of that sequence is the property of having two-thirds of its terms being less than 2/3.