But given a pseudorandom number generator with a known amount of internal state (eg a 32 bit seed) there are hard upper limits on the lengths of sequences like

But given a pseudorandom number generator with a known amount of internal state (eg a 32 bit seed) there are hard upper limits on the lengths of sequences like that that can plausibly be produced. Of course, to get 4 out of a PRNG you probably have to ask it for a random number in a range - if you’re requesting numbers in the range 0-1000 then you would expect fewer long sequences of fours than if you request in the range 0-5. And you can get arbitrarily many 4s by requesting numbers in the range 4-4...