Not having those "3 times the same number in a row" would make it pseudo-random. There are actually applications (e.g. spotify IIRC) where developer do pseudo-random generators such that they feel more "random" to the user. Pretty sure that is not the case here though.
Technically [puts nerd glasses on] a
psuedorandom number generator (PRNG) generates "random" numbers via a deterministic sequence completely based on an initial value (i.e. seed). This is opposed to hardware RNGs which can generate truly random sequences based on a entropy source. The RNG in most (all?) software and games
IS a PRNG, and unless you're doing highly sophisticated Science!!, it's as good as random.
What you describe, where you alter the distribution to "appear more random" [even though it's not...] is a thing, but I can't seem to find a name for it. Like you point out, it's common in music playlist software like iTunes and Spotify when selecting songs. These programs will also do random
orderings (i.e. without replacement) which are also actually random, but in a different kind of way.
It's not about 'confirmation bias'.
I got the same impression with the rebels spam too many time. It's like something lock and unlock with the sub-routine that manage the chances.
With rebels is at times even more dramatic. I got very often increases for 3 months in a row with unrest of "just" 3-4%.
There's like a chance in 10000-30000 that this happens, and I see this happening several times during a campaign. It's too often the same similar pattern with rebels:
no increase for some months and then 2 to 4 increases in a row. It's not just an issue of chances, it's also the distribution that seems to follow a pattern.
And for some reason 50% of chances of ending a siege in 1445 is definitely not the same than 50% of ending a siege in 1750. The second is definitely way more likely.
That's why I wrote about the 'AI' cheating, because -particularly at the beginning of the campaign- the numbers shown to the player do not seem to represent the 'real chances'
And these are all great examples of confirmation bias. Without recording every siege result or every rebel increase, there's just no way to determine whether there's actually something amiss or not. It's not that we don't believe there
could be a bug, it's just that confirmation bias is
way more likely given how human psychology works, and without the evidence, no one will take it seriously.
The "no increase in rebels for some months, then 2-4 in a row" is expected in a random process. Randomness
is streaky and you tend to remember the streaks more than the non-streaks.
Speak for yourself. I get nothing but Quantum entangled Schrödinger's rolls. All numbers at the same time mimicking both all future and all past rolls until I look at them.
As soon as I look, they're all zeros, obviously.
SCIENCE!
Shhhhh!!! We don't talk about Paradox's secret quantum computer. I hear they've been developing it so that we finally have an AI that doesn't leave its armies in The Colonies...