I've seen no source that shows that Xcom fudges its displayed hit chances. You may be thinking of Fire Emblem, whose games use a variety of well-documented approaches to fudging their rolls: https://fireemblemwiki.org/wiki/True_hit

I know at least XCOM 2 does on certain difficulties. The aim assist values are directly in the INI files (it fudges the numbers in your favor for lower difficulties). Here are instructions on how to remove the aim assists: https://steamcommunity.com/sharedfiles/filedetails/?id=61799...

Most big games implement "randomness" with "pseudorandomness" in the name of controlling variance of outcome, chopping off the long tail

Do pseudorandom distributions have chopped tails? Wouldn't that go against the definition of pseudorandom?

To be clear it's a mix of pseudorandomness and "procedural randomness" to increase "fairness"

Is there any game that does NOT use pseudorandom generators? And does this significantly change probabilities?

Think there is confusion here - if I understand correctly you are asking about the number generator, they are talking about the process of determining success. Like in league of legends you have a listed crit chance but the way they determine success isnt to generate a number and compare it to your chance, you start with a smaller base number that gets incremented each time you fail and reset when you succeed - the end result is that your overall chance remains the same but the likelihood oh a streak (of fails or successes) goes down.

Doesnt change the overall probability, drastically reduces variance.

Some games (both computer games and physical board games) intentionally use "shuffled randomness" where e.g. for percentile fail/success rolls you'd take numbers from 1-100 and use true randomness to shuffle that list; in this way the overall probability is the same, but has a substantially different feel as it's impossible for someone to have bad/good luck throughout the whole game and things like "gambler's fallacy" which are false for actual randomness become true.

> the overall probability is the same

Only for the very first roll. After that, the outcome becomes more and more predictable for each roll.

Just as with any standard PRNG (e.g. Mersenne twister) the outcome may be fully predictable with some information about the state or the previous rolls, but its still usable; and the general distribution of values matches what is desired for that section of the game.

That’s not what I meant. Say that the first roll was a 1. Then you know that for at least 100 rolls, you won’t get a 1 anymore. And with more rolls, more numbers are eliminated.

Some games I follow talked about "switching to pseudorandomness" but that may be misuse of terminology.

There's an argument for competitive games to use true randomness to eliminate any possibility of abuse, but I'm not aware of specific examples.

Can you elaborate on how XCOM lies? I often suspected this (but you can never be sure, since human intuition is bad at probabilities). Is there hard evidence?

I believe it fudges the numbers to give you better than expected results on lower difficulties.

"That's XCOM baby!"