As per my prior post, I really think that "I want to know what to expect" is really the wrong route here. The whole reason to have an RNG is permit the unexpected -- there are at least three things it provides (the ability to gamble on a high-risk, high-reward option when it's the only hope you've got; the thrill of an unexpectedly good result [e.g., enemy missing you with a point-blank burst, critically hitting and killing your foe]; the panic of a well-laid plan going awry due to chance). It's true that the frustration of missing your own point-blank burst is extraordinary, but the idea that the frustration stems from an honest belief that the game is cheating seems implausible to me. Instead, I think "CHEATER!" is simply an emotional reaction to the fact that something bad unexpectedly happens to the player for no good reason -- e.g., the player took a conservative, low-risk, low-reward option to finish an opponent off and still missed. As long as there is any random chance, there is a chance of such a thing happening, and the player's reaction will be resultingly foul if the consequences are high enough.
The only ways to address this are: (1) remove bad RNG results for player (yikes); (2) remove RNG entirely (losing the upsides described above); (3) give the player something when he has a bad roll. As my prior posts indicates, I think #3 is the way to go. But what to give? IMO, an achievement is the simplest answer because it's totally extrinsic and can't break anything. Because TNW is a serious setting, I wouldn't recommend in-lore options (e.g., early on you meet some guy from Lady Luck's Jilted Swains who mentions that his elite club's benefactor makes a point of letting in those cursed with a string of unfortunate events, and then in the Habitat you find the club and can get in if you have enough unlucky die rolls), but you could do some kind of extrinsic thing (like the golden die option). But I think having it "outside" the RNG is the key. Trying to adjust the RNG itself just feels weird. It's better to have the game acknowledge you got screwed and offer some offset.