FoxBoy: You 'n me, we's similar cloth.
And it doesn't seem to matter what game is played...my dice-gods snicker at me, no matter what. D&D? Nearly half the games I play, I have a dominant stretch of die-rolling on a d20 that does not exceed 7. I play a campaign of KULT (older Swedish-translated game of horrible, horrible things) where the skill checks and combat rolls are inverse to the D&D system (1s are critical successes, and 20s are baaad news), and my dice nicely accomodate the adjustment.
Designing characters seems almost moot sometimes. I make someone who's a sneaktastic master (had a halfling rogue/ranger multiclass, played the campaign 'til we were about 18th level), and durned if I could make him seem competent at his best skills, with how I rolled. Actually, it seems a LOT that the things my character is SUPPOSED to be able to do- those are the things at which he fails, if called to roll for it.
There was a carryover from a D&D game when some of us were playing a later Star Wars Saga Ed. campaign, where I had posted "Take 10, Dumb@$s!" above my skills.
Now, this is not to say that this is ALWAYS the case. Very occasionally, I have a 'Vegas Baby!' night, where everything I roll is gold. My friends are all aware of this odd, odd tops(1/3)-bottoms(2/3) tendency, to the point that I cannot borrow dice from others...there seems to be a short-term contagion effect as well. An ex-GF has abandoned whole sets of dice because she forgot, and let me borrow a die for a check, or damage roll, and her follow-up dice results were catastrophic.
A D&D group made me a certificate once...I still have it in one of my game binders - "Most Extreme Dice"...appreciation is still appreciation, I guess. Heh.