Numion said:
Or would the possibility of rolling infinitely large be zero? Sorry, just a nit I had to pick. 
But anyways, if you you use this 2d10 method, wouldn't the dice rolling matter even less at higher levels? Because the variance of 2d10 is much less than 1d20. Even with the current 1d20 roll the dice roll is secondary in importance to the modifiers, which can be in the 40+ range even before epic levels. If thats what you were shooting for, then fine. Just a point.
Thanks for the question.
Right now at high levels having +40 to a skill is already making the d20 useless, imho. And, having a really high skill number makes it impossible for your average guy to beat you in opposed checks (say your listen +6 versus the rogue's hide +30). However, the possibility of rolling a double allows you to skew your results higher and gives you at least the possiblity of winning.
There are nine rolls (double 2,3,4,5,6,7,8,9, and 10) or 9% of your rolls will allow you to roll again. I consider this 9% bonus more fun for the players than a simple 5% flat out success possibility of rolling a 20.
My idea is still pretty new in my mind you you guys are getting the rought draft in this post so I will be surprized (or not) with you as I think out loud.
By comparison. Disregard doubles for now (make the math easier)
If you have------Under d20------Under 2d10
to roll---------------You win-----------You win
===============================
11-------------------50%-------------55%
12-------------------45%-------------45%
13-------------------40%-------------36%
14-------------------35%-------------28%
15-------------------30%-------------21%
16-------------------25%-------------15%
17-------------------20%-------------10%
18-------------------15%--------------6%
19-------------------10%--------------3%
20--------------------5%--------------1%
So, under 2d10 having to beat a DC by more than 12 is HARDER, having to beat it by 16 or more is much harder.
I am still thinking about this, and will add more later...
...developing...
g!