d20 rolls

Change the effects of a rolled 20 and 1.

For skills:
When a 20 is rolled, add 20 and roll again.
When a 1 is rolled, take 20 off and roll again.
If you are in the second+ roll, you can't change direction, e.g. if you have started up a 20 line, 1's are now just a number, not a -20 & re-roll.

This allows for a checks to be awesome and really bad, but doesn't mean an automatic 5% chance of failing or succeeding.

example:

hide in shadows skill: 9
roll 20
roll 20
roll 4
total hide in shadows = 53.

When rolling the 20-path, once success is achieved, continued rolling is not required (the DM can tell you when to stop).
When rolling the 1-path, once failure is guaranteed, continued rolling is not required.

For saves, the same method is used.

For attack rolls, there is an addition:

critical hits:
Using stop when achieved rule above, the last die rolled indicates the threat possibility.

e.g.
AC=25, to hit=3, threat = 19-20.
roll 20 (total = 23 - not hit, roll again)
roll 19 (total = 42 - hit and threat - will need a good confirm roll though)

e.g.
AC=25, to hit=10, threat = 19-20.
roll 20 (total = 30 - hit and threat)