Ring of Pure Luck

At first glance, these appear to be ordinary rings with no gems or markings. However, once worn, the wearer will start to notice things start going his/her way more often than not.

When worn, if the character fails a random check or saving throw by 2 or less (10% or less for percentiles), or if the character rolls a critical-failure (such as when disarming a trap), the magic of the ring is triggered. The ring does not trigger on attack rolls.

When the magic of the ring is triggered, the DM rerolls the check or saving throw in secret. If this secret roll is successful, then the failure is instead treated as successful, or the critical-fail is instead treated as a normal failure.

Seccondary Enchantments
A few of these rings will have additional enchantments when found. To determine these additional enchantments, roll a d20 and consult the chart below. Reroll any duplicate result.
Misfortune
Due to the powerful and fickle nature of the magic in these rings, some will have aquired this curse. The ring will appear beneficial when identified, since the curse only reveals itself the first time the ring is triggered by the wearer.
Cursed rings instead trigger on any successful check or saving throw within 2 or less (10% if percentile), and on any failed check that is subject to critical-failures. If the secret roll is a failure, then the ring turns a successful roll into a failure, and turns a normal failure into a critical-failure.
Once the curse is triggered, any other beneficial enchanments on the ring will instead have opposite effect.
The curse only reveals itself when the ring is worn, and the ring may be only be removed from its victim with a "Wish", "Limited Wish", or a "Remove Curse" spell vs. a caster level of 15.