EA's Jeremy Dalberg has posted another one of her "Five on Friday" Q&A features on the official Ultima Online website.
"How is your chance to remove a curse with Chivalry's Remove Curse spell determined?"
(This is my first solo foray into reading the server code, so bear with me :) )
Your chance at success is entirely determined by your karma (referring to Stratics' Fame and Karma chart will give you an approximate idea of your numeric Karma, which will be important in a minute.) If you have negative Karma, your chance to succeed is the square root of 20000 - your (absolute) karma (so remove the negative sign there), and then subtract 122 from the result. This means at just barely negative (-1) you'll have about a 20% chance of success, but at about -5000 (Tier 4 - Evil, etc - and below) you'll have a 0% chance. Dread Lords need not apply!
If your Karma is dead neutral (0) or positive, the chance is determined by taking the square root of your karma and then adding 25. This works out to a 25% chance of success at 0 karma, and 100% chance of success at 5600 or so - a little ways in to Tier 4 (Illustrious, etc.)