I think it would be an interesting experiment to alter the Luck rules for Dungeon Crawl Classics RPG as follows: Instead of a Luck point giving the player character a +1 modifier to an action, it grants a +1d. After all, if Luck is Chance (and it is), shouldn't it have a random element itself instead of a direct modifier that subverts the very concept? Besides, the dice chain is one of the best ideas in DCC RPG and it is woefully underused.
I think I'll try it the next time I judge. A report will be forthcoming.