In the Dungeon Crawl Classics games I referee, I've been playing with a house-rule that modifies DCC's "lucky roll." In the rules as written, characters permanently add their starting Luck modifier to one randomly selected type of roll.
My objection to the rule as written is that for most characters, their supposedly-lucky roll is either going to be unmodified, or it's actually going to be an un-lucky roll because they have a negative modifier. Nearly half of all starting characters, 48%, have no Luck modifiers because their Luck scores are between 9-12. Another quarter, about 26%, have negative Luck modifiers because their Luck scores are 3-8. Using the rule as written, only about 1 in 4 starting characters have a "lucky roll" that's actually lucky.
So, my house rule is that all characters receive a permanent +1 bonus to their "lucky roll," regardless of their starting Luck score.
If a referee felt that this rule deprived characters with extremely high Luck scores of the larger bonus they'd receive under the original rule, she could choose to let those characters receive the superior bonus granted by their higher Luck modifier. That change would only affect about 5% of starting characters though, because only about 1 in 20 would begin with Luck scores 16-18.