Here's a house rule you can use in any version of D&D where you roll stats and roll hit points. It works best with stat generation methods that are restricted to rolling six times, whether its 3d6 or 4d6 drop the lowest. It's better in the latter, but you're probably aiming for "better" characters anyway.
Sometimes, it's better to be lucky than good. Your arrow finds the crack in the orc's armor, the ogre's club catches on the stalactite just as he's about to brain you. Luck gives you a small pool of points that you can use to assuage the cruel vagaries of fate.
When rolling up a character, you receive a luck point for each 1 you roll. If you use the 4d6 method, you get the point even if you drop the die with the 1 on it.
When you're done rolling up your character, record your total number of luck points. That's your luck score.
Whenever you roll a d20 to attack, you can chose to spend a luck point to re-roll the attack. You can also spend a point to force an enemy to re-roll an attack against you. Spend the point after you learn if the attack hit or missed.
You can spend a point of luck to re-roll a thief/assassin skill check.
When you gain a level and roll hit points, you gain 2 luck points if you roll low enough.
d12 or d10: Gain 2 luck if you roll 3 or less.
d8 or d6: Gain 2 luck if you roll a 1 or 2.
d4: Gain 2 luck if you roll a 1.
I came up with this idea while rolling up a series of OSRIC characters for fun. I was tracking the number of 1s I rolled (it's a talent of mine when rolling characters) and tried to think of some way to make that interesting. I kind of like the idea of a gimpy adventurer surviving because of dumb luck.
5e Investigation skill.
14 hours ago