What they are Really.
Luck Points are given by the GM for good behavior outside of the game world. Essentially, any time a player (not character) does something that makes the GM’s job easier, or more enjoyable, they can be rewarded Luck Points. Good roleplaying, helping other players, looking up rules, cleaning up after session, bringing snacks. All of these are ways a player might earn Luck points. GMs are encourages to award more than one luck point at a time, even to the same player, for the same thing.
What they are Mechanically
Luck Points are a +1 or -1 to any roll made by any person, including other players, as well as the GM. Luck Points stack. They can be used after knowing the results of a roll. They can be used after using Luck Points on the same roll. They can be used to increase a die roll higher or lower than it’s maximum or minimum (although the roll plus modifiers can never be less than zero). All Luck Points are lost when a player changes characters because of their death or disability during play.
What they are Thematically
He who lives by the sword, dies by the sword. Most adventurers die at low levels. Only a handful ever reach mid level. Yet it can be quite common for PC’s to reach high, or even epic levels. This isn’t happenstance. Fate has decided to take a special interest in these characters. That’s why they live so long, despite the fact that they should have died dozens of times. Luck Points are Fate’s way of tipping the balance in a character’s favor when they need it most. Characters might even be aware of their Luck Points, on a subconscious level, acting more boldly when they are “feeling lucky”, and more cautiously when Fate isn’t able to help them.
Why use Luck Points in my Campaign?
1) GMs are people too. GMs have a lot of responsibilities. They are the only person who can't miss a session. The only person who prepares ahead of time. The only person who makes difficult decisions regarding game balance. The only person who has to act out many characters at once. Luck Points give them a break, by encouraging players to take up the slack, like rules questions, and even content creation. They can also reward a more fun DM experience, like bringing snacks, and fun roleplaying.
2) Players SHOULD have a reward. I have heard GMs claim that roleplaying rewards don't make sense. After all, we don't reward rulebook knowledge, do we? Well, yes we do. Rulebook knowledge gives players an advantage in the game because they know how to use the system to their advantage. Anybody who has played at the table can admit that experienced players have stronger characters, even within the same build. Roleplaying, helping the GM look up rules, and buying snacks for the group don't have any direct benefit. They should. I want my players to be rewarded for making the game better.
3) Luck Points are temporary. Once a player uses them, they are gone. Unlike XP rewards, which give that player a permanent advantage over the other players. You can give them out a little more freely, without worrying that it will ruin the game permanently.
4) Luck Points promote teamwork. Luck Points, by their nature, are most useful when the players help out each other with them. It can be hard for a player to justify going toe to toe with the BBEG when the rest of the party isn't able to help. But Luck Points can help everybody, even players who aren't in the same location. For this reason, I like to give more Luck points to Players when they work together. For instance, if a single person cleans up after session, I might give them 4 Luck points. If everybody cleans up after session, I give each of them 2 Luck Points.
5) Players get to do the really fun, risky stuff. Ever wanted to leap from building to building? Ride the deadly monster? Run through traps to save the prisoners? One hit KO the bad guy and feel like a boss? Sometimes its fun to do something crazy, without worrying about the fact that if you screw up, you just instant KOed yourself. It's not all the time, mind you, just when you have luck points to burn. But it can be awfully fun.
6) No more encounter fudging. Thematically, every adventure wouldn't be leveled to the characters. Sometimes the players should be able to pick an adventure that is simply to strong for them. They should have the choice to fight the BBEG early. When that happens, what do you do? Lower the encounter? Railroad them someplace else? Fudge dice rolls? Total Party Knockout? Luck Points give you an extra option. Most players will learn to save their luck points till they need them, so that when it's thematically appropriate to throw an encounter at them that is just to hard, you don't have to sacrifice the story, to save the PCs
7) Hardcore Mode. I like to throw tough encounters at my players. Really tough encounters. I used to have a player death, like, once every few sessions. TPKOs weren't that uncommon. My players said they weren't having that much fun in battle. Luck Points changed all that. Now I can just give away loads of Luck Points, and make the battle as tough as I want. Easy.
I hope you try using Luck Points in your own game. I have really enjoyed using them in mine. -Nobody