I've read the Basic D&D rules and Module B2 Keep on the Borderlands. I forgot how deadly the game is at first level and even at third level the Caves of Chaos is very dangerous if you barrel into a cave.

I'm thinking of adding a limited bit of Luck. PCs start with 3 points of Luck and get another point per level. Luck can be used for re-rolling most any roll, for example:

1. character generation ability score
2. character hit points
3. for a magic user if they don't like their free spell they can spend a luck point and choose
4. an attack roll, either PC, monster, or hazard
5. a damage roll, either PC, monster, or hazard
6. re-roll a random encounter (either the roll for encounter or roll for what they encounter)

There will also be a group pool that gets 1 point of Luck per session which any PC can use.

Luck accumulates until used so the group pool may get large.