In LBB original D&D, all weapons do d6 damage. This seems to upset a lot of players who grew up with variable weapon damage. I've been satisfied enough with the "you'll be just as dead if I slit your throat with a dagger or a long sword" rationale that I've stuck with d6 damage in my Stonehell white box game.
However, I recently got pulled into another discussion on the matter, which mentioned a couple of popular d6 damage variants. These variants concern themselves with differentiating short/light weapons (daggers, darts, slings) from normal weapons (swords, spears, maces) from long/heavy weapons (two-handed swords, polearms, lances).
The first method is to roll d6 -1 for light weapons, d6 for normal weapons, and d6 +1 for heavy weapons.
The second method is to roll 2d6 and use the lesser roll for light weapons, roll 1d6 for normal weapons, and for heavy weapons to take the higher of two d6 rolls.
I wondered what sort of damage these methods would yield, so (since I don't really understand more than the most basic dice math) I wrote a little script to do some test rolls.
The mean average is easy enough to figure out. The mean of a d6 roll is 3.5, so d6 +/-1 will give a mean of 2.5 and 4.5. No surprise there, but it's reassuring to see the results I expected (within three-hundredths of a point over 100,000 rolls).
The median is somewhat more interesting. The median of 1d6 will of course be 3 or 4. The median of 2d6-take-the-highest is 5. The median of 2d6-take-the-lowest is 2.
The mode of 1d6 can be anything. The mode of 2d6-take-the-higher is 6. The mode of 2d6-take-the-lower is 1.
If I was a fighter with a two-handed sword, I'd be lobbying for the 2d6 method. It certainly proves more differentiation between the weapons types than the +/-1 method.