I have always been bothered by the fact that LA Harm Ranges are very off-

Let me explain - If I am using a 2 Handed Sword my Harm range is 11-20 so- I am likely to do minimum harm much more often than I am going to do any Harm above it.

This dosen't fit or sit well with me.

I want to make a change in this regard without re-writing the entire LA combat system.

One way I think would work is to include AP or Armor Piercing Value. Now I need to alter the general Dice convention to fit a little better.

I want to maintain the general balance of the game and the intent of the author- so I want to maintain the exploding die for damage.

This is still in the Brain storm realm so bear with me. I realize that Gary wanted it to be 1/2 die for the exploding die but this will work as well.

Sword Cleaving , Heavy (Flamberg or Zwehander (sp) ) harm 4d6 (Re-rolling any d6 that comes up a 6) AP of 6 ( so against an armored opponent the 2 handed sword will do a minimum of 10points Harm.
Dagger Long Harm 2d10 AP1 (re-rolling 10's on d10)

Anyone good with math out there give me an Idea of what the chances are of rolloing a d6 and getting a 6 - so I can see what kind of harm range I'd get if it switched to multiple small dice rather than the single d20?

I ignore all of the extra damage rules, but I think the approach you need to take is to decide one chance do you want for there to be max damage.

The chance of rolling a 6 on a 6 sided die is that same as any other 1/6 or 16.67%. If you used a 10 sided die it would be 10%. Then you need to factor in multiple die and how that affects things. If you used 4d6 then the chance of just one 6 would be 66%.

Do you want this to differ depending on the weapon? If you do not use the same number of dice for each weapon, then the chances are going to be off. If you use a minimum damage and ignore the rest, then you end up with the same problem you have right now.

I am not following the AP thing. I guess that is just a way to get a minimum without extending the maximum.

Just a thought, but maybe go 3d6+2 for everything. This gives you 5-20 for all weapons. You can still use the AP to get higher minimum if you want.

My original scheme would be sort of like this

Small weapons deal d20 Harm (Note d20 harm weapons pick up a d10 when getting maximum harm)
Medium 2d10
Large (large weapons) 3d8 to 4d6 depending - so that some weapons deal more or less base harm than others.

example

Dagger Harm base 1d20 Ap (Armor Piercing 1)
Heavy Cleaving Sword 5d6 AP 6

The ore issue is that the 1d20 with minimum harm works well when comparing to other weapons.
but when comparing it to itself it sucks.

A consequence of this is that people are going to prefer heavy weapons. Not only is the minimal damage right, but so is the max. To top it off, you have have a far greater chance of increased damage. 6/6 is 16.7%, but a 20/20 is 5%. Add in multiple dies and the odds go up even greater.

I think what you are doing posses an interesting reasoning problem. If the intent is to do the most damage, is it better to pick something that has a higher minimum damage and higher max, if the extra damage is less than using another weapon?

Not sure if you actually meant 5d6. If so, then certainly I would abandon to the dagger. So I will stick with 4d6.

4d6 gives 4-24 damage. I have a 66% chance of getting at least one 6 and a 5.6% chance of getting 2 6's.
1d20 gives 1-20. I have a 5% chance of getting 20.

If we keep the odds the same (5%) and go with the minimal base damage, then you have 14+2d6 or 16-26 points of damage. If we go for max damage, then it would be 26+2d6 or 28-38. The D20 would be 20+1d10 or 21-30.

Overall, I think this system prefers heavy weapons. The damage will average out in the middle so around 12 points of damage. But, with a large chance of getting at least one more roll of a d6, it works out well. I, personally, would prefer a higher constant damage over wide variation even if the variation leads to the occasional hit of a huge amount of damage.

Anyway, that is just me. I think I prefer to maximizes the minimum than be more of a gambler. 50% chance of 10 or less isn't worth it for a .5% chance (1/20*1/10) of doing 30 damage.

Not to dissuade you. Personally I have just given weapon different die rolls to generate a range up to 20, but with different probabilities and different minimum damage. I have a two-handed sword doing 1d10+10, a short sword doing 2d10, a dagger doing 1d20, flail doing 2d8+4, etc.

How about 1d10+10 instead of the minimum damage thing? You have an increased chance of exploding damage...

Or you could completely change damages to go in-line with a game like HackMaster which has a lot of exploding damage.