Rolling Damage: 1d6, 1d6+1, 1d6-1, and 2d6 retain the highest

I was thinking about OD&D style damage, and was wondering how the differences between various rolling techniques work out. Specifically, I'm wondering about these:

STRAIGHT DAMAGE: 1d6

HIGH DAMAGE: 1d6+1, 2d6 retain the highest, 1d8

LOW DAMAGE: 1d6-1, 2d6 retain the lowest, 1d4

This post will work out the odds for each case.

STRAIGHT DAMAGE: 1d6
Avg 3.5/Max 6/Min 1
All results are equally likely (17%)

HIGH DAMAGE: 1d6+1
Avg 4.5/Max 7/Min 2
All results are equally likely (17%)

HIGH DAMAGE: 1d8
Avg 4.5/Max 8/Min 1
All results are equally likely (12%). Higher variability than 1d6+1.

HIGH DAMAGE: 2d6 retain the highest; double sixes counts as a 7
Avg 4.5/Max 6/Min 1
1 (3%), 2 (8.33%), 3 (15%), 4 (20%), 5 (25%), 6 (28%), 7 (2.78%)
The distribution is skewed towards higher numbers, i.e., it is the least variable and most "reliable." With 1d6+1, there's a 50% chance that you'll get 4 or fewer points of damage. But with this method, the chance of getting <5 style="font-weight: bold;">ANALYSIS: There are really, fundamentally, only four different "offensive stances" one can assume based on weapons: 2H, 1H + Shield, Dual Wielding, and 1H + Open hand. Using our different damage mechanisms can give each of these a different flavor.

• Two handed weapon: 1d6+1 or 1d6+2. Variable damage.
  
• Dual-wielding two weapons: Roll 2d6, retain the highest. A little less average damage than a two-hander but more reliable. Also, people will "get" rolling 2d6 and taking the highest (it "makes sense"). This is a classic fantasy style for rogues and their ilk, plus, its badass for a fighter to rage away with a sword and flaming torch.
  
• Sword & Shield: 1d6 + Block a hit 1x/encounter + superior total defense option
• One handed weapon + open hand: This one is tough. People used shields and polearms because they were better than keeping a hand open. You can either rigorously enforce rules about drawing equipment and such to make that free hand valuable, or you can give this "stance" a unique bonus of its own to make it a viable choice. I like the idea of giving this style some sort of "Fate" bonus so that swashbucklers with their rapier in one hand can attempt more feats of derring-do. The trick is to keep it from being exploitable -- you don't want the swashbuckler to be able to leap from the chandelier (use his fate point) then whip out a dagger and just start dual-wielding to gain the damage bonus now that he's used his fate wad.
  Perhaps a weapon used one-handed scores more critical hits? This is somewhat historically accurate -- some schools of fighting did promote searching for weak spots in armor as a way to defeat that armor. The trick is to make the math work out so that its perhaps +1 or +2 damage compared to a straight D6 damage roll to keep it comparable with TWF/2HF. You also have to be careful of layering this rule with anything else that makes crits better (like, oh, a battleaxe that has particularly hard crits). If a crit does max damage (basically +2.5 damage) then having a one-handed weapon crit on about every second or third hit would make sense. So, you could expand the crit range to from just 20s to 18-20 on a D20, or any "6" on a D6. This is still slightly less damage than a 2HF or TWF strategy but you do get the versatility of leaving that extra hand open.

ADDENDUM: Why not, instead of more frequent crits, have more effective crits? For example, when you crit using just a 1H weapon, it also imposes some sort of negative status condition, or gives you a free move, etc. That way you don't have the problem with stacking the battle axe on top.

If monster HP are kept in control, then all the options are pretty viable. If monster HP escalate too much, and you're including all sorts of bonus damage sources, then two handed weapons and dual-wielding start to pale because that +1 HP damage has declined from being a 33% boost in damage output to being much less significant.