So, for a weapon like the Great Sword, would the minimum be 6 dmg? (3+3) on 2d6?

I'd guess this is meant to speed up gameplay by replacing the 1d6 rerolls with the average roll, rounded down. Except it wasn't that strong before, and now it's weaker. (And really bad if the weapon uses a d8 or higher.)

But I think rerolling damage dice can be fun, and even more fun if you let them keep rerolling on a 1 or 2. (i.e., I roll a 2, I reroll and get a 1, I reroll and get 5. That's cool.)

Technically minimum would be if you miss, and trigger Graze on Greatsword. Otherwise, min damage on a hit, would be 3+3+Str mod. Since you hit, attribute damage would still apply. As would any spell effects such as Hunter's Mark/Hex etc.

Quote from hermick >>

I'd guess this is meant to speed up gameplay by replacing the 1d6 rerolls with the average roll, rounded down. Except it wasn't that strong before, and now it's weaker. (And really bad if the weapon uses a d8 or higher.)

But I think rerolling damage dice can be fun, and even more fun if you let them keep rerolling on a 1 or 2. (i.e., I roll a 2, I reroll and get a 1, I reroll and get 5. That's cool.)

 This gets better, the more dice you're rolling though. For example, if you were attacking with a Flametongue Greatsword, and had Hunter's mark active, you're rolling 5d6 each attack and this fighting style means you get at least 3 dmg on each of those 5 dice, 10 dice if you crit, that's a minimum of 30+str on a crit.  This significantly impacts your minimum damage rolls, and is WAY better than the 2014 version which ONLY let you re-roll 1-2's, AND you only got 1 re-roll and use whatever result you got, even if it was 1-2. 

If you use a double-bladed scimitar, the minimum is 6, and if you use a bonus action and made another attack, add 3. That is a MINIMUM 9 damage!

As a level 8 Dwarf Rune Knight with the soldier background, i have taken the feats; savage attacker, Great Weapon fighting, Great Weapon Master (2014 rules) and Charger.

Provided both my attacks hit;

I use my bonus action for Giant's might, growing my dwarf to a Large Size. I use a maul 2d6+4, my fire rune 2d6 and +10 great weapon master on my first turn. 4d6+3+10, minimum of 25 damage, and be pushed back 10 feet if I've charged at them from 10feet away, then they have to make a strength saving throw DC15 or be restrained in fiery shackles, and make a Constitution saving throw DC15 from my maul's topple effect, or be knocked prone.

Second attack, with advantage if retrained and/or prone, with my maul 2d6 + 4, my fire rune 2d6 my giant's might 1d6 and my charger 1d8 as I've ran at them after they were pushed back 10 feet and +10 great weapon master... a total of 5d6+3 and 1d8 +10 on one attack. Minimum of 31 damage and make they saving throws again.

A minimum of 56 damage in one turn, and potentially have 2 targets prone and/or retained, while I get to roll damage twice on one attack per turn from Savage Attacker without any magical items.