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!