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I didn't write that formula, but it does make sense to me. To explain: R is the roll N is what is passed in (3) in this case. It says if the result of the roll (d6) is less than 3 (meaning 1 or 2) then roll d6 and return that. If the original roll wasn't 1 or 2 then use the original roll which...

Yes it will. It will average 3.5 as normal as stated above.

I used anydice and calculated it for you. See http://anydice.com/program/6d9e (it only rerolls once). 1d6 is indeed worth 4.17 as I said. On GWF's worth: It is between a 7-18% DPR boost over Defensive style depending on class, level, etc (scales from higher to lower).

No, it wouldn't help Fighter, Barbarian, or Paladin really at all. Ranger would be helped every so slightly with a higher Hunter's Mark damage. No where near enough to compete. It would also heavily boost Hand Crossbow vs Heavy Crossbow/Longbow.

That wouldn't really different from extra attack, would it? You could also take the 3rd option from the level 3 Hunter which allows hitting a second target within 5 ft of the target.

Agreed on the errata - it's part of the CR! I haven't worked out an alternative to volley/whirlwind. I use rend for twf so I don't think I'd use it here. I debated adding a 3rd attack, but I think that may have been too much. I forget. One option is to move the capstone to 11. If that applied...

Ranger has fine DPR until 11 due to 2 attacks, collosus slayer, and hex. I haven't bothered with beast master, though badger is not a good option after the errata. The problem is 11+. Volley and whirlwind are trash. Volleyball has to hit 4 enemies to do more than normal DPR. More for hand...

I found the ranger to be the lowest melee DPR. Hunter's Mark taking a bonus action makes it compete with the offhand. I need to reexamine if that should be removed, but it'll likely just buff hand crossbow too much. What houserules due you use for rapier? I wish 1 handed had a fighting style...

It doesn't need GWM or Polearm to feel inferior. In comparison to a Battle Master TWF Fighter: Monk does similar DPR, but stuns and scales to more defensive. S&B Fighter does similar DPR and has more AC. S&B Paladin has more DPR, has lay on hands, and more AC. Rogue has similar DPR, but brings...

I'm not trying to win an argument. I'm trying to clarify TWF's situation. You have muddied the waters. My only intention is to clarify the math. The situation is the same as it was pages ago: 1-3 TWF is ok. 4+ TWF is decent, but not great if you allow feats 11+ TWF is not good. If feats are...

It's not difficult. First you calculate the total chance to crit (typically 5, 9.75, 14.26, 18.55, etc). You then add in the chance to kill a creature. To calculate the chance to kill a creature you compare your total DPR (besides the cleave part) to the average HP for that CR. For example the...

I don't know what theory you are speaking of. That TWF is somehow more "versatile"? It simply isn't. It has 1 more attack than GWM, sure, but not in comparison to Polearm. Again, my model is unconcerned with min-maxing and I do not assume Vumans. Nor do I allow them. 1-3 assumes no feats. GWM...

Every statistical distrubtion shows that TWF loses. Now if you're trying to make an argument for Overkill being a thing for GWM then there is some argument. However Polearm trumps this as it has more attacks than TWF.

A d6 averages 3.5. So if you have to reroll a 1 the new options are 1,2,3,4,5,6 which averages 3.5 which is exactly what I put above "=AVERAGE(3.5,3.5,3,4,5,6)" The numbers you just outlined assumes half the time you roll a 1 and half the time you roll a 2.5 (for the d4 example)- that's entirely...

Note: I'm not really too interested in optimizing, just understanding the baseline. Though TWF loses in both categories. Some of your math isn't correct. 2d6 with GWF is 8.33. It's AVERAGE(3.5,3.5,3,4,5,6)*2 in excel/google docs. 1d10 with GWF is 6.3. AVERAGE(5.5,5.5,3,4,5,6,7,8,9,10) TWF...

TWF is only viable in the bottom tier (1-3). People, including myself, have shown the math of that here. Polearm is much better than TWF. So is GWM.

I suggested them above. Either render or second bonus attack as part of dual wielded that kicks in at 11. If you use -5/+10 then I suggest you allow a twf version with the other half being +1 dex perhaps.

Some choose to give half proficiency bonus on non proficient saves. Though it's no different than casters currently with str throws. That's just how saving throws work and have largely worked since 3e.

The choice of how to change the game is up to you, but that choice isn't really relevant to the discussion of balance of saving throws as that discussion largely revolves around RAW and RAI.

That is not really what saves as for. See what I quoted above PHB 179. By RAW those are all investigation checks. Phantasmal Force is the only one that I know of that has a save.