

TWF also wastes less damage when finishing off enemies that only a bit of HP left. The GWF fighter has the advantage when it comes to Action Surge and opportunity attacks, but assuming the TWF fighter focused on DEX, they're going to have better initiative, DEX saves, Acrobatics, and make better use of ranged weapons. (This gap is smaller for 1d12 weapon users: 3.83 - Mod.) So with an ability modifier of 3 to 5, that leaves a difference per round of 0.83 to 2.83. Subtracting the TWF damage from the GWF damage leaves 5.83 - Mod.The TWF fighter is going to be doing 3 * (3.5 + Mod), or 10.5 + 3 * Mod.The GWF fighter is going to be doing 2 * (8.66 + Mod), or 16.33 + 2 * Mod.I'm going to assume each have picked the Fighting Style appropriate for their weapons and have equal ability modifier for weapon attacks. GWF Fighting Style is really weak. It only increases the average damage of your hits by at most 1.33. Let's compare two fighters, one with a greatsword and one with two scimitars, at levels 5-10 (because 1-4 inherently favor TWF). Because of his traits, he can do that even though the Saber isn't Light, and he adds his ability modifier on the damage of that bonus attack as well.

Putting all those together, your group's fighter, at level 5, can take an attack action for two attacks with his main weapon, then, if he so desires, can use his Bonus Action to make an additional attack with his off-hand. The condition for two-weapon fighting is to take the Attack Action, regardless of how many attacks that allows you, and enables you to use a Bonus Action for that added benefit. When you take the Attack action, you can make two attacks. The Extra Attack feature doesn't really conflict with any of the above. You still need to hold one-handed weapons, but they can lack the light property, such as wielding a longsword and a shortsword, or two longswords. The Dual Wielder removes the restriction that requires your weapons to be light (among other things). The Two weapon fighting style, now, removes the restriction about not adding your modifier on the damage of your bonus attack. So far so good? If you use the Attack action with a one-handed, light weapon, you can use a bonus action to make an additional attack with another one-handed, light weapon. The conditions for this bonus action can be abbreviated as: "both 1-handed weapons you wield must be light". You don't add your ability modifier in that bonus attack (you do consider penalties, however). Two weapon fighting, the rule, says that whenever you satisfy some conditions, you can take a Bonus action for an attack with your off-hand weapon. Let's see all the effects one step at a time. Monstrous Compendium Vol 3: Minecraft Creatures
