[RPG] Is a hand free to use a Gloves of Missile Snaring reaction if you used a bow during your last turn

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I've DM'd a 5e campaign for about a year and a half (with a decent number of arguments being settled by these boards), and I have a Ranger who's a bit of a drop-in/drop-out player, who recently found a set of Gloves of Missile Snaring, which caused a bit of a debate among the group, as she primarily uses an Oathbow, and I'm trying to decide how the 2-handed property of a longbow or shortbow would function when it's not a player's turn.

The debate is whether or not a longbow (or shortbow) specifically counts as a 2-handed weapon while it's not a player's turn, thereby allowing the gloves effect to work as a reaction.

The Ranger is arguing that if we're looking at real-world examples, then once you fire an arrow, in the next 2-5 seconds, you would have a free hand, because you're not immediately grabbing another arrow and nocking it, then aiming at your target. Arguing further that Rangers can traditionally nock and fire an arrow, use their movement to climb a tree, then fire a second arrow with Extra Attack – of which climbing obviously takes a free hand to do, since they're not characters in Naruto.

Our Druid is arguing that because all the turns happen (essentially) simultaneously, she would have a free hand on her turn for the movement aspect, or to interact with an object; but as soon as she took her shot(s) and ended her turn, the rest of the round would be spent reaching for and nocking an arrow, then start aiming, so she would never technically have a "free hand".

My decision went to the Ranger, solely because of the Extra Attack feature, relating to timeline. If a character can fire more than one arrow per turn, then by default, that would mean that the character requires 2 hands to nock and fire the weapon; but does not require 2 hands to be in use outside of their turn, because they can nock and fire twice in the single turn. But the Druid wanted a community answer, so I come to you:

Does the 2-handed property of a longbow/shortbow apply to the act of firing the weapon, leaving one hand free for the rest of the round?

Or does it apply to the entirety of the round, thereby negating the ability to do anything but fire the bow (removing the option to climb/interact, as well)?

Or, can the turn involve using a free hand for more than just firing the bow, but the rest of the round outside that player's turn is spent with both hands engaged, preparing for the following round?

Best Answer

The description of Two-Handed on PHB 147 reads:

Two-Handed. This weapon requires two hands to use

The PHB Errata clarifies:

Two-Handed (p. 147). This property is relevant only when you attack with the weapon, not when you simply hold it.

Since the Gloves in question use a Reaction, and using the bow takes an Attack action, they wouldn't happen at the same time. That is, any time other than the Attack action is a valid time to do things while you are incidentally holding a bow in one hand, such as catching an arrow or quaffing a potion.