Are opportunity attacks considered my turn?

Question

In Volo's Guide to Monsters the playable Bugbear has an attribute called Long-Limbed which reads

When you make a melee attack on your turn, your reach for it is 5 feet greater than normal.

The Reach property of weapons notes that

This weapon adds 5 feet to your reach when you attack with it, as well as when determining your reach for opportunity attacks with it.

This gave me the idea to play a bugbear fighter that uses polearms for an effective reach of 15 feet.

Now let's say, I have the Polearm Master feat and someone walks within 15 feet of me. Do I get an opportunity attack because my reach is 15 feet with Long-Limbed and a reach weapon? Or do I have to wait until they reach 10 feet as Long-Limbed states it is attacks on my turn that I gain the extra 5 feet?

Answer 1

The wording of "Long-Limbed" as you state is clear (emphasis added):

When you make a melee attack on your turn

Let us have a closer look at opportunity attacks (PHB p73, emphasis added):

You can make an opportunity attack when a hostile creature that you can see moves out of your reach. To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature. The attack occurs right before the creature leaves your reach.

...

You also don’t provoke an opportunity attack when you teleport or when someone or something moves you without using your movement, action, or reaction.

The polearm mastery feat extends the OA condition (emphasis added):

While you are wielding a glaive, halberd, pike, or quarterstaff, other creatures provoke an opportunity attack from you when they enter your reach.

Three things are important here: 1. What are the conditions for OA and 2. when are they executed.

1. OA depend on whether an enemy leaves or enters (due to Polearm Master) your reach.

2. The attack is executed during the movement phase of the enemy, so clearly during their turn and turns are not overlapping.

3. Forced movement like shoving does not trigger OA, even it the enemy is leaving or entering your reach. Forced movement by dominate or similar does indeed trigger OA, as that uses their movement.

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Condensed answer: Your reach during an opportunity attack is 10 feet due to the reach property of your weapon. Your OA can be executed when an enemy is -on its own- about to leave or enter but not move within your reach. During your own turn, your reach for a melee attack is 15 feet.

Answer 2

You ask a number of sub-questions:

1. Are opportunity attacks considered "on my turn"?

(I've edited the question slightly to be more meaningful)

Opportunity Attacks PHB p.195

To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature.

You also don’t provoke an opportunity attack when you teleport or when someone or something moves you without using your movement, action, or reaction.

Reactions PHB p.190

Certain special abilities, spells, and situations allow you to take a special action called a reaction. A reaction is an instant response to a trigger of some kind, which can occur on your turn or on someone else’s.

Answer: They are not considered on your turn unless the opportunity attack occurs on your turn.

Note: the only way a creature can provoke an opportunity attack on your turn is to use its reaction to move, as its movement, action and bonus action are not available outside its own turn. It's not something that is likely to happen often. Also it is common that the abilities that allow movement on a reaction specifically state they don't provoke opportunity attacks (e.g. Relentless Avenger PHB p.88) or are teleportation based (e.g. Misty Escape PHB p.109).

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2. Do I get an opportunity attack using the Polearm Mastery feat when a creature enters 15' range because my reach is 15' with Long-Limbed and a reach weapon?

(question edited to be more meaningful)

Long-Limbed VGM p.119

When you make a melee attack on your turn, your reach for it is 5 feet greater than normal.

Answer: No you don't. Your reach is not 15' until you make an attack.

The ability states you get +5' reach "When you make a melee attack". The order of events is: a creature provokes the opportunity attack, then you take the attack. Therefore the condition is not met until you are already attacking them, at which point it makes no difference.

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3. Or do I have to wait until they reach 10 feet as Long-Limbed states it is attacks on my turn that I gain the extra 5 feet?

Answer: it is not because it is not your turn, it is because you haven't made a melee attack until after the opportunity attack has been provoked already.

Answer 3

Opportunity Attacks are reactions, and reactions can be taken on your turn or on someone else's turn. Reactions are triggered actions, and Opportunity Attacks are triggered when an enemy leaves your reach.

In normal circumstances, your reach is 5'. With a polearm and Polearm Master, it is 10'. When you add Long Limbed, it becomes 15' but only when you attack.

Your reach is only 15' when you attack on your turn. This means you can't benefit from combining Polearm Master and Long Limbed on an opportunity attack to reach 15'.

When an enemy leaves your reach, you can make an opportunity attack. If this happens on your turn, your reach for your attack becomes 15', however the opportunity attack won't be triggered when the enemy leaves 15' from you, it will be triggered when the enemy leaves 10' from you, because it is the attack that increases the reach. Your reach, for purposes of determining whether an Opportunity Attack occurs, is still only 10' (from Polearm Master).