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Scenario: An archer has two targets, both of which are at long range (i.e more than 80 feet and less than 320 feet for a shortbow). One of these targets is invisible. Is it correct that the archer has the same chance of hitting despite the fact that one target is invisible?

PHB Ranged Attacks

Some Ranged Attacks, such as those made with a Longbow or a Shortbow, have two ranges. The smaller number is the normal range, and the larger number is the long range. Your Attack roll has disadvantage when your target is beyond normal range, and you can’t atta⁠ck a target beyond the long range.

PHB Unseen Attackers and Targets

Combatants often try to escape their foes’ notice by Hiding, casting the Invisibility spell, or lurking in darkne⁠ss.

When you Attack a target that you can’t see, you have disadvantage on the at⁠tack roll. This is true whether you’re guessing the target’s location or you’re targeting a creature you can hear but not see. If the target isn’t in the location you targeted, you automatically miss, but the DM typically just says that the att⁠ack missed, not whether you guessed the target’s location correctly.

Assuming there are no other cover modifiers, as disadvantage doesn't stack (no such thing as double-disadvantage) does this mean that a shot at each target is made with disadvantage despite the fact that one is invisible and one's not? And so each shot has the same chance of hitting?

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The attack roll is the same either way

You are correct that both of these cases would roll to attack the target at disadvantage. The section on unseen attackers and targets states (emphasis mine):

Combatants often try to escape their foes' notice by hiding, casting the invisibility spell, or lurking in darkness.

When you attack a target that you can't see, you have disadvantage on the attack roll. This is true whether you're guessing the target's location or you're targeting a creature you can hear but not see. If the target isn't in the location you targeted, you automatically miss, but the DM typically just says that the attack missed, not whether you guessed the target's location correctly.

If you know the location of the invisible target, you have the same (disadvantaged) odds to hit them as you do any other target at long range.

The difference with an invisible target is that you may be shooting at the wrong location, in which case your attack will miss but the DM will not tell you whether it was the attack roll that missed or if the creature was just not in that spot.

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