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At the end of a Dark Eldar turn, a single Space Marine intercessor is left alive. He has a unit of 5 wyches on one side and a succubus on the other. A wych is in base contact whilst the succubus is one millimetre away.

If the intercessor does not move on his turn, is allowed to shoot the succubus with his pistol in his shooting phase? Or is she protected by Look Out Sir (Look Out Ma'am?) despite her being right next to him?

If that Character unit is both visible to the firing model and it is the closest enemy unit to the firing model, it can be targeted normally. Actual quote from the look out sir rule. If the succubus is 1mm away (and within 3" of the wyches), and the wyches are in base contact, the succubus isnt the closest enemy unit.

If both would be in base contact, could you pick similar to smite?

MEASURING DISTANCES
Distances are measured in inches (") between the closest points of the bases of the models you’re measuring to and from. If a model does not have a base, such as is the case with many vehicles, measure to the closest point of any part of that model; this is called measuring to the model’s hull. You can measure distances whenever you wish.

If a rule refers to the closest unit or model, and two or more are equidistant, then the player who is controlling the unit that is using the rule in question selects which unit is the closest for the purposes of resolving that rule.

 Bilge Rat wrote:
At the end of a Dark Eldar turn, a single Space Marine intercessor is left alive. He has a unit of 5 wyches on one side and a succubus on the other. A wych is in base contact whilst the succubus is one millimetre away.

If the intercessor does not move on his turn, is allowed to shoot the succubus with his pistol in his shooting phase? Or is she protected by Look Out Sir (Look Out Ma'am?) despite her being right next to him?

You cannot target the succubus with shooting attacks. You can only target the character if it is the closes enemy unit, which it would not be due to the presence of a closer unit of 5 wyches which are within 3" of the character.

Yeah, that is what I thought. Seems silly, but I guess that how it is supposed to work. Thanks guys.