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It's like Jack is watching the world longest tennis match, and his favorite lovestruck idiots are lobbing a bouncing ball of unresolved sexual tension back and forth.
The Doctor grins from one big ear to the other, being all impressive and she looks at him like he's hung the moon.
Advantage: Doctor.
She saves his arse yet again, does something brilliant and he looks at her like he's not sure whether to congratulate her for a job well done or shag her rotten on the jumpseat.
Advantage: Rose.
He gives her that look. Jack knows his own knees would go weak if the Doctor ever turned that look his way, so he's just a bit jealous that it's all for Rose. Of course the prat doesn't follow it up with any action but she still looks hopeful.
Advantage: Doctor.
Jack's noticed that ball bounces back and forth with greater speed now, and he senses a winner might be declared in this match, possibly soon.
Tonight when Rose makes her entrance in a short red halter dress and heels, Jack sees the Doctor's eyes widen, then darken with want. He doesn't make a joke to distract her. He merely takes her hand, and his eyes don't leave hers.
Jack thinks he'll make himself scarce tonight. He hopes it's game, set, match.
The advantage is definitely Rose's.