An example: in our Classic Traveller game the PC von Jerrel seduced the NPC Imperial Navy Commander Lady Askol, ranking officer of the naval base on the world of Novus. This took place during the course of a week of wining-and-dining which another PC (Vincenzo von Hallucida) was financing, so as to allow the PCs more time before an alien starship they were exploring, which had mysteriously appeared in orbit about Novus, was interdicted by the Navy. The actual reduction was resolved via a roll on the Reaction Table, with +1 for von Jerrel's Liaison-1. The player rolled double 6 - in the system a roll of 12 is unmodified and produce a genuinely and/or strongly friendly result. As the player narrated it, when von Jerrel and Lady Askol kissed it was the most perfect kiss the latter had experienced, and she swooned in his arms.
Thus she willingly joined him when he invited her to accompany him onto the alien vessel. And then was onboard when it jumped out of the system to another world, where the PCs were trying to locate the remnants of the ancient alien civilisation that had built it. During that exploration, von Jerrel was accused by another NPC - Toru von Taxiwan - of using psionics, which is a serious matter in the Imperium. When Lady Askol asked him whether the accusation was true (which it was), lamenting that if it was true then she would have to send him back to his homeworld of Ashar (this last itself being the result of a roll on the reaction-to-use-of-psionics table, modified by +1 for his Liasion-1 and +2 as a GM-stipulated modifier to reflect her affection for him) he denied it. The previous reaction roll stood (ie the natural 12 signifiying genuine and/or strong friendship), and so Lady Askol believed his denial. The upshot is that Lady Askol has declared a provisional "first contact" order in respect of the alien site, thus asserting Imperial authority to displace that of von Taxiwan, and placing von Jerrel in command as Imperial Overseer while she returns to her naval base on Novus to take further steps.
This romance has involved two checks so far: the initial seduction attempt, and the reaction-to-the-use-of-psionics check. But the mechanical outcomes have had ongoing effects. The strongly successful seduction result has underpinned Lady Askol accompanying von Jerrel onto the alien vessel, tolerating being unexpectedly taken to another world in it, and then believing his lie and acting on it. And the result of the psionic reaction roll framed the player's choice to have his PC lie to her, which means we now have a situation where von Jerrel's romance with Lady Askol rests on a fundamental deception.
These events have played out over four sessions. They haven't been the totality of those sessions by any means, although the problem with the psionics was very prominent in the final hour or so of our most recent session. When I read Vincent Baker talking about playing to find out what happens, or read Paul Czege saying that he likes to frame the character into the middle of conflicts I think will push and pull in ways that are interesting to me and to the player and to keep NPC personalities somewhat unfixed in my mind, allowing me to retroactively justify their behaviors in support of this, I think that what I've described in this post is an example of just that. I don't think it's as dramatic (either literarily or emotionally) as the sort of play they are aiming for - my group is solidly low-to-middle-brow melodrama at best - but in the process and the logic of play I think it is exactly what they're talking about.
I think the game would be much more boring for both me and the players if I had a description or a script for Lady Askol that dictated, in advance of the actual play and the actual action declarations, what she is like and how she will respond to things. Whatever that had been, I can't envisage how it would have ended up with von Jerrel stringing her along with a lie that had him appointed Imperial Overseer of a potential first contact site!
