This all seems quite coherent to me: you are using your prep to generate responses to action declarations along the lines of what do we see? or what results do we get from the forensics lab? or we search the Princess's wardrobe and also to feed into scene-framing and some aspects of social resolution, such as We accuse the Princess!I can't just decide "nope, different perp, just 'cause I feel like it." Even if the reason I feel like it is because the players have come up with a really really cool theory, I have to actually do the work of justifying that theory. Otherwise, I'm pulling the wool over my players' eyes; I'm making them believe that there is a real, durable, understandable, predictable world, when there isn't one, there's just "stuff I said before" and "stuff I'm saying now," and the stuff I said before is literally 100% completely malleable if it sounds better for what I'm saying now.
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by preparing, I have more to leverage. I can improvise, but I find that I only have a finite amount of improv in me before I have to tap out.
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My reason for adhering to prep is that I want my players to know that the world is (in some sense) real, durable, predictable. That they can always attempt to validly reason from the information they have.
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If I switch up the killer solely because the players had a good idea, then one of two things happened. The first, as previously discussed, is that I screwed up really badly (and that isn't impossible! My players totally have outsmarted me, more than once!) The second is that I'm now changing what stuff is in the world, but in a way that the players should never be able to determine even in principle, because while last week they would have been wrong to accuse the Princess, this week they're now correct, but nothing about the things they found has changed in any way. The past events have changed, but literally all the evidence available to them has not.
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this is one of the reasons why I try to avoid over-prepping as much as possible. If I haven't got prepped evidence to examine, then it literally cannot be the case that I am giving them evidence that doesn't "work." The players and I are discovering, together, what evidence "works." When I do prep evidence in advance, as I did for this murder mystery, I put a great deal of effort into ensuring that, though it may be a challenge, it should be possible to piece together the truth, just like a good mystery novel.
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I don't want my game to ever be the tabletop equivalent of a bogus mystery novel, so I either avoid unnecessary prep (so that I'm learning the truth right alongside my players), or very thoroughly review my prep to make sure it "works."
In basic structure this seems similar to the "whodunnit" I described upthread, though I am guessing more elaborate than mine!
The one bit I wasn't fully clear about was when you toggle between (i) prepping and relying on prep, and (ii) discovering and learning along with the players. How do the players know you've switched gears from (i) to (ii)?