I need a good, solid mechanic for extended contests in GUMSHOE. An ideal one would work for a wide variety of situations, such as chases and cat-and-mouse games.
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I would treat them like combats. That mechanism is there already, so it's worth using it, if we can. Give both parties a pool like Health, but specific to the contest.
For example, for a psychic duel, use Stability instead of Health. We attack exactly as in the rules (using, perhaps, Magic to attack instead of Scuffling), but take damage from Stability.
For chases and cat-and-mouse games, I'd vary it slightly: instead of a pool for each person, I'd have one between the two. One person adds to it, the other depletes it.
For example, for a car chase, we'd have a Distance pool. It starts at 10. Let's say you're chasing me: you're in a car, I'm on foot.
When you "attack" successfully (using your Driving skill), you roll 1d6 and subtract it from Distance. When I "attack" successfully (using either Athletics or Fleeing), I add to the pool.
If the pool gets to zero, you catch me. If its gets to twice its original value, I get away.
Well, there is an extended contest mechanic already. Each participant takes it in turns to use appropriates skills (eg Driving vs Athletics with a migo chasing a car) against a Difficulty, usually 4. Both sides can spend points before the roll as usual. This continues until one sides fails.
Robin Laws just came out with a rule for Bid Contests that might work quite nicely.