Monday, December 28, 2015

Schrodinger's Lock in Lamentations of the Flame Princess / B/X

For this example, we are playing Lamentations of the Flame Princess (LotFP), though the analysis wouldn't be any different if we were discussing B/X.

The party arrives at the entrance to the dungeon, barred by a locked, wooden door (have we already hit poor adventure design?). Ichabod Salsby, a level 3 specialist, with 1 point assigned to tinker, attempts to pick the lock and fails (rolling a 6 on a 6-sided die).

Under our system, Ichabod may not try to pick the lock again until he reaches the next level. Also, Ichabod's chance to pick the lock was not based on any feature of the lock - he has a 2-in-6 chance to pick any lock in one turn.

Let us construct a model that explains these features. In our fantasy world:
  1. There are a finite number of lock types. Every lock in the world belongs to exactly one of these types, which are all equally probable to occur.
  2. For each lock type, either Ichabod can or cannot pick that lock type - success or failure is automatic depending on type. His tinker skill is a reflection of the number of lock types that he has mastered.
  3. The type of a lock must be determined by a picking attempt. It is not decided by the Judge in advance.
Under this model, prior to Ichabod's attempt, the lock is of indeterminate type. Following the old Schrodinger saw, the lock is of every type simultaneously, until Ichabod's action partially collapses the state of the lock relative to the partition of Ichabod's tinker skill (i.e. the exact lock type is not determined, but only whether the lock is of a type Ichabod can pick, or not).

There are two stubborn facts that contradict this model. First, if Ichabod increases in level but doesn't assign any new skill points to tinker, than why should he be allowed another chance to pick the lock? Ichabod has mastered no additional lock types. Ichabod failed to pick the lock previously because he is unable to pick that lock type, and since he has mastered no additional lock types in his advancement it logically follows that he cannot succeed with another attempt.

Second, allowing Ichabod an independent chance to try a failed lock again after reaching the next level doesn't reflect the true conditional probability of the event. Assuming Ichabod reaches level 4 and places one more point in tinker, his probability of picking the previous lock is now 1-in-4, rather than 3-in-6. The first problem described above is really a special case of this second problem with the model (Ichabod's retry probability would be 0-in-4 rather than 2-in-6 in that case, resulting in automatic failure).

For these problems, I argue that while the model does not perfectly match the mechanics, we have instead a best approximation - to expand the game mechanics to fully match the model would require an unreasonable increase in cost (detail and complexity). The DM would need to track the results of any failed pick attempts and character tinker skill levels over time. The current mechanics match 80% of the model with 20% of the complexity - success.

On the positive side of the ledger, this model explains why:
  • A character may only try to pick a lock once
  • A character may try to pick the lock again after reaching a new level
  • A character with a higher skill may fail, but a character with a lower skill may succeed
  • The chances of picking a lock do not increase with additional time or resources
Part of the reason this combination of model and mechanics works so well in LotFP is because of other mechanics. Lock picking is an improved method of entry (noise, surprise, etc.), but only rarely is it the only method of entry. The characters can always smash the door open with enough time and the right tools. LotFP is very clever in guaranteeing success with a more primitive method, ensuring that no dungeon branch is off-limits due to a bad die roll.