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There are three types of patrol route for a guard to follow-
A stationary guard either does not move their field of view (FOV), which is the most likely cause of boredom - or they rotate their FOV by looking down different direction over time, which is slightly less likely to cause boredom.
There are a starting and ending point for this route along which the guard travels. When reaching the end point, the travel back along the same route.
A circular route is a loop that is only ever travelled in one direction by a guard.
Whenever a Check time is reached, roll the guards Boredom Tolerance number of dice. If you achieve at least one success (ie the die is equal or higher than the Boredom) the guard is not bored.
Guards that have not yet been seen by any thief need not roll for Boredom.
Any guard patrol route that is not on the table should be represented on the Owner's map. Each turn's waypoint (where the guard will be or will be facing) should be marked.