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Obligation is not "rolled" - it doesn't "trigger" at any point.
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Obligation imposes an automatic, individual Strain Threshold penalty on each character, reducing the threshold by 1 for every 5 points of Obligation after the first 5 (so 10 Obligation imposes a penalty of 1, 15 imposes 2, 20 imposes 3, and so on). Edit: Realised it wasn't clear that this is based off each character's individual Obligation, so that each PC has a unique penalty depending on how much Obligation they've taken.
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Each Obligation (or possibly each PC's total Obligation, TBC) increases automatically by 1 at the end of each session, unless something has been done to address that Obligation during the session. Narrative reasons can be come up with to explain why this is for each Obligation (e.g. mounting pressure to pay back a debt, addiction/obsession becoming more prominent, etc.)
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Although no roll is made, the GM should present regular opportunities for each PC to address their Obligation. In addition, players interested in doing so should make suggestions to the GM as to how they might go about it.
Lack of clarity