The 13th Year of Ruin: The Beginning
The escalation die represents a bonus to attacks as the fight goes on.
At the start of the second round, the GM sets the escalation die at 1. Each PC gains a bonus to attack rolls equal to the current value of the escalation die. Each round, the escalation die advance by +1, to a maximum of +6.
Monsters and NPCs do not add the escalation die bonus to their attacks. This does not effect a boss battle.
If the GM judges that the PCs are avoiding conflict rather than bringing the fight to the bad guys, the escalation die doesn’t advance. If combat virtually ceases, the escalation die resets to 0.