Each house (both player and non-player) has 9 Power Tokens. These tokens represent different things based on where they are placed and who owns them:

Any Power Token on the Map of Westeros represents military strength for the house that controls it (see Battling). For instance, a Lannister Power Token in Casterly Rock represents one military strength.

When on the Force Track of your House Mat, these represent military units that you may pay gold to Recruit (see Action: Recruit).

When non-player Power Tokens are in the Ally Pool of your House Mat, they represent leverage that you have gained over that house through Plots (see p13) or from resolving a battle (see Action: Plot). Whichever player has the most Power Tokens of a specific non-player house in their Ally Pool controls that house (see Alliances).

When they are of a non-player house and are on their own House Mat, they are undesignated and can be taken and used for either purpose (to boost a player ally’s troops or to build leverage over the non-player house).