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When do you choose to add stratagems out of your sideboard? When declaring characters or when sideboarding battlecards?
Stratagems are played concurrently with the starting team for a game. This is required otherwise cards like Master Converter and Aerial Enhancements would not effect the starting team, leading Windsweeper to be sad when Blitzwing and Tracks don't count as Planes.
Source: Aequitas Rules Roundup 2021-01-03