Wizkids Rules!

Dark Phoenix: Malevolent Global Ability reads:

Global: Pay bolt and KO one of your character dice. The next die you purchase this turn costs 2 less (to a minimum of 1).

Apocalypse: Wicked Supremacist Global Ability reads:

Global: Pay bolt. Once per turn, KO one of your character dice, and the next die you purchase this turn costs 2 less (to a minimum of 1).

Is making a purchase a requirement to use these global abilities, meaning it could only be used during your main step?

No. You can pay for these Global abilities in your Attack Step or during your opponent’s turn in the applicable global window. Refer to ruling below.

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