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Energy counters are a kind of counter that a player may have. They're not associated with any specific permanents.

Some spells and abilities that give you {E} may require targets. If each target chosen is an illegal target as that spell or ability tries to resolve, it won't resolve. You won't get any {E}.

Some triggered abilities that state that you "may pay" a certain amount of {E} describe an effect that happens "If you do." In that case, no player may take actions to try to stop the ability's effect after you make your choice. If the payment is followed by the phrase "When you do," then you'll choose any targets for that reflexive triggered ability and put it on the stack before players can take actions.