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During each combat, there's a time when attackers are declared. Normally, only the active player declares attackers, but Party Crasher doesn't play by those rules. During the declare attackers step of your opponent's combat phase, after they're done declaring their attackers, you may choose to declare Party Crasher as an attacker. After you declare blockers, the defending player can declare blockers for Party Crasher. All combat damage is dealt simultaneously, unless a strike ability (first, double, last, and/or triple) is involved.

If Party Crasher attacks during an opponent's turn, that opponent could block it with an attacking creature that is untapped as blockers are declared. That creature will then be attacking and blocking at the same time. If Party Crasher is also untapped as blockers are declared, it can block the attacking creature that blocked it. Even if all this happens, the creatures will only deal combat damage to each other once.