During Gold Rush events, you are awarded Gold for destroying Crown Towers in 1v1 Arena battles. The first Princess Tower you destroy gives a certain amount of Gold (say n) depending on Arena level, the second Princess Tower gives 2n Gold and the King's Tower gives 3n Gold. You can get at most 30n Gold during each Event. The Crown Towers are also decorated with gold.
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During Gem Rush events, you are awarded Gems for destroying Crown Towers. The Crown Towers are also decorated with gems. The rewards are the same at all Arenas.
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During some of the events, you get a Quest that is completed by gaining 10 Crowns in 1v1 Arena battles. This Quest can be easily completed together with a Crown Chest.