The Revenge Stick is a Special Item in Bloons Monkey City. In the Flash version, it causes the player to gain an extra 300 Bloontonium when attempting to send a revenge attack, which is lost if the player cancels it. In the multiplatform version, it reduces the cost to send a revenge attack to 
80%.
Strategy
In the Flash version, the bonus Bloontonium allows for a slightly stronger offense against an enemy city, and if your tanks are full then it can potentially be stronger than sending a normal MvM attack, without spending a single Bloonstone.
In the multiplatform version, the 20% discount to Bloontonium only matters for sending MvM attacks more often, to sustain enough players to keep grinding for the Epic Defender (2500 MvM defense wins) achievement. Unless specifically wanting to maximize potential back-to-back enemy cities, it is generally not worth sending an MvM counterattack. The amount of Bloonstones earned from playing MvM games is often better spent grinding game events such as Monkey Teams, for the same amount of time earning better rewards. Ironically, tanking the MvM battles is better in a highly leveled city, since its penalties are minimal, and it's sometimes better to focus on sending MvM attacks to random players in the hopes that they'll lose and earn more currency for your city.
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