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When the wielder attacks an opponent of the same gender as itself, the power of its attack increases by 25%. When the wielder attacks an opponent of the opposite gender, the power of its attack decreases by 25%. The damage is unaltered if either Pokemon has no gender.
Rivalry is a good ability on simulators but generally bad on Wi-Fi or playing Pokemon on cartridges. The simple reason for this is that on nearly all simulators, the default option for gender is male, and no-one really changes it, whereas on the cartridge the gender is almost always totally random. Therefore if you want to abuse Rivalry, stick to playing on simulators and not on the DS itself. The main user of Rivalry is Haxorus, as its Attack stat is among the highest in the game, and another boost to its power will not go amiss. However, since Mold Breaker is a great asset to Haxorus, you won't see Rivalry too often even on simulators, as some of its counters are destroyed by Mold Breaker. Nidoking can also use it but Sheer Force is the more lucrative option.
Found in Dream World