Rivalry

Increases damage inflicted to 1.25× against Pokémon of the same gender, but decreases damage to 0.75× against the opposite gender.

Full effect

This Pokémon inflicts 1.25× as much regular damage against Pokémon of the same gender and 0.75× as much regular damage against Pokémon of the opposite gender. If either Pokémon is genderless, damage is unaffected.

In game description

The Pokémon's competitive spirit makes it deal more damage to Pokémon of the same gender, but less damage to Pokémon of the opposite gender.

Pokemon with Rivalry

#0029

Nidoran F #0030

Nidorina #0031

Nidoqueen #0032

Nidoran M #0033

Nidorino #0034

Nidoking #0267

Beautifly hidden #0403

Shinx #0404

Luxio #0405

Luxray #0519

Pidove hidden #0520

Tranquill hidden #0521

Unfezant hidden #0610

Axew #0611

Fraxure #0612

Haxorus #0667

Litleo #0668

Pyroar Male

Using Rivalry in Cobblemon

Abilities are passive and always active, so Rivalry costs you nothing to run. If it is marked hidden on a species above, expect it to be harder to obtain: servers differ in whether hidden abilities come from breeding, an Ability Patch, or events.

See the Pokedex for which abilities each species can have, and IVs, EVs and breeding for how to actually pass one down.