Indipendent materias are pink and can't be used in combination with other materias. Some of them raise parameters, others give different abilities.

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Chocobo Lure
Stars: 4
Effect:
Luck +01

AP:
1x: 0
1,5x: 3000
2 x: 10000
3 x: 30000

Effect: Allows to encounter chocobos (walk on their tracks in the world map). The higher the level, the higher the chance to find a chocobo.
Where it is: you can buy it in the Chocobo Farm, for 2000 Gil

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Counter attack
Stars: 5
Effect:
No effect

AP:
+20%: 0
+40%: 10000
+60%: 20000
+80%: 500000
+100%: 100000

Effect: counterattacks with a physical attack
Where it is: beat the "Materia Keeper" or win a bet on the chocobo races (only in ranks A and S)

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Cover
Stars: 5
Effect:
Vitality +01

AP:
+20%: 0
+40%: 2000
+60%: 10000
+80%: 25000
+100%: 40000

Effect: the wearer protects an ally
Where it is: in the garden next to Aeris' home, or buy it in the Wall Market for 1000 Gil

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Enemy away
Stars: 3
Effect:
Luck +01

AP:
- 1/2: 0
- 3/4: 8000
Master: 50000

Effect: lowers the frequency of random encounters
Where it is: win a bet on chocobo races (only ranks B, A and S)

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Enemy lure
Stars: 3
Effect:
Luck -01

AP:
1,5x: 0
2 x: 8000
Master: 50000

Effect: increases the frequency of random encounters
Where it is: in exchange for 250 or 800 BP in the Golden Saucer Battle Square
EXP. plus
Stars: 3
Effect:
Luck +01

AP:
1,5x: 0
2 x: 60000
Master: 150000

Effect: raises the amount of earned EXP
Where it is: in exchange for 2000 GP in the Golden Saucer

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Gil plus
Stars: 3
Effect:
Luck +01

AP:
1,5x: 0
2 x: 80000
Master: 150000

Effect: raises the amount of earned Gil
Ottenibile: in exchange for 1000 GP in the Golden Saucer