Sin's Left Fin is a boss in Final Fantasy X. This battle takes place during the fight to get inside Sin, and is the first of a series of boss fights. Like the battle against Evrae, the player is on the Fahrenheit and can fly in and out of range of physical attacks. Left Fin is almost identical to the Right Fin.
Sin will attack less frequently when the player is out of range. In short range, it uses Negation, a Dispel-like attack that dispels all positive status buffs, as a counter to many Skill-type attacks. It also uses Gravija, and can attack the entire party for approximately 1,000 damage.
The Fins' AI differs slightly, specifically, while fighting them close-up, on the turns not used for charging or unleashing Gravija. The Fins sometimes attack, and sometimes don't, but the exact mechanics of this differ between the two Fins. The attacks themselves are identical. In both cases, it is determined on how many times the party has attacked the arm since the last time it used its physical attack (whether close-up or at distance). Also in both cases, an attack from an aeon counts as two attacks.
The Left Fin follows the following:
0 attacks: 33% chance of attacking
1 attack: 66% chance of attacking
2+ attacks: 100% chance of attacking
This counter is also used at a distance (for both arms), but the requirements vary. The Left Arm requires 7 hits to trigger an attack at distance, the Right Arm requires 5 hits prior to reaching 16,250 HP, and 3 hits after reaching 16,250 HP. The counter is reset whenever the attack is used. Up close and distance don't have separate counters; they run off the same one, just with up close having lower requirements to trigger.