Sin's Right Fin is a boss in Final Fantasy X. This battle takes place during the fight to get inside Sin, and is the second of a series of boss fights. The right fin is almost identical to the Left Fin, and the battle plays out in more or less the same way.
The player is on the Fahrenheit and can fly in and out of range of physical attacks. Sin's attacks are Negation, which removes all status buffs from the party, Gravija, and a physical attack on the party.
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 Right Fin is always predictable. After 4 attacks or if it falls below 16,250 HP, it will attack. This continues even if the Fin is later healed back above 16,250 HP; it is impossible to revert him to the 4 attack requirement. Otherwise, it won't attack.
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.