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 2.5 Desperation Attacks
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If you attack while the character's current HP < their max HP / 8, then there
is a 1 in 16 chance of doing a desperation attack instead of a normal attack.
Gau and Umaro do not have desperation attacks.
If the character has any of the following statuses, then they will never do
a desperation attack: Muddle, Image, Clear, Zombie
Characters will never use their desperation attack more than once each combat.
While the Battle Time Counter (See section 2.8 Battle Timing) is less than
768, characters won't use their desperation attacks. (i.e. Characters will
never use Desperation Attacks during the first 25.6 seconds of combat)
All Desperation attacks are unblockable (see step 3 in hit determination)
All Desperation attacks are magical attacks, that ignore defense (skip steps
5, 6b, 6c, 6d, 6e, 6f, and 7 in damage calculation.)
Sabre Soul and Star Prism are instant death attacks, rather than damage-dealing
attacks like the others. Shadow Fang will also inflict seizure status.
Here is every character's desperation attack:
Char     Attack              Power
Locke    Mirager             139
Terra    Riot Blade          142
Celes    Spin Edge           143
Edgar    Royal Shock         143
Sabin    Tiger Break         140
Cyan     Back Blade          140
Mog      Moogle Rush         150
Strago   Sabre Soul            0
Relm     Star Prism            0
Shadow   Shadow Fang         140
Setzer   Red Card            147
Gogo     X-Meteo             146
so it'd take at least 25 seconds within each battle for them to be able to pull one off.