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All tactics and exact numbers here: http://www.legacyofathousandsuns.com/forum/showthread.php?10329
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This is simplified, but still somewhat complicated. If you don't have one of these, don't apply anything!
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Name (abbreviation)		Avg +%dmg/slot	Proc rate 	WHEN??
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Name (abbreviation)		Avg +%dmg/slot	Proc rate 	When to apply
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Quiskerian Psi-Eye (Psi)	100		~10%		All the time on Quisk Psi-Hound
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Asymmetric Warfare (AW)		45		passive		All Small raids
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Biological Warfare (BW)		30		low		All >10m OS biological raids (check wiki)
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Angel of Death (AoD)		28,5		low		All >10m OS N/H raids
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Trick or Treat (ToT)		26,5		low		All >10m OS L/NM raids
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Last Stand (LS)			26		~10%		Only when boss health <20%, so BtR is better
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Last Stand (LS)			26		~10%		Useless*
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Final Assault (FiA)		25		~10%		All >10m OS raids
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EdC chain			23 ea.		passive		Raids with <10m OS with 3 or more slots
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  +Prep				+19		passive		If no one has the tops and it has 4+ spots
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Fear the Reaper (FR)		20		low		Only when officers/summoner is very active.
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What 'ya Gonna do? (WYGD)	15		passive		Raids with <10m OS and 
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Better to Recieve (BtR) is special. It gives 1 more epic, and so it can do as much as double your loot. On huge raids, LS could have been used, but it's a small chance both the ones who have BtR and LS and the summoner/an officer are on actively during that time.
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Better to Recieve (BtR) is special. It gives 1 more epic, and so it can do as much as double your loot. Always apply near the end, or from start on very small raids.
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*On huge raids, LS could have been used, but it's a small chance both the ones who have BtR and LS and the summoner/an officer are on actively during that time.