[ITEM:(1936)Bumba's Cudgel]
Normally I would say run bumba's cudgel as Loki is ability based however this makes it so that late game win you're more relying on the crits your basic attack damage will do good damage
[ITEM:(233)Tekko-Kagi]
You want to get this first as it'll make you move faster so that you can get from location to location quicker right off the bat. With Loki and Thanatos it will improve their already fast movement speed and for thin rear it'll make it where he can compete with other high movement speed jungles
[ITEM:(1901)Transcendence]
This item is just good as it gives you Mana so you won't run out, strength and Mana regen. It will not be good on Thanatos as he does not have Mana so you can use the second build that is designed for him specifically.
[ITEM:(196)Titan's Bane]
This will give you a good burst of damage as well as penetration and most likely around the time that you get this you'll have built up a decent amount of transcendence Stacks meaning that you'll have high penetration and high damage
[ITEM:(178)Musashi's Dual Swords]
This item gives another 40 strength and critical chance. The key take away from this is that it gives you movement speed when you crit making you even faster
[ITEM:(156)Deathbringer]
And
[ITEM:(144)Demon Blade]
Can both be used here. Demons blade will make it so that you have more chances to create since you'll attack faster, but you'll hit weaker. Deathbringer makes it where you'll hit harder and your crits will have more damage, but you won't be able to crit as often because you don't attack as quickly.
[ITEM:(163)Gem of Focus]
The 40 Intelligence on this item literally does nothing and the 20 cooldown rate is not that big. The main takeaway from this is it has the same passive as[ITEM:(233)Tekko-Kagi]
Meaning that you can get 30% movement speed simply by using your abilities. If you get a crit you get an additional 10% for a total of 40% movement speed.
[ITEM:(235)Hastened Fatalis]
And
[ITEM:(221)Avatar's Parashu]
Are the two optional items instead of gym of focus, or as a replacement to Transcendence on Thanatos.
Hastened Fatalis gets rid of the basic attack debuff making it where you can attack and still keep up with people
Avatar's Parashu is just damage so that you can burst people down late game
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