Changes: Magic items

Revision as of 06:48, 30 October 2018

Magic items are special ingredients that can be obtained after the completion of a ritual or by buying them in the store. There are four magic items: Unlucky Clovers, Bone Dust, Amanita Mushrooms, Guard's Eyes. Magic items are used to craft and upgrade thrones, and to obtain costumes in the Style o' Thief machine.

Unlucky Clover

Unlucky Clovers () are the cheapest and most common magic item. Unlucky Clovers are required to craft Wealthy Duke and Lucky Crystal. They are purchasable directly from the shop for 10 orbs each.

“

Four-Leaf clovers are rare because leprechauns tear off a leaf, if they don't keep it for themselves.

-Description in Guild Armory

”

Bone Dust

Bone Dust () is rarer than Unlucky Clovers.Bone Dust is used to craft Wealthy Duke and Lucky Crystal. Its are purchasable directly from the shop for 35 orbs each.

Amanita Mushroom

Amanita Mushrooms () is rarer than Bone Dust. Amanita Mushrooms are used to craft Wealthy Duke, Lucky Crystal, Wise Judge, Sun Lit and Foreseer. They are purchasable directly from the shop for 95 orbs each.

Guard's Eye

The Eyeball (Blue Eye), the best and rarest magic item in the game.

Guard's Eyes () are the rarest magic item. They cannot be obtained at the first ~3 totems. Guard's Eyes are used to craft Wise Judge, Sun Lit and Foreseer. They are purchasable directly from the shop for 295 orbs each.

Odds

The chance of receiving magic items on a spinner changes as you progress through the first ~6 totems. The odds cap at the 8 hour totem, and don't change from that point onward.

Zone	Clover	Dust	Mushroom	Eye
1	?% (>)	?% (>)	?%	0%
2	40%	35%	20%	5%
3	35%	35%	20%	10%
4	35%	35%	20%	10%
5	35%	35%	20%	10%

Math and Strategy

Assuming a magic item is valued at its shop price, the average value of a roll on the spinner can be modeled as:

(average roll) = (10 * 0.35) + (35 * 0.35) + (95 * 0.2) + (295 * 0.1) = 64.25 orbs

The net gain of a re-roll can be modeled as:

(net gain) = (average roll = 64.25) - (cost of current item) - (cost of re-roll)

As an example: if your initial roll lands on clovers, the net gain of a re-roll would be:

(net gain) = 64.25 orbs (average value of roll) - 10 orbs (loss of leaf) - 5 orbs (cost of re-roll) = 49.25

Re-rolling is effective as long as the net gain of the re-roll is greater than 0, that is:

(net gain) > 0

(cost of item) + (cost of re-roll) < 64.25

Thus, the optimal strategy for maximizing your return on the spinner is as such:

If the spinner lands on Unlucky Clovers, re-roll as long as the cost of the re-roll is 40 or less.
If the spinner lands on Bone Dust, re-roll as long as the cost of the re-roll is 20 or less.
If the spinner lands on Amanita Mushrooms or Guard Eyes, do not re-roll.

Trivia

The store price of magic items is expensive; buying them directly should be avoided. Instead, run rituals, using the optimal re-rolling strategy as detailed in the section above.

@@ Line 1: / Line 1: @@
-Magic items are special ingredients that can be obtained after the completion of a ritual or by buying them in the store. The magic items can be leaves, powders, mushrooms and eyeballs. Magic items are used to craft and upgrade outfits.
+Magic items are special ingredients that can be obtained after the completion of a ritual or by buying them in the store. There are four magic items: Unlucky Clovers, Bone Dust, Amanita Mushrooms, Guard's Eyes. Magic items are used to craft and upgrade thrones, and to obtain costumes in the [[Style o' Thief]] machine.
-== Leaves ==
-Leaves ([[File:Leaf16.png]]) are the cheapest and easiest magic items to get. You can use leaves to craft [[Outfits#Nimble_Foot|Nimble Foot]]. It costs 10 orbs in the shop.
-== Powders ==
+== Unlucky Clover ==
-Powders ([[File:Sand16.png]]) are rarer than leaves. You can use them to craft [[Outfits#Golden_Blaze|Golden Blaze]] and [[Outfits#Lucky_Face|Lucky Face]]. It costs 35 Orbs in the shop.
+Unlucky Clovers ([[File:Leaf16.png]]) are the cheapest and most common magic item. Unlucky Clovers are required to craft [[Thrones#Wealthy_Duke|Wealthy Duke]] and [[Thrones#Lucky_Crystal|Lucky Crystal]]. They are purchasable directly from the shop for 10 orbs each.{{Quote|Four-Leaf clovers are rare because leprechauns tear off a leaf, if they don't keep it for themselves.
+-Description in Guild Armory}}
-== Mushrooms ==
+== Bone Dust ==
-Mushrooms ([[File:Mushroom.png]]) are rarer than powders, and even rarer than leaves. You can use them to craft [[Outfits#Golden_Blaze|Golden Blaze]] , [[Outfits#Lucky_Face|Lucky Face]] , [[Outfits#Wise_Eye|Wise Eye]], [[Outfits#Purple_Splash|Purple Splash]] and [[Outfits#White_Shadow|White Shadow]] . It costs 95 Orbs in the shop.
+Bone Dust ([[File:Sand16.png]]) is rarer than Unlucky Clovers.Bone Dust is used to craft [[Thrones#Wealthy_Duke|Wealthy Duke]] and [[Thrones#Lucky_Crystal|Lucky Crystal]]. Its are purchasable directly from the shop for 35 orbs each.
-== Eyeballs ==
+== Amanita Mushroom ==
+Amanita Mushrooms ([[File:Mushroom.png]]) is rarer than Bone Dust. Amanita Mushrooms are used to craft [[Thrones#Wealthy_Duke|Wealthy Duke]], [[Thrones#Lucky_Crystal|Lucky Crystal]], [[Thrones#Wise_Judge|Wise Judge]], [[Thrones#Sun_Lit|Sun Lit]] and [[Thrones#Foreseer|Foreseer]]. They are purchasable directly from the shop for 95 orbs each.
-[[File:Eyeball.png|thumb|The Eyeball (Blue Eye), the best and rarest magic item in the game.]]
-Eyeballs ([[File:Eyeball-0.png]]) are the rarest magic items, and they cannot be obtained at the first zone's totems. You can use them to craft [[Outfits#Wise_Eye|Wise Eye]], [[Outfits#Purple_Splash|Purple Splash]] and [[Outfits#White_Shadow|White Shadow]]. It costs 295 Orbs in the shop.
+== Guard's Eye ==
+[[File:Eyeball.png|thumb|The Eyeball (Blue Eye), the best and rarest magic item in the game.]]
+Guard's Eyes ([[File:Eyeball-0.png]]) are the rarest magic item. They cannot be obtained at the first ~3 totems. Guard's Eyes are used to craft [[Thrones#Wise_Judge|Wise Judge]], [[Thrones#Sun_Lit|Sun Lit]] and [[Thrones#Foreseer|Foreseer]]. They are purchasable directly from the shop for 295 orbs each.
 == Odds ==
+The chance of receiving magic items on a spinner changes as you progress through the first ~6 totems. The odds cap at the 8 hour totem, and don't change from that point onward.
-All the values were rounded to make it easier to understand.
 {| class="article-table"
 !Zone
+!Clover
-!Leaves
+!Dust
-!Powder
 !Mushroom
+!Eye
-!Eyeball
 |-
 |1
@@ Line 54: / Line 55: @@
 |10%
 |}
+== Math and Strategy ==
+Assuming a magic item is valued at its shop price, the average value of a roll on the spinner can be modeled as:
+ (average roll) = (10 * 0.35) + (35 * 0.35) + (95 * 0.2) + (295 * 0.1) = 64.25 orbs
+The net gain of a re-roll can be modeled as:
+ (net gain) = (average roll = 64.25) - (cost of current item) - (cost of re-roll)
+As an example: if your initial roll lands on clovers, the net gain of a re-roll would be:
+ (net gain) = 64.25 orbs (average value of roll) - 10 orbs (loss of leaf) - 5 orbs (cost of re-roll) = 49.25
+Re-rolling is effective as long as the net gain of the re-roll is greater than 0, that is:
+ (net gain) > 0
+ (cost of item) + (cost of re-roll) < 64.25
+Thus, the optimal strategy for maximizing your return on the spinner is as such:
+* If the spinner lands on [[File:Leaf16.png|18x18px]] Unlucky Clovers, re-roll as long as the cost of the re-roll is [[File:Orbs.png|21x21px]] 40 or less.
+* If the spinner lands on [[File:Sand16.png|18x18px]] Bone Dust, re-roll as long as the cost of the re-roll is [[File:Orbs.png|21x21px]] 20 or less.
+* If the spinner lands on [[File:Mushroom.png|18x18px]] Amanita Mushrooms or [[File:Eyeball-0.png]] Guard Eyes, do not re-roll.
+== Trivia ==
+* The store price of magic items is expensive; buying them directly should be avoided. Instead, run rituals, using the optimal re-rolling strategy as detailed in the section above.
 [[Category:Game elements]]
 [[Category:Outfits]]
+[[Category:Thrones]]
+[[Category:Currency]]
+[[Category:Incomplete]]