Shrine of Chance

The Shrine of Chance is one of the Shrines in Risk of Rain 2. It is shaped like a Stone GolemStone Golem
HP: 480 (+144 per level)
Damage: 20 (+4 per level)
Class: Ranged / Melee
Speed: 6.6 m/s
Armor: 0. Upon purchase, the player will have a chance to receive an item of a random rarity or a random equipment.

The base cost is $17, increasing by 40% with each activation. Receiving two items from a Shrine of Chance will prevent any further interaction with it. However, until both items are obtained, there is no limit—save the amount of gold in the player's possession—to the number of times a Shrine of Chance can be activated.

Reward	Chance
Nothing	45%
Common Item	36%
Uncommon Item	9%
Legendary Item	1%
Equipment	9%

Notes

• The first use of a Shrine of Chance is less expensive than a small chest, making it a cheap way to obtain items if lucky.
• Failing a Shrine of Chance three times in a row will complete the "Is This Bugged?" Challenge.
• The chance to receive an item is not affected by the 57 Leaf Clover57 Leaf Clover
  Luck is on your side.
  All random effects are rolled +1 (+1 per stack) times for a favorable outcome. or PurityPurity
  Reduce your skill cooldowns by 2 seconds. You are unlucky.
  All skill cooldowns are reduced by 2 (+1 per stack) seconds. All random effects are rolled +1 (+1 per stack) times for an unfavorable outcome..
• Shrines of Chance cannot spawn on Siren's CallSiren's Call (Stage 4)
  Ship Graveyard
  You dream of wind.
  
  .
• Shrines of Chance will not spawn if the Artifact of SacrificeSacrificeMonsters drop items on death, but Chests no longer spawn.
  Code:
  
  ▲▲▲
  ▲▲▲
  ▲♦▲
  is active.

Math

The possible chains of independent random binary events where termination occurs after two successes can be represented as a tree $T_2$, where

$T_{2}=(T_{2},T_{1});{\text{ }}T_{1}=(T_{1},T_{0});{\text{ }}T_{0}=()$

The expected cost of getting 2 items out of a Shrine of Chance is then $C_2$, where

$C_{0}=0;{\text{ }}C_{1}=0.55(1+1.4C_{0})+0.45(1+1.4C_{1});{\text{ }}C_{2}=0.55(1+1.4C_{1})+0.45(1+1.4C_{2})$

$C_{k}$ here represents the expected cost of getting $k$ items out of a Shrine of Chance as a multiple of the current cost of activating the shrine. Successive simplification gives

$C_{0}=0;{\text{ }}C_{1}={\frac {100}{37}}\approx 2.7;{\text{ }}C_{2}={\frac {11400}{1369}}\approx 8.3$

This means that getting one item out of an unused Shrine of Chance is initially expected to be about 1.8 times as expensive as a small chest for a slightly rarer reward on average; emptying a Shrine of Chance costs on average about 1.5 times as much as opening two large chests for a more common reward.

Gallery

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