Runes

Runes are cosmetics that can be applied to items to give them particle effects upon use.

Runic Mobs
Runes are obtained from Runic Mobs. Runic Mobs are normal SkyBlock Mobs, but with higher, and deal double. They have a purple name tag, and a much lower chance to spawn. When killed, they are guaranteed to drop a Rune.

All mobs can be Runic except Ender Dragon, Crimson Isle Mini-bosses, Slayer Boss/Miniboss, Dungeon Boss or Dungeon Boss Minion.

Certain runes are also obtained from Slayer or as special rewards.

Runic Pedestal
Runes can be fused on the Runic Pedestal, found behind the and owned by.

Fusing two runes together will have a chance of upgrading the rune to the next level, up to the maximum level of 3. Upon success or failure, the second rune is consumed. If this process does not succeed, the remaining rune will not gain the level. The chance of success can be seen in the Runic Pedestal while hovering over the apply trigger. Regardless of the outcome, this will also grant Runecrafting experience. More experience is awarded upon success.

Runes can be fused onto Swords, Bows, Chestplates, and Boots, depending on the type of rune. The player must have their Runecrafting level either equal to or greater than the level of the rune, or they won't be able to fuse it. This only applies to fuse runes to items; runes above the player's Runecrafting level can still be combined together. Fusing runes onto items will also grant Runecrafting experience.

Rates
Different rune rarities grant differing amounts of experience and have different success rates when fusing. F(n), the probability of successfully fusing on the nth attempt is represented as a function of P(n), the probability of merging on a given attempt. This distribution is binomial in nature.

$$ F(n) = P(n) * (1 - P(n))^{n-1}$$

C(n) the cost in runes on the nth attempt is

$$C(n) = 1 + n$$

Therefore, we can represent E(n), the expected number of runes during fusing as E(n) = ∑ F(n) * C(n)

$$E(n) = \sum P(n) * (1-P(n))^{n-1} * (1+n)$$ In order to calculate the expected runes to acquire

$$T_3$$ , we can represent the cost C(n) in terms of the cost of T2, or

$$C_3(n) = E(n) + E(n)*n$$

Therefore, the cost of T3 rune is

$$E_3(n) = \sum P(n) * (1-P(n))^{n-1} * (1+n) + n * \sum P(n) * (1-P(n))^{n-1} * (1+n)$$ $$= E(n) ^ 2$$ Alternatively, where

$$L$$ is the level of the rune desired:

$$ E_L(n) = (P(n)^{-1} + 1)^{L - 1} $$