Cubing (Rerolling)

- basics, technicalities, and odds


Table of Contents
- [1] Basics of Cubing
- [2] Required "Item Level"
- [3] Cubing Odds

Level Terms
Alvl: area level
alvl: affix level
ilvl: internal level ("item level")
mlvl: monster level
magiclvl: magic level
qlvl: base item quality level


This guide assumes no basic knowledge of cubing (rerolling). You may want to read over section [1] or simply skip it if you believe you are familiar with the basics.


[1] Basics of Cubing

The Horadric Cube recipe,

3 Perfect Gems + 1 Magic Item 1 New Random Magic Item of the Same Type

preserves the ilvl of the magic input (output ilvl = input ilvl). The original item properties are rerolled.

• Any mixture of 3 perfect gems (including perfect skulls) will work.
• The recipe may be used repeatedly. Simply use the output as the new input.
• The item affixes are randomly generated, restricted only by ilvl and qlvl (read section [2]).
• Base defense as well as any auto mods and/or staffmods are rerolled as well.
• Even if the input item is ethereal, the output will not be ethereal.

Cubing (or rerolling, as it is sometimes called) with 3 perfect gems is basically no different from having the item drop. All it takes to cube something worthwhile is a bit of patience and quite often a LOT of gems.

Note : ONLY item type and affix level matter. Character class, character level, difficulty, act, and number of players play NO role when using the above recipe.

ilvl (input item)
This is determined by drop location. For monster drops, ilvl = mlvl. Items found on dead bodies, weapon racks, in chests etc. are either ilvl = Alvl (chest drops) or ilvl = Alvl - 1. For a complete list of area levels,
refer to the links in section [1] of the Treasure Classes guide.

Gambled items are ilvl = clvl - 5 + rnd[10]. That is, ilvl ranging from clvl - 5 to clvl + 4 (randomly), with a minimum of ilvl 5.

Items shopped at NPCs are ilvl = clvl + 5. In Normal however, there are maximum ilvls set by act,


For more information on gambling and shopping at NPCs, refer to the links of the "Diablo II Resources" section in my profile.


[2] Required "Item Level"

First thing to note is that some items have a magic level bonus (magiclvl). They are,

• orbs, staves, wands (except elite wands): magiclvl = 1
• Circlet: magiclvl = 3
• Coronet: magiclvl = 8
• Tiara: magiclvl = 13
• Diadem: magiclvl = 18

For an item having affixes, the affix level is calculated as follows,


That is,

• IF the item has magiclvl > 0 (i.e. the item is in the beforementioned list), THEN the alvl is given by (1).
• ELSE we consider max{ilvl,qlvl}. IF max{ilvl,qlvl} < 99 - int(qlvl / 2), THEN the alvl is given by (2), ELSE the alvl is given by (3).

Base item quality levels (qlvl) @ the Arreat Summit ("Quality Level"): http://www.battle.net/diablo2exp/items/weaponsandarmor.shtml

Quality levels for other items,

• Amulet, Ring, Jewel: qlvl = 1
• Small Charm: qlvl = 28
• Large Charm: qlvl = 14
• Grand Charm: qlvl = 1

Note that by (2)-(3), if qlvl 1, then the affix level is simply equal to the item level (alvl = ilvl). Another extreme case is a Diadem (qlvl 85). By (1), it will ALWAYS have alvl 99. This property is evidently not shared
by any other item in the game, and it is also this property that enables a Diadem to receive any affix possible. The entire affix pool for Diadems is available, regardless of ilvl.

Required alvl
Why bother with the affix level at all ? Because, for an item having affixes, it is the affix level that limits the affixes which the game can possibly choose. The higher the affix level, the more affixes are available
(larger affix pool). For instance, just to keep it simple, an ilvl 49 Grand Charm (alvl = ilvl) could never ever spawn with the often desired +1 to <skill tree> prefix, as it requires at least alvl 50.

Magic Prefixes and Suffixes: http://www.battle.net/diablo2exp/items/magic/

Note : The levels in ( ) at the Arreat Summit are NOT item levels. People often confuse affix level with item level. Just remember that they are different terms.

If you have not worked with affix levels before, you are probably confused by now. Read the 3 examples below to get a sense of what is going on. In what follows, P and S denote "prefix" and "suffix".

Grand Charm (qlvl 1)
Some of the desired affixes,

(P) +1 to <skill tree> (level 50)
(P) "Sharp" (level 29), +(7-10) to Maximum Damage, +(49-76) to Attack Rating
(S) "Balance" (level 1), +12 % Faster Hit Recovery
(S) "Vita" (level 77), +(36-40) to Life
(S) "Vita" (level 91), +(41-45) to Life

Since alvl = ilvl for Grand Charms, we need a GC of at least ilvl 91 to have even the slightest chance of the last "Vita" suffix. The only monsters that drop magic items of ilvl >= 91 are Diablo [H] {mlvl 94},
Nihlathak [H] {mlvl 95}, and Baal [H] {mlvl 99}. Which is why Grand Charms dropped from either of these particular bosses are commonly used for rerolling.

Monarch (qlvl 72)
Suppose we want a JMoD ("Jeweler's Monarch of Deflecting"). The desired affixes are then

(P) "Jeweler's" (level 55), Socketed (4)
(S) "Deflecting" (level 11), +30 % FBR, +20 % ICB

Alright, we need at least alvl 55. BUT ... this time, the qlvl is not 1. We would like to know what minimum ilvl the required affix level (55) corresponds to. Look at the inequality used to decide between (2)
and (3): max{ilvl,qlvl} < 99 - int(qlvl / 2)

Inserting qlvl = 72, we get max{ilvl,72} < 63. This is obviously impossible, so we should use (3). Remembering that we want alvl >= 55, we get

2*max{ilvl,72} - 99 >= 55 <=> max{ilvl,72} >= 77

Hence, we need a magic Monarch of at least ilvl 77 to have a chance of rolling a JMoD.

Tiara (qlvl 70)
This is one of the items that have a magic level > 0 (Tiara: magiclvl = 13). By (1) then, alvl = max{ilvl,70} + 13. Now, suppose we want +2 skills,

(P) +2 to <class> skills (level 90)

We need at least alvl 90. From (1) we get max{ilvl,70} + 13 >= 90 <=> max{ilvl,70} >= 77. That is, even a magic Tiara having ilvl 77 will suffice to roll +2 skills, due to the inherent magic level bonus.

Notice the general pattern from the above examples,

• ilvl < alvl (required ilvl is less than required alvl if the item has magiclvl > 0, e.g. a Tiara)
• ilvl = alvl (required ilvl is equal to required alvl if the item has qlvl = 1, e.g. a Grand Charm)
• ilvl > alvl (required ilvl is higher than required alvl if the item has qlvl > 1, e.g. a Monarch)

Amazon Javelins
Using the formulae (1)-(3) and appropriate quality levels, we can work out the minimum ilvl needed to roll any of the possible affixes on any magic item. For instance, you could verify the following minimum
values for "Lancer's Maiden/Ceremonial/Matriarchal Javelin of Quickness",

Maiden Javelin (qlvl 23): ilvl 71
Ceremonial Javelin (qlvl 35): ilvl 77
Matriarchal Javelin (qlvl 65): ilvl 80

The "Lancer's" prefix stacks with the amazon javelin auto mod +(1-3) to Javelin and Spear Skills. This is how those "6/40" magic amazon javelins are possible ("Lancer's" is a magic-only prefix).


[3] Cubing Odds

Now that we know how to determine the required ilvl, what about the odds ? In practice, we may want a range of useful ilvls rather than limiting ourselves to one value. For instance, when cubing for the
+(41-45) to Life suffix ("Vita") on a Grand Charm, it does not make any difference if the GC is ilvl 94, 95, or 99, because the "Vita" suffix has the highest level (91) of all GC affixes. Depending on the item
type and what affixes we want, sometimes using an ilvl much higher than necessary means that we expand the affix pool and thus risk rolling higher (unwanted) affixes.

To have the best possible odds when cubing, we should use at least the required ilvl, but less than the ilvl corresponding to a higher affix if we want to prevent it from spawning. Don't get too excited yet,
as the odds are usually rather discouraging even then. But we cannot do better than that.

Affix Frequencies
When a magic item is dropped (or cubed), the game determines if it gets a prefix only, a suffix only, or 1 of each, with these probabilities,

• Prefix only: 25 %
• Suffix only: 50 %
• Prefix + Suffix: 25 %

Notice, "Suffix only" is twice as likely as each of the other options.

Next, the game picks affixes accordingly, as either P, S, or P+S have been selected,

• Affixes are selected from the appropriate affix pool
• If P+S was chosen, P and S are picked independently of each other
• Each affix has its own affix frequency (weight) which is the "likeliness to be picked"
• If an affix has several possible values, all of which may spawn, the game randomly picks one of them
• The probability of picking a certain affix is equal to the affix frequency divided by the sum of affix frequencies (P or S)

Refer to the affix tables @ inDiablo for affix frequencies. The numbers used below were obtained from the 1.11 LoD affix tables @ inDiablo.

One would then use these formulae to calculate the odds,


The affix calculator @ inDiablo returns the same odds as given by the formulae.

Grand Charm
Suppose we have 2 GCs, one is ilvl 50 (from somewhere in A3 Nightmare), label this "A3NM", and the other one is from Dia, Nith, or Baal (ilvl 94, 95, or 99), label this "DNB". We want to know the odds of

• (P) +1 to <skill tree> specific (level 50, freq 1) and ANY suffix or NONE
• (P) +1 to <skill tree> random (level 50, freq 1) and ANY suffix or NONE
• (P) +1 to <skill tree> specific (level 50, freq 1) and (S) "Balance" (level 1, freq 4), +12 % FHR
• (P) +1 to <skill tree> random (level 50, freq 1) and (S) "Sustenance" (level 45, freq 4), +(26-30) to Life

The first two cases are handled by using (4) and (6). In the first case, we want a specific skill tree (1 of 21). Since the skill tree prefixes each share the same affix frequency, there is no need to specify
exactly which one (your choice). In the second case, any of the 21 skill trees will do. Using the affix tables, we get

• A3NM (1/4 + 1/4)*(1/230) = 1/460 ~ 0.22 % vs 0.21 % ~ 1/484 = (1/4 + 1/4) * 1/242 DNB
• A3NM 21*(1/460) = 21/460 ~ 4.57 % vs 4.34 % ~ 21/484 = 21*(1/484) DNB
• A3NM (1/4)*(1/230)*(4/84) = 1/19 320 ~ 0.0052 % vs 0.0041 % ~ 1/24 200 = (1/4)*(1/242)*(4/100) DNB
• A3NM 21*(1/19 320) = 21/19 320 ~ 0.109 % vs 0.087 % ~ 21/24 200 = 21*(1/24 200) DNB ("Balance" and "Sustenance" have the same affix frequency)

The difference in each case is not very significant. And since GCs from Diablo, Nihlathak, and Baal can potentially get +(41-45) to Life, you might as well stick to rerolling them and simply leave the rest.

Tiara
Normally, each affix is weighed by its frequency (as in the previous example). However, when there is a magic level, it is instead weighed by its frequency times its alvl. Meaning that a frequency 1 affix
that requires alvl 50 (weight: 1*50 = 50) is five times as likely as a frequency 2 affix requiring alvl 5 (weight: 2*5 = 10). Because of this, high-level affixes are more likely. Suppose we want to determine
the odds of rolling each of the following on a magic Tiara of at least ilvl 77,

• (P) "Valkyrie's" (level 90, freq 2), +2 to Amazon Skill Levels and (S) "Speed" (level 37, freq 4), +30 % Faster Run/Walk
• (P) "Artisan's" or "Jeweler's" (level 33 or 55, freq 2 or 1), Socketed (3) and (S) "Speed" (level 37, freq 4), +30 % FR/W

Note that since headgear cannot get 4 sockets, "Jeweler's" will indeed give 3 sockets in this case, just like "Artisan's". We get the following odds,

• +2 ama, +30 % FR/W : Prob_P+S = (1/4)*({2*90} / 8 310)*({4*37} / 9 746) = 111 / 1 349 821 ~ 0.0082 %
• 3 sockets, +30 % FR/W : Prob_P+S = (1/4)*({2*33 + 1*55} / 8 310)*({4*37} / 9 746) = 407 / 7 362 660 ~ 0.0055 %

Rolling a magic Tiara with 3 sockets and +30 % FR/W is thus roughly just as hard as rolling a specific skiller (Grand Charm) with 12 % FHR.

You can easily conceive of other magic items and affixes. Simply crunch the numbers ... or have the affix calculator do it for you. Using the calculator is definitely less time-consuming and more convenient
when several affixes are desired and you want to know the odds of obtaining any of them. Besides, you have hopefully got at least a sense of how everything works by now.


Acknowledgments

• The Arreat Summit - Horadric Cube recipe [1], magic level, base item quality level [2]
• Baron's Bazaar - "Gta's Guide to all that is items", gambling, shopping [1]
• Basin D2 Wiki - "D2 Affix Level Chart", affix level formulae [2]
• inDiablo - affix tables, affix calculator (reference) [3]

Any comments, thoughts, questions ? Fire away ...

This post was edited by RaBBit3x on Oct 27 2008 05:21pm

That's more than I ever wanted to know about rolling items, but damn, good work.

There should be a "Faelwen" section in the stickies about Diablo 2 mechanics.

Much more than i ever needed.
GJ though.
Thx for the Guide

Really usefull info

nice

thanks very much info

Nice guide, nice lay out and I'm so pleased to see a friendly color for section titles etc. instead of big fat red otc ^^.

Nice job,1 question thou.Where do i look for scs if i want 20/5?Act 5 nm?