How Many El runes to Zod Maths

Beardozer wrote: 4 years ago

Either 1.4 thousand years, or 1.3 million years. Quite the spread there.

Well, I did check the math and it is definitely closer to 1.3m than 1.4k.

(3^20)^13 = 3^260 = 1.12596846425e+124

no recipe for El, so there are 20 runes that need 3 like runes to transmute, each rune is 3^1, 3^2, 3^3 ... 3^n respectively. Then we need each one of those for a Pul rune which is the new base in the 2fer formula, there are twelve 2fer runes to get to Zod but the second exponent is actually a 13 because (3^20)^1 gets you 1 Pul, (3^20)^2 gets you Um and so forth, so continuing to Zod you get the the exponent of 13. (3^20)^13 = 1.12596846425e+124.

EDIT: whoops I way overdid this problem and arrived to an incorrect answer. OP is right; 3^20 = El to Pul, 2^12 = Pul to Zod, multiply the two to get 14 trillion 281 billion 868 million 906 thousand 496 or about 48 times the estimated amount of stars in our galaxy, good luck!

aight now we need to know how many mules and accs you need to STORE all runes

Lets make a game " El Dumpster" to get this startet anyone is without plans for the next few decades?

BillyMaysed wrote: 4 years ago

Necroing this thread because math.

Necroing this thread because of necromancy.

Before proceding i want to present OP's math in what i hope is a more readable form.

For reference let's use this page as it contains and index for each rune. Let's denote #X a variable describing the index of a rune.

Take Runes #2 ( Eld) and #3 ( Tir).

• And Eld rune is 3^1 El runes and is #2
• And Tir rune is 3^2 El runes and is #3

From that we deduce that, up to a Pul rune, the number of El runes to get rune #X is:

3^(X-1) El runes

Pul is #21. So a Pul rune = 3^20 El runes

After that we need to multiply by powers of two. Similarly

• Um is 2^1 Puls and is #22
• Mal is 2^2 Puls and is #23

So, from Um to Mal, the number of Pul runes to get to rune #Y is:

2^(Y-21) Pul runes

Zod is #33 So putting both together:

3^19 * 2^(33-21) = 14,281,868,906,496

Or 14 trillion, 281 billion, 868 million, 906 thousand and 496 El runes.
Lastly, let's have some fun.

Okay, so what does it say to players? Not much. There are 33 runes in this game - no one is trying to cube El up to a Zod.

Let's take the Cow Level. Conveniently enough it is packed with lots hell cows and a regular (white) Hell Bovine can drop up to a Zod. So our parameter for drop chances will be a white Hell Bovine. Let's assume a reasonable 5 minute length for a cow run in players 7 and an average of 400 cows per lvl. So 5 minutes = 400 cows. Let's ignore the champion and unique cows for simplicity.

Let's call D the drop chance of a chosen rune from a single white cow. Consequently the chance for getting said rune a given run is about 400*D.

So the number of runs expected for a single drop is:

(400*D)^1

Let's pretend rune X has a 1 in 800 chance to drop from a white cow. Given our 400 cows/run:

(400/800)^1 = 800/400 = 2 runs per drop

Lastly, to get our time per drop in hours we multiply by 5 min and divide by 60 min/h.
As you can see the number of runes to cube grows exponentially but drop chances are a hell of a mess grows waaay slower and even with some non-linearities.

You would need 8 Gul runes to cube up to a Lo. That is about 23.06*8=184,48 hours of playtime, while a Lo rune is about "only" 49.24 hours. If cubing were to follow drop chance, a Lo rune would be about 2 Gul runes.

Lession learned? Cubing high runes is HIGHLY inefficient in terms of drop times. So only do it if you can get a lot of value out of it in the form of making that Runeword you've always wanted and/or you will get a lot of trade value out of it. Trading is highly non-linear

Once i get some more free time I'll post some graphics.

wow, almost exact number of El i found so far (too bad, did not pick all them)

ladydorcas wrote: 4 years ago

aight now we need to know how many mules and accs you need to STORE all runes

That is an easy answer since we know open slots for each character and shared stash.

Each stash tab is 100 slots, inventory is 40 slots. We can gain 8 slots (takes 2*2, gives 4*3) if we use cube. So, shared stash holds 300 slots and account with 20 characters holds exactly 2960 slots (with cube), so 3260 slots per account.

Divide needed runes by slots per account and we get =4,380,941,382.36 or 4,380,941,383 (nearly 4.4 billion) accounts if rounded up.

Also need same amount of cubes.

This is not conclusive answer though since we need to store gems, too.

So I'm a tad late on this post, but cubing an El--> Zod is a Googleplex.... more runes are required than there are spaces in the game...

Cubing an El rune all the way up to a Zod rune in Diablo 2 requires an astronomical number of steps! The math behind it is quite intense, but the final number comes out to 14.281 trillion El runes

Schnorki wrote: 1 year ago

Just for the nerdy hell of it, to round this off, cubing from El runes up to a single Zod requires:
[...] and 1x Flawless Emerald.

Hey... I have that Flawless Emerald, all I need now is the rest of the items

And a few mice. I also think you'll get your finger damaged by so many clicks

Banjo wrote: 4 years ago

lol right. there is appx three trillion seconds in a century. which means you could cube a trillion every century(assuming 3 secs per cubing). so to do the whole thing would require 1400 years. and thats just to cube them assuming three secs per cube which obviously is the most ideal scenario.

And the math has been screwed up since this post. There are about 3 billion seconds in a century, not 3 trillion. As we have all known since that time since someone dragged each of us individually to the musical Rent, there are 525,600 minutes in a single year,

525,600
* 60
31,536,000 seconds in a year

Then, 100 years of that is 3,153,600,000 seconds. Three trillion seconds is then about 100,000 years; 95,064 years, 96 days, 3 hours, 45 minutes, and 9.6509016 seconds to be precise. So not 1400 years of clicking, but roughly 1.33 million years of clicking. Literally, the length of time of 1400 years of clicking is actually just the rounding error of the time it would really take.

Put simply all Bots running D2 together would easily take one year.

Bounder wrote: 4 years ago

Here's a more interesting question: what rune is the lowest rune such that you could still cube up to Zod within an average human lifetime? You may assume you have a cube at hand and other players are dropping you the same rune right next to you so that your only job is to pick them up for transmutation. Let's also say they drop you the right gems as you need them.

Assuming 3s per cubing and runes + gems dropped at cubber's feet:

Thul = 68.98 years, 1 human life time

Or, 1 botter with 19,683 accounts would need to wait 68.98 years (with additional accounts for finding the runes and managing inventory)


New fun fact, cubeing from El will require about 6.5 million mice, assuming 20mil average click life of a mouse

Logitech and Blizzard are already monitoring this thread. Probably already discussing whether El should only drop from heralds.

This of course all assumes that the Horadrim designed the cube to operate indefinitely.. what if the Cube is only designed (or programmed) to carry out 100,000 cubing operations before becoming inert?