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Hey everyone! Sorry if I'm posting this in the wrong forum, but I really want to know the odds for this one.

I'm not very good at math so it would be awesome if someone could calculate this for me.

So I have this SoJ which I must have enchanted over 30 times by now and still no arcane damage to be seen. There is 16 different stats in the "pool" and as we all know I get the option to choose from 2 new ones every time I enchant it. Now, I know that there probably is different chance to get different stats, like I have gotten vitality x2 quite some times and stuff, but let's count that out to make it simpler (and more QQ-worthy ;p).

So to sum it up, what is the chance (roughly) that after 30 enchants, arcane damage is yet not to be seen. Serious question, an answer would be much appreciated!

(15/16)^30 = 0.144 so rougly 15%. If you try five times more you get (15/16)^35 = 0.104 so rougly 10% chans of you not getting the stat you want after 35 trys.

(15/16)^30 = 0.144 so rougly 15%. If you try five times more you get (15/16)^35 = 0.104 so rougly 10% chans of you not getting the stat you want after 35 trys.

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(15/16)^30 = 0.144 so rougly 15%. If you try five times more you get (15/16)^35 = 0.104 so rougly 10% chans of you not getting the stat you want after 35 trys.

if it was 15% at the start, it will remain 15% all the time.

Roll a dice, you have a 1 in 6 chance of rolling a 4, roll the dice again, you still have a 1 in 6 chance of rolling a 4, Roll the yet again, you still have a 1 in 6 chance of rolling a 4.

I'm quite sure the chance is actually a lot lower. None of you factor in that you get TWO new choices with every enchant. Since the results are independent (= you can get the same affix twice), we can just regard every enchant as two independent events, giving us a total of 2*30 enchanting events, each with a 15/16 chance to not roll the desired affix.

So, it should be
(15/16)^(2*30) = 0.0208102158.
Which is more like 2.1%.

Sigma:
Guess that's one way to look at it, but consider this: you roll a dice 30 times, what's the chance that you wont get a 4 in any of those rolls? That's more like the question I was asking.

Angzt seems to be on the money here. 2 % is a little bit depressing but as I mentioned before, stats like vitality probably have a higher chance of rolling so in reality it should be higher, but yes that seems to be the correct answer to my question. :p

Sigma:
Guess that's one way to look at it, but consider this: you roll a dice 30 times, what's the chance that you wont get a 4 in any of those rolls? That's more like the question I was asking.

Angzt seems to be on the money here. 2 % is a little bit depressing but as I mentioned before, stats like vitality probably have a higher chance of rolling so in reality it should be higher, but yes that seems to be the correct answer to my question. :p

The amount you roll does not matter, you can "in theory" roll a dice a million times and never roll the number your looking for, it will always be a 1 in 6 chance.

The odds of rolling Arcane% damage would be 1 in 16. Seeing how you get 2 options when rerolling, it becomes a 1/8 chance. So over 30 different rerolls it would be (1/8)^30 but seeing how it didn't roll arcane % damage when you first picked up the item (a.k.a it's original stat roll) it is (1/8)^31. (1/8)^31=1.009742e-28 %.... so 28 zeros after the decimal point =P

P.S- not sure why people are saying it is (15/16)^60 that is not how you calculate the odds.

The odds of rolling Arcane% damage would be 1 in 16. Seeing how you get 2 options when rerolling, it becomes a 1/8 chance. So over 30 different rerolls it would be (1/8)^30 but seeing how it didn't roll arcane % damage when you first picked up the item (a.k.a it's original stat roll) it is (1/8)^31. (1/8)^31=1.009742e-28 %.... so 28 zeros after the decimal point =P

P.S- not sure why people are saying it is (15/16)^60 that is not how you calculate the odds.

Uhm, not trying to sound too much like a smartass but there are at least 4 mistakes in that post...

Rollback Post to RevisionRollBack

I post guides and sometimes news around these parts. Also, I'm on Twitter.

I only made one critical mistake after reading what i had done, and it was a big one. However I don't think I was wrong in saying that (15/16)^60 is incorrect. Arcane % damage is a 1/16 chance, seeing how you choose between 2 options during each reroll, your chances of getting arcane % damage are doubled. Therefore, it is a 2/16 or 1/8 chance. This means that the odds of rolling anything else is 7/8. To roll any other stat 30 times in a row would be (7/8)^30. (7/8)^30=0.01820713409 %

P.S- didn't mean to sound like a snob, sorry about the mistake, but im pretty sure this makes more sense after rereading...i could still be wrong so let me know what you think.

You can't just multiply 1/16 by 2 to get the chance that at least one of the two possible affixes is the desired one.

You have four possible events for the affixes to roll on a single enchant:
(1) desired & desired -> 1/16 * 1/16 = 1/256
(2) desired & undesired -> 1/16 * 15/16 = 15/256
(3) undesired & desired -> 15/16 * 1/16 = 15/256
(4) undesired & undesired -> 15/16 * 15/16 = 225/256

Now, since you want at least one desired affix all events except for (4) are what you're looking for. The sum of (1) + (2) + (3) is 31/256, which is the same as 1 - (4) = 256/256 - 225/256 = 31/256 since (1) to (4) all add up to 1.
Hence, the chance to roll at least one desired affix on a single enchant is 1 - (15/16 * 15/16) = 1 - (15/16)^2 = 31/256.

Another way to look at it is to ignore that you get two choices with every enchant and instead view every enchant as two independent enchanting events, each with a 15/16 chance to not get the desired affix, which will lead you straight to 1 - (15/16)^2 as the solution for a double-enchanting event.

While I guess that the following is clear to you, just for completeness:
Of course, while we want to get a desired affix, the original question was how likely it is NOT to get one after 30 enchants. This is why we calculate ((15/16)^2)^30 = (15/16)^(2*30) = (15/16)^60 and not 1 - (15/16)^60.

Edit: Your other two mistakes weren't really related to the actual calculation.
One was that you just added 1 to the power at the end to account for the basic rolls. Since you only added it to the 30, you suddenly had two rolls to choose from (like you did with the enchanting) when the item rolled initially, according to your calculation.
The other was even more minor: 1e-28 only has 27 zeroes after the decimal point since 1e-1 = 1 * 10^(-1) = 1 * 1/10 = 0.1 has no zeroes after the decimal point.

Sigma:
Guess that's one way to look at it, but consider this: you roll a dice 30 times, what's the chance that you wont get a 4 in any of those rolls? That's more like the question I was asking.

Angzt seems to be on the money here. 2 % is a little bit depressing but as I mentioned before, stats like vitality probably have a higher chance of rolling so in reality it should be higher, but yes that seems to be the correct answer to my question. :p

The amount you roll does not matter, you can "in theory" roll a dice a million times and never roll the number your looking for, it will always be a 1 in 6 chance.

Still a silly little mathematical law called the "Law of Averages." Probably not important

This makes much more sense to me now after you showed the process of how you squared the odds of undesirable traits and then used that number to the exponent of how many trials took place. I knew that the 1 - (15/16)^30 was incorrect, similar to what I had done in my first response but I'm glad that you clarified how you got the answer. Thanks a bunch!

I'm not very good at math so it would be awesome if someone could calculate this for me.

So I have this SoJ which I must have enchanted over 30 times by now and still no arcane damage to be seen. There is 16 different stats in the "pool" and as we all know I get the option to choose from 2 new ones every time I enchant it. Now, I know that there probably is different chance to get different stats, like I have gotten vitality x2 quite some times and stuff, but let's count that out to make it simpler (and more QQ-worthy ;p).

So to sum it up, what is the chance (roughly) that after 30 enchants, arcane damage is yet not to be seen. Serious question, an answer would be much appreciated!

Getting your question answered will NOT help your mood. In any way.

Edit: 15%? Well thats not too bad then. ^^

Roll a dice, you have a 1 in 6 chance of rolling a 4, roll the dice again, you still have a 1 in 6 chance of rolling a 4, Roll the yet again, you still have a 1 in 6 chance of rolling a 4.

So, it should be

(15/16)^(2*30) = 0.0208102158.

Which is more like 2.1%.

I post guides and sometimes news around these parts. Also, I'm on Twitter.

Guess that's one way to look at it, but consider this: you roll a dice 30 times, what's the chance that you wont get a 4 in any of those rolls? That's more like the question I was asking.

Angzt seems to be on the money here. 2 % is a little bit depressing but as I mentioned before, stats like vitality probably have a higher chance of rolling so in reality it should be higher, but yes that seems to be the correct answer to my question. :p

P.S- not sure why people are saying it is (15/16)^60 that is not how you calculate the odds.

I post guides and sometimes news around these parts. Also, I'm on Twitter.

P.S- didn't mean to sound like a snob, sorry about the mistake, but im pretty sure this makes more sense after rereading...i could still be wrong so let me know what you think.

took me 48 rerolls, just 18 more! :p

Syldra - S1/S8/S10 Wizard - http://eu.battle.net/d3/en/profile/TwlJoch-2650/hero/165214

Syndragosa - S8 DH - http://eu.battle.net/d3/en/profile/TwlJoch-2650/hero/84195597

Akara - S1/S11 Crusader - http://eu.battle.net/d3/en/profile/TwlJoch-2650/hero/38654558

You have four possible events for the affixes to roll on a single enchant:

(1) desired & desired -> 1/16 * 1/16 = 1/256

(2) desired & undesired -> 1/16 * 15/16 = 15/256

(3) undesired & desired -> 15/16 * 1/16 = 15/256

(4) undesired & undesired -> 15/16 * 15/16 = 225/256

Now, since you want at least one desired affix all events except for (4) are what you're looking for. The sum of (1) + (2) + (3) is 31/256, which is the same as 1 - (4) = 256/256 - 225/256 = 31/256 since (1) to (4) all add up to 1.

Hence, the chance to roll at least one desired affix on a single enchant is 1 - (15/16 * 15/16) = 1 - (15/16)^2 = 31/256.

Another way to look at it is to ignore that you get two choices with every enchant and instead view every enchant as two independent enchanting events, each with a 15/16 chance to not get the desired affix, which will lead you straight to 1 - (15/16)^2 as the solution for a double-enchanting event.

While I guess that the following is clear to you, just for completeness:

Of course, while we want to get a desired affix, the original question was how likely it is NOT to get one after 30 enchants. This is why we calculate ((15/16)^2)^30 = (15/16)^(2*30) = (15/16)^60 and not 1 - (15/16)^60.

Edit: Your other two mistakes weren't really related to the actual calculation.

One was that you just added 1 to the power at the end to account for the basic rolls. Since you only added it to the 30, you suddenly had two rolls to choose from (like you did with the enchanting) when the item rolled initially, according to your calculation.

The other was even more minor: 1e-28 only has 27 zeroes after the decimal point since 1e-1 = 1 * 10^(-1) = 1 * 1/10 = 0.1 has no zeroes after the decimal point.

And now I do, indeed, sound like a smartass.

I post guides and sometimes news around these parts. Also, I'm on Twitter.

http://www.diablofans.com/forums/diablo-iii-general-forums/diablo-iii-general-discussion/83779-list-of-percentages-of-re-enchanting-a-certain