Do rods and artifact effects stack?

I know there's a lot of questions about whether or not runes stack but I haven't really seen one about this: If you have a rod that says improves skill recharge rate (20% chance) and an artifact that also says the same thing does that mean you have a 40% chance of improved ksill recharge rate?

When it says 20% chance of improved skill recharge. It is 20 out of 100 chance that you will get 33% improved recharge rate (not sure about 33%, too lazy to check it).

So with 20%+20%, you will have 40% of the time improved recharge rate.

wrong. they do not stack. They are SEPERATE chances. So your wand has a 20% chance of faster skill recharge. And your focii ALSO has a 20% chance of faster skill recharge. However, you DO have the chance that they will both occur at once, but that is like 1/100 chance. EACH item has a SEPERATE 20% out of 100% chance to occur.

That make sense? So your chances do NOT become 40% out of 100% of faster skill recharge. Each chance work seperatly, but like i said there is that small chance that both chances occur at once, which would give you that stacked effect of chances...

However, this is all assuming that 2x (improves skill recharge rate) actually stats 2gether. This effect has not been confirmed yet...

well, however you look at it 20% chance + 20% chance is 40% chance, even if they work seperatly, you still technically get 40% chance one of the two will work

Well, statistics and probabilities are a fun subject. Technically, I don't think it's a 40% probability because for the very reason, they DON'T stack. IE, the game doesn't add the 20 + 20 then make a SINGLE roll. It actually makes TWO separate rolls to determine if the 20% applies. So technically, you don't have a full 40% chance, you have TWO 20% chances which are not really the same.

It's not like the lottery. For example, you could say if the lottery had 100 balls. And each time they drew a ball, that would increase your odds of getting the next one because there was now 1 fewer numbers to pick from. Here, that doesn't happen.

It's complicated.

There was a very complicated thread here on Guru about four or five months ago when Ensign, I think, was discussing this exact type of subject, probabilities and % chances and how they interact in situations such as this where multiple tries are made with the same % success rate. Maybe I can find that post.

Your actual chance, formula wise, of having improved skill recharge is:

(20%) + (20%) - (20% * 20%)

Or:

36% chance of improved skill recharge. Pretty close.

In a word: no.

This is because the seconds 20% chance may "cross-over" the first, thus you get:

Success:
20% (first success) * 80% (second one failing) = 16%
80% (first failing) * 20% (second one succeeding) = 16%
20% (first success) * 20% (second one succeeding) = 4%
Total = 36%

Failure:
80% (first failing) * 80% (second one failing) = 64%


Bottom line: 32% chance of getting one, 4% of getting both (whether this makes the recharge even faster is another question), 64% chance at getting neither.