But what chance of no fail in 50 tries?

[Obina]

We had a brief question on the pottery board that may be of general interest. It was "Oh my, I failed 5 out of 38 in the kiln, it can't really be 5%. Hmm perhaps the RNG is broken."

So how likely is it to fail on 5 out of 38 if the triv is 5%? Yes they are hopefully fixing the Kiln thing, but low failure items will remain a part of tradeskilling.

We can all understand that if there is a 5% chance of failure, we expect to fail 1 in 20. But what are the odds of failing more or less than this? And how often will we fail exactly once?

The right equation turns out to be pretty basic statistics. That's because there are only 2 things that can happen, success and failure. It involves a few factorials. I'll write it in Excel code since that is where I played with it if you want to try it yourself. It is

=(FACT(20)/FACT(20-N)*(0.95^(20-N))*(.05^N))/FACT(N)

Just make N the number of times you "expect" to fail. And of course you can make the 20 any number of times you want to make an item.

So what are the results? I ran making for 10 items, 20 items, and 50 items. For ten items, there is a 60% chance you will not fail, 31% chance you will fail once, 7% chance you will fail twice, 1% chance you will fail 3 times and .1% chance you will fail 4 times. The numbers look small, but think of how many combines there are by all players. Some poor soul fails 4 out of ten on a trivial item every day! So when it happens to you, we offer our /hugs, but it does not mean the RNG is broken, or the triv is wrong.

For 20 it is 0=35%, 1=37%, 2=19%, 3=6%, 4=1.3%, and 5=.22%
For 50 it is 0=7.7%, 1=20.2%, 2=26.1%, 3=22%, 4=13.6%, 5=6.6%, 6=2.6%, 7=.86%.

This goes the other way too. If you try an uber item 20 times, there is still a 35% chance you will not get any joy.

Hope a few of you find this of interest. And sorry if this has been covered before, I did not see it in a brief search.

BTW, the chance of firing 38 things and getting 5 failures is

[(38!/33!) x (95%^33) x (5%^5)] / 5! = 2.8%

Obina R

[Boleslav]

Sometimes knowing the probability of getting exactly 5 failures out of 38 tries is important. More often, you want to know the probability of getting less than 5, or more than 4 failures. In this case, you need to find the probability of getting 0,1,2,3,and 4 failures and subtract that from 1.

Probability of getting 0 – 4 failures out of 38 way trivial attempts = 96%

So there is a 2.8% chance of getting 5 failures and a 1.2% chance of getting more than 5 failures. Which would indicate leaving you without joy 4% of the time after such a run of attempts.

Boleslav Forgehammer
Paladin of Brell in his 62nd Campaign
E'ci – Sacred Destiny

[Luneward]

Personally I feel applying this sort of math is pointless. You can calculate probabilities of what chance you will to have to fail a certain number of times in any lot, but unless you're talking in the 1000s of combines it won't ever manifest perfectly.

Not to mention it doesn't change the fact that no matter how many succesful combines you have, it doesn't change the fact that the next combine will always have a 5% chance to fail. It doesn't matter if you had 4 failures in a row. The next one still has at least a 5% chance to fail.

Also, we're comparing a perfectly random number to probability. We're talking about a RNG, which are never random. All a RNG number is take a 'seed' number from a source (usually a time clock of some source) and sticks it into an equation. So technically the number isn't random. It's one of the reasons the RNG seems so flaky sometimes. You are on a bad stretch of seed numbers.

[Obina]

Fair points. This math doesn't change the chance of the next combine. It is "same as it ever was".

But to defend the RNG, I've heard many times how it isn't really random, any more than any seed-based RNG is. But IMHO I think this difference is theoritical only and does not effect the game. That's because of math like this that shows that real random numbers have all the quirkiness of the game RNG.

When one notices it is streaky, and concludes the RNG is less than perfect, it is the opposite. Real random numbers are streaky. For a real 1 in 20 event, it still sometimes happens 6 or 7 times in 20. Or happens 4 times in a row etc. When this happens, people say the RNG is broken. In fact this happens because it is working.

Many tradeskillers (myself included) would be happier if the RNG had a "fairness" step. Like if you have made 60 non trivial items with no skill up, it sort of remembers, and you get one. But it doesn't work like that. In fact if one looks at all the evidence on this board - praise of the good luck, comments on normality, and primal screams on the unfairness - there is every reason to believe the RNG is very good indeed.

Obina R