The Chances of Making Two 5% Failures

[Mayonnaise]

I was just curious, what's the mathematical chance of this?


I just failed two 95% chances in a row!

[Zapnl]

5%/100%=0,05
0,05x0,05 = 0,0025
0,0025x100%= your chance is 0,25%, or 1 in 400

[Yellena]

Random number generators aren't really random.
I often notice this enchanting and also by playing a DC mage. Sometimes numbers "locks", and enemies gets like, two, three and sometimes even four "20s" in a row. That circle repeats itself and I am not sure if it's related to server reset + character, or character + login "slot".
I am still experimenting to find a pattern.
One day tought, I was trying to delevel and my enchanting "locked" into a 20. Made two 5% out of four or so impossible enchantments.

[Lorkas]

Of course it isn't truly random (is anything? we don't know for sure), but the important thing to realize about events like that is that in a given trial, it's very unlikely, but when we are constantly rolling dice hundreds-to-thousands of times, events as improbable as these become virtually guaranteed to happen at some (unpredictable) point.

A level 30 character has 600 crafting points per RL day to play with. If someone was dedicated to using every single one of these available CPs, they could expect to see 2 1s in a row roughly 3 times every 2 days.

3 1s in a row (1-in-8000 event) could happen on average every 13 days for such a player, and 4 1s in a row (a 1-in-160000 event) on crafting is still more frequent than once per year for just this one character. Considering the large number of characters (and therefore large number of rolls) completed by the server every day, it is not at all that amazing that we have seen a 1-in-20 event happen 3 or 4 times in a row.

[msterswrdsmn]

It happens a lot. And I mean, a LOT. I can't even begin to tell you how many 95% or 90% chance items i've blown up on the first enchantment attempt.

[Dinosaur Space Program]

My record is six 95%'s in a row.

[furryn]

My record is six 95%'s in a row.

Funny thing about that is that it's (1/20)^6 = 0.000000016 or 1 to 64000000

Anyhow, I'd like to offer what insight i can on this, programatically speaking.
Firstly:

"Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin."

This relates to the fact that you can put as many variables in as you like, but by the end of the day, the number will be predictable - non random (or pseudo random, as it's usually put). If you don't believe me, go ahead and try to make an equation that, arithmetically, generates random numbers.

The solution for when you truly want random numbers, is that you need something from "the outside" world to relate to. There is hardware for this, that picks up things like background radiation and such, but when it comes to games, and often programs that doesn't REALLY need random numbers, you settle for pseudorandom, it often works by:

- Generating an object called a "Random" containing the current time (taken from your PC or the internet, this is all language dependant, and will differ, but it's a commonly used method)
- An equation is used, that uses the "time" as a seed, and then produces a number, based on a certain interval, like for 1d6, it'd be 1 to 6.
- The next time the code is called, the equation is moved about a bit, and it might be using a different number (again language dependant) of the number in the current time, to generate the next number.

The product of the issue is when you observe something incredibly unlikely. Many of these "Random libraries" also have issues with creating "new Randoms" if they are created too quickly in succession, the seed will be at least almost identical, and therefore it will be the same case with the produced numbers.

Other programmers might have something to add, or correct. I often have a difficult time explaining these things to non-programmers.

[Mithreas]

I don't have logs for how often the enchantment basin is used, but say we have 500 players a week who average using it 3 times each (obviously some will do a lot more than this, some will do very little).

That's 1500 attempts per week. A 1 in 400 event should happen multiple times per week

[TeeHeeTummyTums]

(inversely) The chance for succeeding after two 5% rolls is something like 7%. To get about 50%, it's 14 rolls. I can figure exact numbers if you like.

Edit:
Guess I was a little off on the first one, but here's the numbers anyway. All the numbers are + or - 1%, didn't bother rounding.

1= 5%
2= 11%
3= 15%
4= 19%
5= 23%
6= 27%
7= 31%
8= 34%
9= 36%
10= 41%
11= 44%
12= 46%
13= 49%
14= 52%
15= 54%
16= 56%
17= 59%
18= 61%
19= 63%
20= 65%

[God In Action]

1 in 400 sounds unlikely, but in fact it isn't at all.

Consider the sheer number of dice rolls made in the entire server, between all PCs and NPCs. Millions upon millions of rolls. Managing to roll 2 1s in a row, or even 4 or 5 20s, would be unbelievable if you only had say, 5 chances of the dice roll to do it. Out of millions of rolls, you eventually see rolls which look like a pattern when in fact it is just an unlikely event having enough chances to happen that it becomes a likely event.