Theory on refining (To end all 'how much suns do i need topics')

msTeeQ · 01:41 AM

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Like I stated in a previous topic about my theory on refining I made a little simulator which shows you how random upgrade successes can be.

My post:

Quote:

My theory, which probably matches how it really works:

We have 2 different values here or 2 numbers, however you wanna name it.

Say, value 1 is the range of value 2. Value 1 always goes between 0 and 100. Say, 10-20-30-40, etc. etc.
Now, value 2 is a random number between 0 and 100.

Alright, now we have our 2 values.
You want to upgrade a +1 weapon to +2, then the first number has a value of 10. and the second is just (like i said) a random number between 0 and 100.

If Number2 is bigger than Number1 Then the upgrade will succeed.

Everytime you upgrade a weapon higher, the first number will increase by 10 (90 max).

So lets say, you're going from +7 to +8, the first number has a value of 70. Take the random number if its above 70, it'll succeed. Is it below 70 (in-range of number1), it'll fail.

So from +7 to +8 has a 30% success chance. (which is compared to other flyff refines, alot).
But infact, create a program in any basic programming language;

You'll most likely have a "rand" or "rnd" option. Print out the result of "rnd(0,100)", it'll return a random number between 0 and 100, you'll be surprised how small the chance is to reach above a certain point.

Sorry for the long and weird story, I tried to explain it as simple as I could ;x

Simulator:
http://212.187.74.244

Just keep refreshing the page to see the amount of tries change.
I tried to make this as accurate as possible like how it is ingame.

So, basically what my point is; If people say, you need 100 sunstones minimum to get from +9 to +10, it's bullcrap. You cannot say which amount of things you need to get success from something which is totally random.

P.S. That link is redirected to my own computer so it might not work 24/7.
P.S.S I'll upload this thing to a normal webhost later.

I'll try to add some more to the page later, like chances of success etc.etc.

Winged · 02:10 AM

Quote:

Upgrade from 9 to 10....Success after 524 tries. (908 ~ 1000)

dot dot dot.
sucks for the person that takes that many times. >>;

Edit: I beat my own record

Quote:

Upgrade from 9 to 10....Success after 765 tries. (945 ~ 1000)

**ItsReiko** · 05-01-2008, 02:25 AM

Quote:

FlyFF Refining Simulator

# Upgrade from 0 to 1....Success after 1 tries. (147 ~ 1000)
# Upgrade from 1 to 2....Success after 1 tries. (418 ~ 1000)
# Upgrade from 2 to 3....Success after 4 tries. (203 ~ 1000)
# Upgrade from 3 to 4....Success after 2 tries. (388 ~ 1000)
# Upgrade from 4 to 5....Success after 1 tries. (562 ~ 1000)
# Upgrade from 5 to 6....Success after 7 tries. (703 ~ 1000)
# Upgrade from 6 to 7....Success after 4 tries. (791 ~ 1000)
# Upgrade from 7 to 8....Success after 36 tries. (715 ~ 1000)
# Upgrade from 8 to 9....Success after 4 tries. (956 ~ 1000)
# Upgrade from 9 to 10....Success after 5 tries. (928 ~ 1000)

I shouldve done it in game

Edit: nvm

Quote:

FlyFF Refining Simulator

# Upgrade from 0 to 1....Success after 1 tries. (370 ~ 1000)
# Upgrade from 1 to 2....Success after 1 tries. (500 ~ 1000)
# Upgrade from 2 to 3....Success after 2 tries. (426 ~ 1000)
# Upgrade from 3 to 4....Success after 8 tries. (424 ~ 1000)
# Upgrade from 4 to 5....Success after 3 tries. (575 ~ 1000)
# Upgrade from 5 to 6....Success after 2 tries. (868 ~ 1000)
# Upgrade from 6 to 7....Success after 4 tries. (634 ~ 1000)
# Upgrade from 7 to 8....Success after 20 tries. (770 ~ 1000)
# Upgrade from 8 to 9....Success after 1 tries. (813 ~ 1000)
# Upgrade from 9 to 10....Success after 1 tries. (926 ~ 1000)

Edit: 2 ok I read your theory, but its too bad the success rates are actually lower than what you say rofl

guorbatschow · 04:38 AM

so you are saying the probability for +0 to +1 is 0.9, +1 to +2 is 0.8 etc

p(n) = 1 - n/10

right?

then there would be one small flaw:
either
1) the first number for +0 to +1 is 0, then the first upgrade will succeed always, or
2) the first number for +9 to +10 is 100, then it will always fail, or
3) you cap at 90 for the second number, which means +8 to +9 has the same probabilty as +9 to +10

from what i saw, i guess you implemented the first option.

the expected value for this would be, since this is a geometric sequence, 1/p
and variance would be (1-p)/p^2

X (from)	X+1 (to)	p(X) (chance)	E(X) (average)	∑(E(X)) (sum)	Var(X)	s(X)
0	1	1.0	1	1	0	0
1	2	0.9	1.1111	2.1111	0.1235	0.3514
2	3	0.8	1.25	3.3611	0.3125	0.6603
3	4	0.7	1.4286	4.7897	0.61225	1.0238
4	5	0.6	1.6667	6.4564	1.1111	1.4695
5	6	0.5	2	8.4564	2	2.03944
6	7	0.4	2.5	10.956	3.75	2.8124
7	8	0.3	3.3333	14.289	7.7777	3.9607
8	9	0.2	5	19.290	20	5.9739
9	10	0.1	10	29.290	90	11.211

X is the random variable. upgrade goes from +X to +(X+1)
p(X) is the single probability for success for the upgrade from X
E(X) is the expected value (average) for the amount of attempts and is computed by 1/p
∑(E(X)) is the amounted number of attempts from +0 up to +(X+1) and is calculated recursively as ∑(E(X)) = ∑(E(X-1)) + E(X) and ∑(E(0)) = E(0)
Var(X) is the variance, which happens to be the square of the standard deviation. calculated by sum(n=0 to infinity) p(X)*(X-E(X)) = (1-p)/p^2
s(X) is the summed up standard deviation for the upgrade from 0 to X+1 and calculated as sqrt(sum(n=0 to X) Var(X))

29.290 from +0 to +10 and 14.289 for +0 to +8 (~57 attempts for a +8 set)

maybe a bit too low for the +8 set?

using chebychev's inequality it means that the probability for using more than 100 attempts for a +8 set is lower than 10%

edit: had some miscalculations, fixed.

defiantforce · 05-01-2008, 02:33 AM

Nice work, for a theory that has probably quite a high grounding in what is the real case.
Plus it's fun trying to get higher than 700 fails on +10

guorbatschow · 05-01-2008, 03:19 AM

if we gather more empirical data i could run a chi-square test to confirm the hypothesis :P

Elie Fiore Inverse · 05-01-2008, 03:54 AM

I hate math. My brain is burning at the sight of all those numbers. Not really.

I'm just going to buy suns and spros and try and try until eventually I manage to success. *shrugs*

Pikmario · 05-01-2008, 04:53 AM

Quote:

# Upgrade from 0 to 1....Success after 1 tries. (22 ~ 1000)
# Upgrade from 1 to 2....Success after 3 tries. (174 ~ 1000)
# Upgrade from 2 to 3....Success after 1 tries. (717 ~ 1000)
# Upgrade from 3 to 4....Success after 1 tries. (359 ~ 1000)
# Upgrade from 4 to 5....Success after 5 tries. (453 ~ 1000)
# Upgrade from 5 to 6....Success after 7 tries. (595 ~ 1000)
# Upgrade from 6 to 7....Success after 6 tries. (795 ~ 1000)
# Upgrade from 7 to 8....Success after 12 tries. (941 ~ 1000)
# Upgrade from 8 to 9....Success after 29 tries. (825 ~ 1000)
# Upgrade from 9 to 10....Success after 819 tries. (906 ~ 1000)

Nais.

Eternalmagus · 05-01-2008, 05:06 AM

Upgrade from 0 to 1....Success after 1 tries. (41 ~ 1000)
Upgrade from 1 to 2....Success after 1 tries. (876 ~ 1000)
Upgrade from 2 to 3....Success after 11 tries. (886 ~ 1000)
Upgrade from 3 to 4....Success after 2 tries. (408 ~ 1000)
Upgrade from 4 to 5....Success after 3 tries. (804 ~ 1000)
Upgrade from 5 to 6....Success after 9 tries. (840 ~ 1000)
Upgrade from 6 to 7....Success after 13 tries. (770 ~ 1000)
Upgrade from 7 to 8....Success after 35 tries. (736 ~ 1000)
Upgrade from 8 to 9....Success after 13 tries. (813 ~ 1000)
Upgrade from 9 to 10....Success after 128 tries. (952 ~ 1000)

First try :<

Upgrade from 0 to 1....Success after 1 tries. (4 ~ 1000)
Upgrade from 1 to 2....Success after 1 tries. (307 ~ 1000)
Upgrade from 2 to 3....Success after 5 tries. (340 ~ 1000)
Upgrade from 3 to 4....Success after 1 tries. (459 ~ 1000)
Upgrade from 4 to 5....Success after 4 tries. (480 ~ 1000)
Upgrade from 5 to 6....Success after 3 tries. (600 ~ 1000)
Upgrade from 6 to 7....Success after 3 tries. (667 ~ 1000)
Upgrade from 7 to 8....Success after 54 tries. (740 ~ 1000)
Upgrade from 8 to 9....Success after 22 tries. (905 ~ 1000)
Upgrade from 9 to 10....Success after 6 tries. (916 ~ 1000)

:3

pederz · 05:50 AM

hey msTeeQ could you PM me the asp/source code... trying to simulate it but keep getting 29.3 in average of suns needed to upgrade from +0 to +10, which seems unlikely (compared to your simulator).

guorbatschow · 05:25 AM

i think the random generator he is using is flawed =x
or he could be initializing the random generator everytime he wants a random number using current time. and since current time doesnt change as fast, he gets a lot of same numbers in a row.

the numbers dont correspond to his theory.

29.3 as average is correct, as my table states.

msTeeQ · 05-01-2008, 05:34 AM

@guorbatschow:

Nice table there. The flaw you talked about doesn't apply to my simulator/script. I made the first range number 0 so from +0 to +1 always succeeds, and this way +9 to +10 has a chance of 10% success.

Like I said, I tried to make this as accurate as possible, but since we all dont have the official caluclations of the refining, we can't really know.

I'm not using a timer based randomizer btw. Although, my randomizer gives me high numbers too often, so I used 2 different randomizers. It all works a bit weird, but these methods gave me the best results.

I'm not at home right now, but I'll post the source tonight. (It's plain PHP btw)