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+--- Thread: Scroll probability formula (/showthread.php?tid=23874)
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Scroll probability formula - Kabanaw - 2010-03-24
This is the formula to determine the chance of getting a certain number of scrolls to work a certain number of times. It's not technically a MapleStory formula since it can be applied to pretty much anything with a success rate, but you would use this to find the chance of multiple scrolls working.
S^n*F^(t-n)*t!/(n!*(t-n)!) *100%
S= success rate
F= fail rate
n= number of times it succeeds
t = total number of tries
So an example, what's the chance of landing 7 60% scrolls on an overall?
.6^7*.4^(10-7)*10!/(7!*(10-7)!) *100%
there is a 21.599% chance of landing 7 60% scrolls. To find the chance of 7 or more scrolls working, you need to use the formula again for 8, 9, and 10 working and add the chances together.
Scroll probability formula - Kortestanov - 2010-04-12
We just learned that formula in math class today, were learning probabilities\combinatorics, lol
Scroll probability formula - Kabanaw - 2010-04-12
Kortestanov Wrote:We just learned that formula in math class today, were learning probabilities\combinatorics, lol
Hah, I just kind of came up with it myself after thinking about it for a while. I find it pretty useful.
Scroll probability formula - Johnnywup - 2010-04-13
couldnt you just 60^7 divided by 100^7?
Scroll probability formula - Sn1perJohnE - 2010-04-13
Since this falls in probabilities, you could find the success of the for 10 in a row by (iirc) taking the probability of 10, with an success rate or 60% (.6) and like subtract it from the rate of passing 9. Not sure, as I dont really care for the stats class im in, just as long as I pass it.
Scroll probability formula - Fumni - 2011-02-05
I hope you guys don't mind me adding to this and bumping this topic.
Scroll probability can be easily calculated using binomial distribution, in particular, the probability mass formula "
![[Image: 68d0ba6ef5dfb8c654702c3290128b10.png]](http://upload.wikimedia.org/math/6/8/d/68d0ba6ef5dfb8c654702c3290128b10.png)
." In this case, P represents the percentage rate (or the percentage the scroll is,) N is number of attempts (or number of slots in equipment) and K is the total number of successes (or landed scrolls.) The first part (n,k) or n chooses k, is the binomial coefficient, which can be calculated with the formula "
![[Image: a12375b9f5661262cf951dc829a33262.png]](http://upload.wikimedia.org/math/a/1/2/a12375b9f5661262cf951dc829a33262.png)
". Using Excel, I made some basic chart graphics to visualize the probability mass function. The following scenarios are for an overall with 10 slots, using 10%, 30%, 50%, 60% and 70% scrolls.
Success rate (10%)
| number of successes | percentage rate |
|---|---|
| 0 | 34.87% |
| 1 | 38.74% |
| 2 | 19.37% |
| 3 | 5.74% |
| 4 | 1.12% |
| 5 | 0.15% |
| 6 | 0.01% |
| 7 | 0.00% |
| 8 | 0.00% |
| 9 | 0.00% |
| 10 | 0.00% |
Spoiler
![[Image: pmf10scroll10.jpg]](http://img17.imageshack.us/img17/6898/pmf10scroll10.jpg)
Success rate (30%)
| number of successes | percentage rate |
|---|---|
| 0 | 2.82% |
| 1 | 12.11% |
| 2 | 23.35% |
| 3 | 26.68% |
| 4 | 20.01% |
| 5 | 10.29% |
| 6 | 3.68% |
| 7 | 0.90% |
| 8 | 0.14% |
| 9 | 0.01% |
| 10 | 0.00% |
Spoiler
![[Image: pmf10scroll30.jpg]](http://img713.imageshack.us/img713/2423/pmf10scroll30.jpg)
Success rate (50%)
| number of successes | percentage rate |
|---|---|
| 0 | 0.10% |
| 1 | 0.98% |
| 2 | 4.39% |
| 3 | 11.72% |
| 4 | 20.51% |
| 5 | 24.61% |
| 6 | 20.51% |
| 7 | 11.72% |
| 8 | 4.39% |
| 9 | 0.98% |
| 10 | 0.10% |
Spoiler
![[Image: pmf10scroll50.jpg]](http://img225.imageshack.us/img225/8710/pmf10scroll50.jpg)
Success rate (60%)
| number of successes | percentage rate |
|---|---|
| 0 | 0.01% |
| 1 | 0.16% |
| 2 | 1.06% |
| 3 | 4.25% |
| 4 | 11.15% |
| 5 | 20.07% |
| 6 | 25.08% |
| 7 | 21.50% |
| 8 | 12.09% |
| 9 | 4.03% |
| 10 | 0.60% |
Spoiler
![[Image: pmf10scroll60.jpg]](http://img821.imageshack.us/img821/553/pmf10scroll60.jpg)
Success rate (70%)
| number of successes | percentage rate |
|---|---|
| 0 | 0.00% |
| 1 | 0.01% |
| 2 | 0.14% |
| 3 | 0.90% |
| 4 | 3.68% |
| 5 | 10.29% |
| 6 | 20.01% |
| 7 | 26.68% |
| 8 | 23.35% |
| 9 | 12.11% |
| 10 | 2.82% |
Spoiler
![[Image: pmf10scroll70.jpg]](http://img121.imageshack.us/img121/8213/pmf10scroll70.jpg)
Point out any errors, if you see any.
Scroll probability formula - Kabanaw - 2011-02-05
Fumni Wrote:I hope you guys don't mind me adding to this and bumping this topic.
Scroll probability can be easily calculated using binomial distribution, in particular, the probability mass formula "
Using Excel, I made some basic chart graphics to visualize the probability mass function. The following scenarios are for an overall with 10 slots, using 10%, 30%, 50%, 60% and 70% scrolls.
Success rate (10%)
number of successes percentage rate
0 34.87%
1 38.74%
2 19.37%
3 5.74%
4 1.12%
5 0.15%
6 0.01%
7 0.00%
8 0.00%
9 0.00%
10 0.00%
Spoiler
Success rate (30%)
number of successes percentage rate
0 2.82%
1 12.11%
2 23.35%
3 26.68%
4 20.01%
5 10.29%
6 3.68%
7 0.90%
8 0.14%
9 0.01%
10 0.00%
Spoiler
Success rate (50%)
number of successes percentage rate
0 0.10%
1 0.98%
2 4.39%
3 11.72%
4 20.51%
5 24.61%
6 20.51%
7 11.72%
8 4.39%
9 0.98%
10 0.10%
Spoiler
Success rate (60%)
number of successes percentage rate
0 0.01%
1 0.16%
2 1.06%
3 4.25%
4 11.15%
5 20.07%
6 25.08%
7 21.50%
8 12.09%
9 4.03%
10 0.60%
Spoiler
Success rate (70%)
number of successes percentage rate
0 0.00%
1 0.01%
2 0.14%
3 0.90%
4 3.68%
5 10.29%
6 20.01%
7 26.68%
8 23.35%
9 12.11%
10 2.82%
Spoiler
Point out any errors, if you see any.
The formula you posted is esentially a more statistic-savvy version of what I came up with. But still. looks good.
Scroll probability formula - Fumni - 2011-02-05
It is statistics.
Scroll probability formula - Kabanaw - 2011-02-05
Fumni Wrote:It is statistics.
I realize, but not everybody knows what a bionomial coefficient is. Somebody could use the formula I posted with no background in statistics, and still use it.
But as I said, they're the same formula, so this whole discussion is pretty pointless.
Scroll probability formula - Fumni - 2011-02-05
Kabanaw Wrote:I realize, but not everybody knows what a bionomial coefficient is. Somebody could use the formula I posted with no background in statistics, and still use it.
But as I said, they're the same formula, so this whole discussion is pretty pointless.
Yep, they're pretty much the same formula.
Scroll probability formula - Stereo - 2011-02-05
Cursed scrolls mislead - there's only a 19.69% chance of putting 10 on an item without it blowing up (.85^10). So the most common result (80.31%) should really be destroyed.
Once you eliminate that, you have .7/.85 = 82.35% success rates on the rest. So it's gonna be skewed closer to +10 on the ones that don't break. Or in other words, the more that fail - the higher the chance it breaks - so low numbers are unlikely to occur.
| break | 80.3126% |
| +0 | 5.7e-7 % |
| +1 | 2.7e-5 % |
| +2 | 5.7e-4 % |
| +3 | 7.0e-3 % |
| +4 | 0.057% |
| +5 | 0.3216% |
| +6 | 1.2508% |
| +7 | 3.3353% |
| +8 | 5.8369% |
| +9 | 6.053% |
| +10 | 2.825% |
Scroll probability formula - hadriel - 2011-02-05
Much easier to calculate P(n failures) for small n. It's also important to calculate SD, variance and expectation for n trials. Basic statistical assumptions apply.
And generally a more rigorous discussion would be better for this topic. I really wonder how many people don't know what probability is, or how many people's (un)common sense fails them.
Oh, with WolframAlpha and Mathematica and Excel, I don't ever need a calculator anymore.
Hadriel
Scroll probability formula - Kaasoljoyyx - 2011-02-05
Fumni Wrote:It is statistics.
No it's not, it's probability.
Scroll probability formula - Fumni - 2011-02-05
Kaasoljoyyx Wrote:No it's not, it's probability.
Statistics involves probability theory, it just gets associated with people to differentiate from it. Let's not make this discussion become another statistic and help to improve it.
Scroll probability formula - Shidoshi - 2011-02-05
As you add in more complex effects as trying to find out the cheapest way to scroll a certain item to certain stats considering you have at your disposal a group of N different types of scrolls with success/boom/price all different things start to get interesting.
I believe someone somewhere had made a page that calculated the cheapest way to achieve what you wanted.
Scroll probability formula - Kaasoljoyyx - 2011-02-05
Fumni Wrote:Statistics involves probability theory, it just gets associated with people to differentiate from it. Let's not make this discussion become another statistic and help to improve it.
Yes statistics does that, but this isn't that. Finding out scrolling probabilities is just basic combinatorics, i don't think anymore really needs to be said since all the formulas were written out already.
Probability vs statistics with a coin
The chance of getting a heads from a fair coin = 50% --> probability
Flipping a coin X times and checking to see if it is a fair coin --> statistics
Scroll probability formula - vx-2 - 2011-02-06
Kaasoljoyyx Wrote:The chance of getting a heads from a fair coin = 50% --> probability
Flipping a coin X times and checking to see if it is a fair coin --> statistics
Yeah good one there.
And, statistics can be used to predict (aka forecasting) based on previous gathered data, but Probability can't.
I think getting an accurate "forecast result" on "Scrolling" will be alil hard...... that's why scroller use "pattern" and burned scolls method; whereby one is "forecasting" the next scrolling result based on past scrolled results; works for some, and not for others...
Scroll probability formula - Shidoshi - 2011-02-06
vx-2 Wrote:Yeah good one there.
And, statistics can be used to predict (aka forecasting) based on previous gathered data, but Probability can't.
I think getting an accurate "forecast result" on "Scrolling" will be alil hard...... that's why scroller use "pattern" and burned scolls method; whereby one is "forecasting" the next scrolling result based on past scrolled results; works for some, and not for others...
No, statistics does not let you predict events if they are independent events (like scrolls).
Scroll probability formula - vx-2 - 2011-02-06
Shidoshi Wrote:No, statistics does not let you predict events if they are independent events (like scrolls).I don't think we can actually proved if it's dependent and independent? Not on server-side, not on coding? or packet-editing?
Just my opinion that I blif it does; just that it might not be as accurate.... lols; that's what I just mentioned in my post -_-"
Scroll probability formula - Shidoshi - 2011-02-06
Occam's Razor:
-Scrolls take information from past scrollings made by the user in X ammount of time in order to average out to about Y% probability to work, demanding the server to remember past events.
-Scrolls work Y% of the time.