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Scrolling probabilities


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#1 Arcane

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Posted 11 October 2006 - 06:21 PM

We all want to know what are the chances of "getting a 10atk glove" or "3 10%'s scrolls working". Well, now we can. If wizet's scrolls work as they say they do, my calculations should be correct. The equation to figure it out is the Binomial Probability Formula, which is based on bernoulli trials. The equation is: IPB Image, whereas (N / R) would be the Combination formula: IPB Image.

Here, N would be the number of scrolls you use, R would be the number of scrolls you want to work, and P would be the probability of the scroll working (say 60%--60% would be inputted as0.6).

I've taken the liberty of doing a chart of scrolls used/working in my free time at school, and the figures come out like this:

10% Scrolls
N---------------R---------------%
1---------------1---------------10
2---------------1---------------18
2---------------2---------------1
3---------------1---------------24.3
3---------------2---------------2.7
3---------------3---------------0.1
4---------------1---------------29.16
4---------------2---------------4.86
4---------------3---------------0.36
4---------------4---------------0.01
5---------------1---------------32.805
5---------------2---------------7.29
5---------------3---------------0.81
5---------------4---------------0.045
5------------5------------0.001
6---------------1---------------35.4294
6---------------2---------------9.8415
6---------------3---------------1.458
6---------------4---------------0.1215
6---------------5---------------0.0054
6---------------6---------------0.0001
7---------------1---------------37.20087
7---------------2---------------12.40029
7---------------3---------------2.29635
7---------------4---------------0.25515
7---------------5---------------0.01701
7---------------6---------------0.00063
7------------7------------0.00001
8---------------1---------------38.263752
8---------------2---------------14.880348
8---------------3---------------3.306744
8---------------4---------------0.45927
8---------------5---------------0.040824
8---------------6---------------0.002268
8---------------7---------------0.000072
8---------------8---------------0.000001
9---------------1---------------38.7420489
9---------------2---------------17.2186884
9---------------3---------------4.4641044
9---------------4---------------0.7440174
9---------------5---------------0.0826686
9---------------6---------------0.0061236
9---------------7---------------0.0002916
9---------------8---------------0.0000081
9---------------9---------------0.0000001
10---------------1---------------38.7420489
10---------------2---------------19.37102445
10---------------3---------------5.7385628
10---------------4---------------1.1160261
10---------------5---------------0.14880348
10---------------6---------------0.0137781
10---------------7---------------0.0008748
10---------------8---------------0.00003645
10---------------9---------------0.0000009
10------------10------------0.00000001
Pretty depressing, eh? Sorry, no 50dex sauna any time soon ;_;

60% Scrolls
N---------------R---------------%
1---------------1---------------60
2---------------1---------------48
2---------------2---------------36
3---------------1---------------28.8
3---------------2---------------43.2
3---------------3---------------21.6
4---------------1---------------15.36
4---------------2---------------34.56
4---------------3---------------34.56
4---------------4---------------12.96
5---------------1---------------7.68
5---------------2---------------23.04
5---------------3---------------34.56
5---------------4---------------25.92
5------------5------------7.776
6---------------1---------------3.6864
6---------------2---------------13.824
6---------------3---------------27.648
6---------------4---------------31.104
6---------------5---------------18.6624
6---------------6---------------4.6656
7---------------1---------------1.72032
7---------------2---------------7.74144
7---------------3---------------19.3536
7---------------4---------------29.0304
7---------------5---------------26.12736
7---------------6---------------13.06368
7------------7------------2.79936
8---------------1---------------0.786432
8---------------2---------------4.128768
8---------------3---------------12.386304
8---------------4---------------23.22432
8---------------5---------------27.869184
8---------------6---------------20.901888
8---------------7---------------8.57952
8---------------8---------------1.679616
9---------------1---------------0.3538944
9---------------2---------------2.1233664
9---------------3---------------7.4317824
9---------------4---------------16.7215104
9---------------5---------------25.0822656
9---------------6---------------25.0822656
9---------------7---------------16.1243136
9---------------8---------------3.0466176
9---------------9---------------1.0077696
10---------------1---------------0.1572864
10---------------2---------------1.0616832
10---------------3---------------4.2467328
10---------------4---------------11.1476736
10---------------5---------------20.03581248
10---------------6---------------25.0822656
10---------------7---------------21.4990848
10---------------8---------------12.0932352
10---------------9---------------4.0310784
10------------10------------0.60466176

The bolded ones are commonly used scrolling ways. If you want to do mixed scrolling, the probability would be the two outcomes multiplied together. Say you want 4 60% scrolls to work and 3 10% scrolls to work, the probability would be 3/3 10%'s multiplied by 4/4 60%'s.

Of course, these are just theoretical, and you shouldn't rely too heavily on them. However, this can give you an idea of the chances of getting the item you want, and can save you some dough.


--EDIT--10/13/06
QUOTE(Dibs)
Also, if you are scrolling to get 'x' number of scrolls to work or more, than you can add the percentages of that number and up.

Example:
71.00% you succeed 4+ out of 7 60% scrolls.
41.97% you succeed 5+ out of 7 60% scrolls.


Used for finding the probability of "x scrolls working or more

A TI BASIC program for your TI graphing calculator. Works with 10%, 60%, and 100% scrolls.
CODE

:Lbl A
:Prompt N,R,P
:100*(N nCr R)*(P*R)*(1-P)^(N-R) sto-> X
:Disp "Percent=",X
:Pause
:Goto A


--EDIT--12/4/06
By request of Ktk and Kyyuna, I've tried to do 30% and 70% scrolls, but they get complicated. So far, I've gotten this as the equation of getting what you want:
Let's call this equation IPB Image
*substitutes it with the first greek letter that comes to mind* Δ Delta
So the equation would be [Δ- (1-Δ)/2].

My outcomes so far for 70% scrolls are:
1------1------55%
5------5------24.7105%
7------7------11.853145%

Seems like cursed scrolls work better when used en masse, but I'm not sure of the validity of this equation yet. This is where you, the wealthy reader and scroller, comes into play mush1a.gif
I'd like anyone who uses a cursed scroll of 70% and is willing to share their Legitimate information with me, and with the rest of the mapling world, to please PM me with the following information:
CODE

[b]Amount of scrolls used:[/b] <insert amount here>
[b]Amount of scrolls worked:[/b] <insert amount here>


Thank you for your cooperation mush1a.gif

Edited by Arcane, 04 January 2007 - 12:50 PM.




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#2 Chasofito

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Posted 11 October 2006 - 06:29 PM

So its a probability chart. In the words of Han Solo. "Never tell me the odds." If a scroll works, then it works. No point getting your hopes up or down because of the chances and there is always the chance that the odds can be beaten.

#3 Hobbes

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Posted 11 October 2006 - 06:30 PM

So you're saying if i wanted to scroll something with a 10% twice and i wanted them bith to work, it would be a 1% chance or 100% chance?

Nice work Arcane, kinda confusing but good anyways. =D

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#4 Arcane

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Posted 11 October 2006 - 06:31 PM

It would be a 1% chance. And yes, this is only theoretical probability, but I usually feel safer if I know what I'm doing mush1n.gif

#5 legendaryhen

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Posted 11 October 2006 - 11:12 PM

this is what arcane learned in 8th grade O.O

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#6 Haelionis

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Posted 11 October 2006 - 11:26 PM

This looks too scientific for a game.


Thanks to Faded

#7 Kyyuna

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Posted 11 October 2006 - 11:34 PM

rofl leet chart D=
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#8 Paper

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Posted 11 October 2006 - 11:40 PM

QUOTE(haelionis @ Oct 11 2006, 10:26 PM) View Post

This looks too scientific for a game.

try taking a look at the numbers in disgaea
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#9 Arcane

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Posted 12 October 2006 - 07:11 PM

QUOTE(haelionis @ Oct 11 2006, 10:26 PM) View Post

This looks too scientific for a game.

It's mathematical, not scientific mush1o.gif. Anyway, more numbers updated! mush1i.gif

#10 Elite Jeff

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Posted 12 October 2006 - 07:19 PM

I think this should be pinned, it's very useful to know the odds, just as a warning. Of course, maybe you'll beat them, as Chasofito said, but it's best to know.

Good work on the guide.

#11 Liquid

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Posted 13 October 2006 - 02:58 PM

You forgot 100% =P, wow 7 10% scrolls working without hacking = when pigs have wings.

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#12 Luke

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Posted 13 October 2006 - 09:31 PM

I guess the odds where in my favor when I scrolled my ET on my priest. The 2.79936% chance that 7 60% scrolls would succesfully work...... wow.
thumbsup.gif

Edited by Grim Phantom Watch, 13 October 2006 - 09:32 PM.

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#13 Dibs

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Posted 13 October 2006 - 09:39 PM

Also, if you are scrolling to get 'x' number of scrolls to work or more, than you can add the percentages of that number and up.

Example:
71.00% you succeed 4+ out of 7 60% scrolls.
41.97% you succeed 5+ out of 7 60% scrolls.

This is all mathematical of course.

Edited by Dibs, 13 October 2006 - 09:40 PM.

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#14 Seagull

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Posted 13 October 2006 - 09:41 PM

Nice chart, man! Saved me a lot of math work. I can see why items with multiple 10%s working are so valuble... o.O

You may want to extend it to 10 scrolls, because overalls have 10 slots. If you have the time, that is. =3

#15 Tichondrius

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Posted 13 October 2006 - 11:21 PM

Some things have 10 slots, you know =P

#16 Arcane

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Posted 14 October 2006 - 10:30 AM

QUOTE(Dibs @ Oct 13 2006, 08:39 PM) View Post

Also, if you are scrolling to get 'x' number of scrolls to work or more, than you can add the percentages of that number and up.

Example:
71.00% you succeed 4+ out of 7 60% scrolls.
41.97% you succeed 5+ out of 7 60% scrolls.

This is all mathematical of course.

I got that added, but I'm still testing it out to see if it's valid.

QUOTE(Magical Moses @ Oct 13 2006, 08:41 PM) View Post

Nice chart, man! Saved me a lot of math work. I can see why items with multiple 10%s working are so valuble... o.O

You may want to extend it to 10 scrolls, because overalls have 10 slots. If you have the time, that is. =3

I'll get to work on that tomorrow. It's pretty easy, because I made a program on my calc which calculates it and all those lower/higher automatically mush1a.gif

Alright, got the 10slot part of the table added in.

Edited by Arcane, 14 October 2006 - 10:31 AM.


#17 Hobbes

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Posted 14 October 2006 - 12:16 PM

QUOTE(banditbruce @ Oct 13 2006, 04:58 PM) View Post

You forgot 100% =P, wow 7 10% scrolls working without hacking = when pigs have wings.

Dude... 100% scrolls always work, so theres no point in putting that in the chart.
Lol... 1337 chart xD

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#18 Dibs

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Posted 14 October 2006 - 02:56 PM

I delved into the binomial theorem and nCr in my precal class last year and got interested in scrolling probabilities. There are other guides that have figured them out already, but keep up with the good work.

I forget the calculations to prove my previous point but in a logical way it sorta works out XD

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#19 Ktk_

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Posted 14 October 2006 - 06:47 PM

can u try these formulas for 30% and 70% scrolls? o-o since it's more difficult as there's a percent chance that it totally kills your item ..
( ppl would rly want to know the chances of that happening, rite? )


#20 plusminus

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Posted 14 October 2006 - 07:27 PM

QUOTE(haelionis @ Oct 12 2006, 01:26 AM) View Post

This looks too scientific for a game.
This game wouldn't exist without science.

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