Who's good at probability?

[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).]

n = number of trials
k = number of successes
n – k = number of failures
p = probability of success in one trial
q = 1 – p = probability of failure in one trial

Spoiler: 10% scrolls

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

Spoiler: 60% Scrolls

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

30% & 70%



CBB to make it.

GL.

 

meaning I'm too lazy haha

 

Challenge question: You have an infinite number of work gloves and 60% gfa scrolls, and want a perfect work glove. If you fail a scroll, you stop scrolling the glove early (since it's no longer perfect) and move on to the next one. What is the expected number of scrolls needed for a perfect glove? What is the expected number of gloves needed?

 

Man don't copy my fucking post
https://forums.mapletip.com/index.php?/topic/76088-scrolling-probabilities/

Also the bad assumption is that you always start from clean which is not the case, this is because the formula you copied is used for independent events which is not valid for scrolling, your next action is dependent on where you passed your previous attempt or not.

I guess it would be fine for ball parking but it's not accurate.

PS cite your sources you plagiarizing shit

 

I think you need to offer some meso as a prize for the effort to solve it.

While I think anyone can answer this easily which is (1/(0.6^7))=35.72~ 36 brown work gloves, assuming no white scroll is used.

P/S: don't rely too much on the probability, probability theory assumes the system is perfectly random while algorithms can only be pseudorandom

 

Wow dude.. that's just edgy as hell.
OP asked for solutions and John provided one, its not like he went out of his way to claim "i did this calculation".
Please drink a cup of coffee and calm down.

 

Sorry for reviving, in case there's still any interest, I think this is the solution:

Approach #1: Solve using a Markov chain with transitions defined by success rate. There are 8 states, clean to fully scrolled with transitions between adjacent states. Can setup a system of equations which solves expected hitting time to the last state.

E[0 successes to completion] = 0.4 * E[0 successes to completion] + 0.6 * E[1 success to completion] + 1
...
E[7 successes to completion] = 0

Code:

A = array([[-0.6,  0.6,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.4, -1. ,  0.6,  0. ,  0. ,  0. ,  0. ,  0. ],
       [ 0.4,  0. , -1. ,  0.6,  0. ,  0. ,  0. ,  0. ],
       [ 0.4,  0. ,  0. , -1. ,  0.6,  0. ,  0. ,  0. ],
       [ 0.4,  0. ,  0. ,  0. , -1. ,  0.6,  0. ,  0. ],
       [ 0.4,  0. ,  0. ,  0. ,  0. , -1. ,  0.6,  0. ],
       [ 0.4,  0. ,  0. ,  0. ,  0. ,  0. , -1. ,  0.6],
       [ 0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. , -1. ]])
y = array([-1., -1., -1., -1., -1., -1., -1.,  0.])

np.linalg.solve(A, y)
array([86.80612711, 85.13946045, 82.36168267, 77.73205304, 70.01600366,
      57.15592135, 35.72245085, -0.        ])

So on average you need 86.8 60% scrolls to perfect a work glove.

Approach #2: This is shorter way to solve it using the previous answer:

And divide it by the failure rate. Every time we use a scroll, there’s a 40% chance of ruining a work glove, therefore E[# gloves ruined] = 0.4*E[# of scrolls]

(35.72 - 1) / .4 = 86.8 scrolls.

The parameters can be changed for 10% scrolls too.
1 / (0.1^7) = 1,000,000 work gloves
(1,000,000-1) / 0.1 = 9,999,990 10% scrolls

 

The math checks out, i fucking love it. But do you want to know how long it would take to do 1 million work gloves, with 10 million scrolls, ON AVERAGE (you won't get it, i bet). But, it would take you over a month of straight scrolling.