Glove scrolling probability help

[color="#cc8899"]
Disclaimer: Yes, I know it'd be cheaper to just buy a 13 attack. If you find me that 13 attack warrior glove, let me know, because I'd buy it in an instant. Until then (assuming my perma Agent glove turns out badly, I haven't gotten it yet to chaos), I'll view this as the next best thing. Besides, getting a 15 att warrior glove would be amazing, and a huge screw you to SCG enthusiasts.
For all you math geeks out there
The plan - with 500m, have a decent chance of scrolling a 13,14, or 15 attack lv100 warrior glove. I will begin by landing consecutive 10%s on the first 2 slots (resulting in 6 attack 3 slot), finishing with 30s and 60s (60%s are the emergency option, provided that I don't have enough 12 attacks to risk a final 30 (which I won't do unless I have 4+).

The assumptions are that I won't spend more than 500k per glove, 2.5m per 10% glove attack, 9m 30% glove attack, and 6m 60% glove attack.
Failures (12 attacks or lower non boom) will be used to fund further scrolling, excepting the best glove currently scrolled, which will be kept for personal usage.

What I want to know is,

A) with appx 250m (100 10% glove attacks), what are the odds of landing 2 10%s on a single glove, assuming a glove is abandoned if first slot fails.

B) with a base of 10 6 attack gloves (3 slots), what are the odds of at least 4 becoming 9 attack 2 slot using 30% scrolls

C) with a base of 4 9 attack (2 slot) gloves, what are the odds of at least 2 becoming 12 attack (1 slot) using 30% scrolls

D) What are the odds of landing 10%, 10%, 30%, 30%, 60% on at least one glove, given the funding/prices above and abandoning a glove at the first failure? How much do the odds improve by aiming for 10,10,30,60,60 instead?[/COLOR]

1/

basicly, you have a 1% chance of landing two 10%s in a row. so with 90 10%s you would have 9 3atk 4slots, and 10 slots left over.

so you'd have a 9/10 chance to have a single 6atk 3slot glove if youd think about it and a single scroll left. if youd scroll at average rate and be not lucky nor not unlucky.
to theoretically have a 6atk 3slot glove, you need 110 10% scrolls


2/

your wanting 4 30s to work, wich is 720 to work out of 1000, so the chance would be 72% that it work.

30+30+30+30+6*100 to know the odds of 4 times working ith no care for the last 6.


3/

30+30+100+100 so 260/400 so uhm, 65%.


hope this helps

[color="#cc8899"]A) with appx 250m (100 10% glove attacks), what are the odds of landing 2 10%s on a single glove, assuming a glove is abandoned if first slot fails.

B) with a base of 10 6 attack gloves (3 slots), what are the odds of at least 4 becoming 9 attack 2 slot using 30% scrolls

C) with a base of 4 9 attack (2 slot) gloves, what are the odds of at least 2 becoming 12 attack (1 slot) using 30% scrolls

D) What are the odds of landing 10%, 10%, 30%, 30%, 60% on at least one glove, given the funding/prices above and abandoning a glove at the first failure? How much do the odds improve by aiming for 10,10,30,60,60 instead?[/COLOR]

A) The expectation-value is at 110 scrolls needed in order to hit 2 10% in a row. In order to calculate the chance for 2 in a row with 100 scrolls, you'll need some matrix-calculations I've not worked with yet. (I should really finish that theory...) The probability wouldn't be too far away from 90% though.

B) 10 gloves with 6 watk, at least 4 becoming 9 watk through using 30%s?

That's 1 - 0.7^10 - 0.7^9*0.3*10 - 0.7^8*0.3^2*(10 chance 2) - 0.7^7*0.3^2*(10 chance 3)

(I don't have a calc atm, so I'm sorry for not evaluating the expression.)

C) 34,83 percent.

D) You gotta be funny. This would require so advanced mathematics I'm not going to even look at it as of today. Maybe in a year or so.

1/

basicly, you have a 1% chance of landing two 10%s in a row. so with 90 10%s you would have 9 3atk 4slots, and 10 slots left over.

so you'd have a 9/10 chance to have a single 6atk 3slot glove if youd think about it and a single scroll left. if youd scroll at average rate and be not lucky nor not unlucky.
to theoretically have a 6atk 3slot glove, you need 110 10% scrolls.

You can't add probability.

Chance of 9 10%s failing in a row = 38%, so that means the odds of at least 1 working is only 62%. Of course that includes multiple successes. But those are only a small fraction.

Just wondering, why don't you just buy common class ATT gloves?

ATT gloves are probably the worst thing to scroll in MS, and almost always guarantee a loss by scrolling them. I wouldn't be suprised if scrolling a 13 attack glove costs more than simply buying a 14 attack glove, or maybe even a 15 attack one (although I haven't done any math). Not to mention the higher resale value of common gloves, and the ability to also use them on your slinger/outlaw.

You can't add probability.

Chance of 9 10%s failing in a row = 38%, so that means the odds of at least 1 working is only 62%. Of course that includes multiple successes. But those are only a small fraction.

one question, how did you come to the fact i added there?

cause if i use the same logic as i used, i end up at a 38ish chance of failing 9 too.

or are you talking about how i added 9 to get that 90 10s would work him out 9 gloves with 3attack 4 slots.

[color="#cc8899"]
D) What are the odds of landing 10%, 10%, 30%, 30%, 60% on at least one glove, given the funding/prices above and abandoning a glove at the first failure? How much do the odds improve by aiming for 10,10,30,60,60 instead?[/COLOR]

0.00054% on the first one and 0.00108% on the second one. Your abysmally low chances double. :v

0.00054% on the first one and 0.00108% on the second one. Your abysmally low chances double. :v

You're not including the moneyrange. You're not including abandoning. You're showing basic 0.1*0.1*0.3*0.3*0.6 and 0.1*0.1*0.3*0.6*0.6. I think most people already know how to do that.

Work backwards from the result, then.
10 10 30 30 60 -> you end up with a 14 atk glove.
You need about 1/.6 = 1.666 12 atk 1 slot gloves + 60%s for a 60% to work.
1.666/.3 = 5.555 9 atk 2 slot gloves + 30%s for a 30% to work
5.555/.3 = 18.51 6 atk 3 slot gloves + 30%s
18.51/.1 = 185.1 3 atk 4 slot gloves + 10%s
185.1/.1 = 1852 clean gloves + 10%s
= 2037 10%s, 24 30%s, 1.6 60%s, 1852 clean gloves.

10 10 30 60 60 ->
1.666 (60)
2.777 (60)
9.25 (30)
92.5 (10)
925 (10)
= 925 gloves, 1010 10%s, 9 30%s, 4.4 60%s.

Less than half the cost again.

This is just the average chances though.. anyway, 1000 * 2.5mil per scroll = 2.5 billion for a 13 atk glove? 5 billion for a 14? >_>

Say you went with 30%s more instead...
10 30 30 30 60 = 14 atk
1.666 60
5.555 30
18.5 30
61.73 30
617 10
= 617 gloves, 617 10%, 86 30%, 2 60%. Only works out to 2.3 billion mesos. I believe this (10 30 30 30 60) is the cheapest path to a 14 atk class glove, on average.

Same holfs true for 13:
10 30 30 60 60 = 13 atk:
1.666 60
2.777 60
9.25 30
30.9 30
308.6 10
= 309 gloves, 309 10%, 41 30%, 4.4 60%. Only 1.1 billion.

Work backwards from the result, then.
10 10 30 30 60 -> you end up with a 14 atk glove.
You need about 1/.6 = 1.666 12 atk 1 slot gloves + 60%s for a 60% to work.
1.666/.3 = 5.555 9 atk 2 slot gloves + 30%s for a 30% to work
5.555/.3 = 18.51 6 atk 3 slot gloves + 30%s
18.51/.1 = 185.1 3 atk 4 slot gloves + 10%s
185.1/.1 = 1852 clean gloves + 10%s
= 2037 10%s, 24 30%s, 1.6 60%s, 1852 clean gloves.

10 10 30 60 60 ->
1.666 (60)
2.777 (60)
9.25 (30)
92.5 (10)
925 (10)
= 925 gloves, 1010 10%s, 9 30%s, 4.4 60%s.

Less than half the cost again.

This is just the average chances though.. anyway, 1000 * 2.5mil per scroll = 2.5 billion for a 13 atk glove? 5 billion for a 14? >_>

Say you went with 30%s more instead...
10 30 30 30 60 = 14 atk
1.666 60
5.555 30
18.5 30
61.73 30
617 10
= 617 gloves, 617 10%, 86 30%, 2 60%. Only works out to 2.3 billion mesos. I believe this (10 30 30 30 60) is the cheapest path to a 14 atk class glove, on average.

Same holfs true for 13:
10 30 30 60 60 = 13 atk:
1.666 60
2.777 60
9.25 30
30.9 30
308.6 10
= 309 gloves, 309 10%, 41 30%, 4.4 60%. Only 1.1 billion.

[color="#cc8899"]/dreams
Thank you though, good information. And to people telling me to buy a common glove, thank you for forcing your belief that common is better on me, I appreciate it - I asked this because I want a class glove, which is far more useful to me than a common one - I specifically want a warrior glove for the extra stats it would add and because I highly dislike using low level common gear where I can avoid it. But yes, thank you for entirely missing that and deciding for me that the question I was asking didn't deserve a valid answer, and instead I should just be told to go buy a common.[/COLOR]

I specifically want a warrior glove for the extra stats it would add and because I highly dislike using low level common gear where I can avoid it.

I'm waiting on Maker + Reverse glove (whatever it's called). 6 str clean + 3-5 crystal + 3 levelups = makes up for way more stats than a 5 str korben. Even a 10 atk one would be as good as my 12 atk SCG.

Heck even an 8 atk one I'd use over my SCG, so I didn't have to share it between 2 characters. Might be cheaper to use common gloves+cape+shoes but I don't like having to transfer NL to Paladin when I want to train it (theyre on different accounts).

I'm waiting on Maker + Reverse glove (whatever it's called). 6 str clean + 3-5 crystal + 3 levelups = makes up for way more stats than a 5 str korben. Even a 10 atk one would be as good as my 12 atk SCG.

Heck even an 8 atk one I'd use over my SCG, so I didn't have to share it between 2 characters. Might be cheaper to use common gloves+cape+shoes but I don't like having to transfer NL to Paladin when I want to train it (theyre on different accounts).

I may do the same. And, of course, there's the possibility that my Agent O glove turns out godly. I'd love if it turned out 13+.

We must remember that statistics applied to games is a bit different from what we learn from theory. I believe that Nexon's uses a simple Pseudorandom number generator algorithm (PRNG) to generate random numbers applied to damage calculation, skills % to work, scrolls, etc. Remembering that many people found "patterns" in 30% or 70% scrolls, which indicates that the Nexon's PRNG, found its frequency or the seeds used in the generation of numbers is repeated. Well, it is huge and very diverse subject.

I am currently developing software to deal with problems of physics, chemistry and engineering, generate billions of random numbers, using the entropy of the servers to create seeds. After generating the data, then we will start the simulations like how atoms can escape from an optical trap, or optimize the production of a remedy to how much tension can wings of airplanes support, or even the behavior of a coffee shop over time (discrete event simulation).

Sorry about my english, still learning.

Some usefull links:

PRNG
Randomness
Monte Carlo Method
Entropy
Discrete event simulation
Random Seed

A) with appx 250m (100 10% glove attacks), what are the odds of landing 2 10%s on a single glove, assuming a glove is abandoned if first slot fails.

B) with a base of 10 6 attack gloves (3 slots), what are the odds of at least 4 becoming 9 attack 2 slot using 30% scrolls

C) with a base of 4 9 attack (2 slot) gloves, what are the odds of at least 2 becoming 12 attack (1 slot) using 30% scrolls

D) What are the odds of landing 10%, 10%, 30%, 30%, 60% on at least one glove, given the funding/prices above and abandoning a glove at the first failure? How much do the odds improve by aiming for 10,10,30,60,60 instead?

A) In a simulation of 50,000 attempts per your specifications only 533 met your targeted goal. That is 0.01066, or 1.066% (note this is about expected for 10% of 10%, which is 1%). Generally if you continued along the premise of your assumption and did 100 scrolls worth of 10%s consecutively, 1 pair of gloves will meet your goal. The actual number of gloves required to meet that goal is estimated between 110 and 150.

Rather than giving the convoluted and boring math behind things like this, I prefer to show simulated results. Seeing the results of a what if is more meaningful than hearing percentages.

Here's a simulation of your 100 scrolls using the logic provided.
2009-07-05 024114 100 - 2 slots

 Spoiler

2009-07-05 024114 100 - 2 slots

# Slot1 Slot2 Success Failed 1 Nuked -1 -1 2 Nuked -1 -1 3 Nuked -1 -1 4 Pass Nuked -1 -1 5 Nuked -1 -1 6 Nuked -1 -1 7 Nuked -1 -1 8 Nuked -1 -1 9 Nuked -1 -1 10 Nuked -1 -1 11 Nuked -1 -1 12 Nuked -1 -1 13 Nuked -1 -1 14 Nuked -1 -1 15 Nuked -1 -1 16 Nuked -1 -1 17 Nuked -1 -1 18 Nuked -1 -1 19 Nuked -1 -1 20 Nuked -1 -1 21 Pass Nuked -1 -1 22 Nuked -1 -1 23 Nuked -1 -1 24 Nuked -1 -1 25 Nuked -1 -1 26 Nuked -1 -1 27 Nuked -1 -1 28 Nuked -1 -1 29 Nuked -1 -1 30 Pass Pass 2 0 31 Nuked -1 -1 32 Nuked -1 -1 33 Nuked -1 -1 34 Nuked -1 -1 35 Nuked -1 -1 36 Nuked -1 -1 37 Pass Nuked -1 -1 38 Nuked -1 -1 39 Nuked -1 -1 40 Nuked -1 -1 41 Nuked -1 -1 42 Nuked -1 -1 43 Nuked -1 -1 44 Pass Nuked -1 -1 45 Nuked -1 -1 46 Nuked -1 -1 47 Nuked -1 -1 48 Nuked -1 -1 49 Nuked -1 -1 50 Nuked -1 -1 51 Nuked -1 -1 52 Nuked -1 -1 53 Nuked -1 -1 54 Nuked -1 -1 55 Nuked -1 -1 56 Nuked -1 -1 57 Nuked -1 -1 58 Nuked -1 -1 59 Nuked -1 -1 60 Nuked -1 -1 61 Nuked -1 -1 62 Nuked -1 -1 63 Nuked -1 -1 64 Nuked -1 -1 65 Nuked -1 -1 66 Nuked -1 -1 67 Nuked -1 -1 68 Nuked -1 -1 69 Nuked -1 -1 70 Nuked -1 -1 71 Nuked -1 -1 72 Nuked -1 -1 73 Pass Nuked -1 -1 74 Nuked -1 -1 75 Nuked -1 -1 76 Nuked -1 -1 77 Pass Nuked -1 -1 78 Nuked -1 -1 79 Nuked -1 -1 80 Nuked -1 -1 81 Nuked -1 -1 82 Nuked -1 -1 83 Nuked -1 -1 84 Nuked -1 -1 85 Nuked -1 -1 86 Nuked -1 -1 87 Nuked -1 -1 88 Pass Pass 2 0 89 Nuked -1 -1 90 Nuked -1 -1 91 Nuked -1 -1 92 Nuked -1 -1 93 Nuked -1 -1 94 Nuked -1 -1 95 Nuked -1 -1 96 Nuked -1 -1 97 Nuked -1 -1 98 Pass Nuked -1 -1 99 Nuked -1 -1 100 Nuked -1 -1

#30 and #88 both achieved your goals so statistical variance can favor you on the small sample size.

B) & C) Continuing the simulation of 50,000 gloves, exactly 74 gloves survived 2 10s followed by 2 successful 30s. Exactly 1 pair of gloves survived 2 10s and 3 successful 30s

D) This question actually fails to identify what the intended goal truly is - Maximum survival of items, or maximum potential of items.

Here's the breakdown of 50k of those:

10s	10s	30s	60s	60s	Survived	3 Success	4 Success	5 Success
4820	523	184	187	170	298	87	179	32

10s	10s	30s	30s	60s	Survived	3 Success	4 Success	5 Success
4951	537	160	107	122	252	66	145	7

Basically this is a break down of how many times out of 50,000 each step was met with success. It assumed the following things -
Any 10% failure resulted in discard
Any 30% failure that did not result in destruction kept for future tries.
Any 60% failure was kept for future tries.

Interpreting the results - Two sixties instead of 2 thirties increases chance of overall item survive by over about 18% but the trade off of course is weaker end results since the maximum value in 32 +5 situations is +11. In either situation you're talking about a success probability of 0.014% to 0.064%

Here are simulations of 10 pair of gloves that you succeeded your 10s on already with the additional scrollings:

30x1, 60x2

 Spoiler

30x1, 60x2
# 30s 60s 60s Success Failed 1 Pass Pass Pass 3 0 2 Fail Pass Pass 2 1 3 Pass Pass Pass 3 0 4 Fail Pass Pass 2 1 5 Pass Pass Pass 3 0 6 Fail Pass Pass 2 1 7 Fail Pass Pass 2 1 8 Fail Pass Fail 1 2 9 Pass Pass Fail 2 1 10 Nuked -1 -1

30x2, 60x1

 Spoiler

30x2, 60x1
# 30s 30s 60s Success Failed 1 Pass Nuked -1 -1 2 Fail Fail Fail 0 3 3 Pass Fail Pass 2 1 4 Nuked -1 -1 5 Fail Pass Fail 1 2 6 Fail Fail Pass 1 2 7 Nuked -1 -1 8 Nuked -1 -1 9 Fail Nuked -1 -1 10 Pass Fail Pass 2 1

Note the results of section 1 indicate that you will require approximately 1000 gloves (and scrolls) just to get your 10 gloves that have a base of 6 already and then you lost 1 to 3 of those.

A) In a simulation of 50,000 attempts per your specifications only 533 met your targeted goal. That is 0.01066, or 1.066% (note this is much higher than 10% of 10%, which is 0.01%). Generally if you continued along the premise of your assumption and did 100 scrolls worth of 10%s consecutively, 1 pair of gloves will meet your goal. The actual number of gloves required to meet that goal is estimated between 110 and 150.

Rather than giving the convoluted and boring math behind things like this, I prefer to show simulated results. Seeing the results of a what if is more meaningful than hearing percentages.

Here's a simulation of your 100 scrolls using the logic provided.
2009-07-05 024114 100 - 2 slots

 Spoiler

2009-07-05 024114 100 - 2 slots

# Slot1 Slot2 Success Failed 1 Nuked -1 -1 2 Nuked -1 -1 3 Nuked -1 -1 4 Pass Nuked -1 -1 5 Nuked -1 -1 6 Nuked -1 -1 7 Nuked -1 -1 8 Nuked -1 -1 9 Nuked -1 -1 10 Nuked -1 -1 11 Nuked -1 -1 12 Nuked -1 -1 13 Nuked -1 -1 14 Nuked -1 -1 15 Nuked -1 -1 16 Nuked -1 -1 17 Nuked -1 -1 18 Nuked -1 -1 19 Nuked -1 -1 20 Nuked -1 -1 21 Pass Nuked -1 -1 22 Nuked -1 -1 23 Nuked -1 -1 24 Nuked -1 -1 25 Nuked -1 -1 26 Nuked -1 -1 27 Nuked -1 -1 28 Nuked -1 -1 29 Nuked -1 -1 30 Pass Pass 2 0 31 Nuked -1 -1 32 Nuked -1 -1 33 Nuked -1 -1 34 Nuked -1 -1 35 Nuked -1 -1 36 Nuked -1 -1 37 Pass Nuked -1 -1 38 Nuked -1 -1 39 Nuked -1 -1 40 Nuked -1 -1 41 Nuked -1 -1 42 Nuked -1 -1 43 Nuked -1 -1 44 Pass Nuked -1 -1 45 Nuked -1 -1 46 Nuked -1 -1 47 Nuked -1 -1 48 Nuked -1 -1 49 Nuked -1 -1 50 Nuked -1 -1 51 Nuked -1 -1 52 Nuked -1 -1 53 Nuked -1 -1 54 Nuked -1 -1 55 Nuked -1 -1 56 Nuked -1 -1 57 Nuked -1 -1 58 Nuked -1 -1 59 Nuked -1 -1 60 Nuked -1 -1 61 Nuked -1 -1 62 Nuked -1 -1 63 Nuked -1 -1 64 Nuked -1 -1 65 Nuked -1 -1 66 Nuked -1 -1 67 Nuked -1 -1 68 Nuked -1 -1 69 Nuked -1 -1 70 Nuked -1 -1 71 Nuked -1 -1 72 Nuked -1 -1 73 Pass Nuked -1 -1 74 Nuked -1 -1 75 Nuked -1 -1 76 Nuked -1 -1 77 Pass Nuked -1 -1 78 Nuked -1 -1 79 Nuked -1 -1 80 Nuked -1 -1 81 Nuked -1 -1 82 Nuked -1 -1 83 Nuked -1 -1 84 Nuked -1 -1 85 Nuked -1 -1 86 Nuked -1 -1 87 Nuked -1 -1 88 Pass Pass 2 0 89 Nuked -1 -1 90 Nuked -1 -1 91 Nuked -1 -1 92 Nuked -1 -1 93 Nuked -1 -1 94 Nuked -1 -1 95 Nuked -1 -1 96 Nuked -1 -1 97 Nuked -1 -1 98 Pass Nuked -1 -1 99 Nuked -1 -1 100 Nuked -1 -1

#30 and #88 both achieved your goals so statistical variance can favor you on the small sample size.

B) & C) Continuing the simulation of 50,000 gloves, exactly 74 gloves survived 2 10s followed by 2 successful 30s. Exactly 1 pair of gloves survived 2 10s and 3 successful 30s

D) This question actually fails to identify what the intended goal truly is - Maximum survival of items, or maximum potential of items.

Here's the breakdown of 50k of those:

10s	10s	30s	60s	60s	Survived	3 Success	4 Success	5 Success
4820	523	184	187	170	298	87	179	32

10s	10s	30s	30s	60s	Survived	3 Success	4 Success	5 Success
4951	537	160	107	122	252	66	145	7

Basically this is a break down of how many times out of 50,000 each step was met with success. It assumed the following things -
Any 10% failure resulted in discard
Any 30% failure that did not result in destruction kept for future tries.
Any 60% failure was kept for future tries.

Interpreting the results - Two sixties instead of 2 thirties increases chance of overall item survive by over about 18% but the trade off of course is weaker end results since the maximum value in 32 +5 situations is +11. In either situation you're talking about a success probability of 0.014% to 0.064%

Here are simulations of 10 pair of gloves that you succeeded your 10s on already with the additional scrollings:

30x1, 60x2

 Spoiler

30x1, 60x2
# 30s 60s 60s Success Failed 1 Pass Pass Pass 3 0 2 Fail Pass Pass 2 1 3 Pass Pass Pass 3 0 4 Fail Pass Pass 2 1 5 Pass Pass Pass 3 0 6 Fail Pass Pass 2 1 7 Fail Pass Pass 2 1 8 Fail Pass Fail 1 2 9 Pass Pass Fail 2 1 10 Nuked -1 -1

30x2, 60x1

 Spoiler

30x2, 60x1
# 30s 30s 60s Success Failed 1 Pass Nuked -1 -1 2 Fail Fail Fail 0 3 3 Pass Fail Pass 2 1 4 Nuked -1 -1 5 Fail Pass Fail 1 2 6 Fail Fail Pass 1 2 7 Nuked -1 -1 8 Nuked -1 -1 9 Fail Nuked -1 -1 10 Pass Fail Pass 2 1

Note the results of section 1 indicate that you will require approximately 1000 gloves (and scrolls) just to get your 10 gloves that have a base of 6 already and then you lost 1 to 3 of those.

[color="#cc8899"]I hate when math stomps on my hopes and dreams...
Guess I'll just pray for a nicely chaos'd Leather Glove then. Godspeed minidungeons, godspeed![/COLOR]

[color="#cc8899"]I hate when math stomps on my hopes and dreams...
Guess I'll just pray for a nicely chaos'd Leather Glove then. Godspeed minidungeons, godspeed![/COLOR]

Welcome to my misery.
I saved up ~30 ish maple magician shields just to have enough to use as 70% scroll fodder... Now I just need the money to afford 300 70 shield mattack scrolls and for the market to spontaneously provide them for me.

Since I'm more into the cost side of things, I'll introduce more scenarios for price comparison.
1) 10 30 30 10 60, white scrolled last 2 slots: 14 atk glove
1.666 60%+WS
10 10%+WS
3.333 30%
11.111 30%
111.11 10%
Total: 111 gloves, 121 10%, 14.5 30%, 12 White Scrolls
This is only 433 million in scrolls, plus 12 White Scrolls - from previous 2.3 billion, this is cheaper if you can get White Scrolls for less than 160mil each (with previous prices on other scrolls)

2) 10 30 30 30 60, WS 1 slot: 14 atk glove
1.666 WS+60%
3.333 30%
11.11 30%
37.03 30%
370 10%
= 370 gloves, 370 10%, 51.4 30%, 1.6 WS
1.4 billion of scrolls, plus 1.6 white scrolls - off of 2.3 billion, this is cheaper for 450mil or lower WS. I'd say this is definitely worthwhile if you get a 12 atk 1 slot glove...
2a) 10 30 30 30 10, WS 1 slot: 15 atk glove
= 370 gloves, 380 10%, 51.4 30%, 10 WS
1.4 billion of scrolls, 10 white scrolls - no direct comparison in price, but this is the best you can do.

3) 10 30 30 60 60 (white scrolled 60s): 13 atk glove
1.666 60+WS
1.666 60+WS
3.333 30%
11.111 30%
111.11 10%
Since first 3 slots are the same, this is again 433mil base, but only 3.333 WS this time. From previous 1.1 billion, that gives 700m for the White Scrolls = cheaper for 210m or lower WS.

4) 10 30 30 30 60, WS last 2 slots: 14 atk glove
1.666 60%+WS
30% + White Scrolls is more complicated, since they can break too. You'll need 3.333 tries to get a success, but of the ones coming from the next round, any that hit that 35% breakage cannot be used twice.
Used once + break: 35%
Used twice + break: 35%*65% = 22.75%
Used 3x + break: 35%*65%*65% = 14.8%
etc. 4-9.61%,5-6.24%,6-4.06%,7-2.6%
= average of around 2.4 tries per glove.
3.333/2.4 = average number of gloves input to get expected output, or 1.394.

4.63 30%
15.4 30%
154 10%
Total: 154 10%, 23.3 30%, 5 WS
= 594mil + 5 WS, for 2.3bil previous glove -> 340mil or cheaper is better.


Cheaper white scrolls favour the lower base costs which use more White Scroll, higher prices favour the ones that use just a couple.
eg. @ 100m
1) 1.6bil 14 atk
2) 1.56 bil 14 atk
2a) 2.4bil 15 atk
3) 760mil 13 atk
4) 1.1bil 14 atk

@ 50m
1) 1bil 14 atk / 1.4bil 15 atk (10 30 30 10WS 10WS)
2) 1.48bil 14 atk
3) 580mil 13 atk
4) 850mil 14 atk

Comparison in prices to actual 14-16 atk WGs is looking somewhat decent with White Scrolls getting cheaper, and SCG/BWG more expensive..

We must remember that statistics applied to games is a bit different from what we learn from theory. I believe that Nexon's uses a simple Pseudorandom number generator algorithm (PRNG) to generate random numbers applied to damage calculation, skills % to work, scrolls, etc. Remembering that many people found "patterns" in 30% or 70% scrolls, which indicates that the Nexon's PRNG, found its frequency or the seeds used in the generation of numbers is repeated. Well, it is huge and very diverse subject.

I am currently developing software to deal with problems of physics, chemistry and engineering, generate billions of random numbers, using the entropy of the servers to create seeds. After generating the data, then we will start the simulations like how atoms can escape from an optical trap, or optimize the production of a remedy to how much tension can wings of airplanes support, or even the behavior of a coffee shop over time (discrete event simulation).

Sorry about my english, still learning.

Some usefull links:

PRNG
Randomness
Monte Carlo Method
Entropy
Discrete event simulation
Random Seed

I'm afraid that this is not the case. We "all" know a random number isn't "random", but due to all variables we're working with, we know that on average, a 30%-scroll will work 30% of the time, and we can base ourselves on that.

A) In a simulation of 50,000 attempts per your specifications only 533 met your targeted goal. That is 0.01066, or 1.066% (note this is much higher than 10% of 10%, which is 0.01%). Generally if you continued along the premise of your assumption and did 100 scrolls worth of 10%s consecutively, 1 pair of gloves will meet your goal. The actual number of gloves required to meet that goal is estimated between 110 and 150.

10% of 10% is 1%. 0.1 * 0.1 = 0.01 = 1%.
Thus, I have high doubts with your simulations, unless this 50k simulation is scrolling 10%s in a row, where 533 were 2 in a row. Which would be really close to the real thing.

(Though, I like simulations, but they only lead to an approximate probability.)

10% of 10% is 1%. 0.1 * 0.1 = 0.01 = 1%.
Thus, I have high doubts with your simulations, unless this 50k simulation is scrolling 10%s in a row, where 533 were 2 in a row. Which would be really close to the real thing.

That was the stated target of his A) scenario and the simulation bore that out by achieving 1.066%, well within the standard deviation for probability.

[color="#cc8899"]A) with appx 250m (100 10% glove attacks), what are the odds of landing 2 10%s on a single glove, assuming a glove is abandoned if first slot fails.
[/COLOR]

That was the stated target of his A) scenario and the simulation bore that out by achieving 1.066%, well within the standard deviation for probability.

The probability of landing 2 10%s on a single glove, assuming a glove is abandoned if the first slot fails will thus be a bit higher than 1.066% if you have 100 scrolls. But indeed the simulation's correct based on trying to achieve 2 10%s in a row.

Noah