Glove scrolling probability help

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.