I'm back!!

I was on a week-long cruise.

Long story short, I didn't not enjoy it as much as staying at home.

Anyways... onto business of this thread!

[SPOILER=What's going on in MapleStory?]I can get that there's Mu Lung Dojo and Monster Carnival 2 and the rest of the works that come with them.

Then I read up on weekly spirit events from Cassandra or something, and the "let's spell crap" event. I even saw the reward lists and the letter drop lists.

There's one thing that I'm perplexed about: 100% GM scrolls. Where are they coming from? o.O Also, am I missing anything else? =D

 Calling all math geeks!

So I tried figuring out on average how many gems/crystals it would take to create an advanced grade. I'm aiming for a general formula, not necessarily a correct model of MapleStory's Maker systems (although that would be nice). I need help verifying that my math is correct.

I started with three equations:

Code:

100C = 75B + 24I + A
I = 10B + (10/7)B = (80/7)B
A = 10I + (10/3)I = (40/3)I

Where C are ungraded gems/crystals, B are basic crystals, I are intermediates, and A being advanced.
The first equation describes the probabilities of getting B, I, and A from C.
The second equation describes the average amount of B needed to make I. This is assuming a 70% success rate for convertion of 10B into I.
The third equation describes the average amount of I needed to make A. 30% success rate this time.

The basic goal is to crunch the first equation into the form x*C = A, which should tell us how many crystals/gems, on average, it takes to get an advanced grade.

I decided to work this two ways: Determining the answer assuming you can't appraise C into A directly (this changes equation 1 to 99C = 75B + 24I), and determining the answer the regular way.

Method 1:

Code:

99C = 75B + 24I
99C = (105/16)I + 24I
99C = (489/16)I
99C = (1467/640)A
[color=Red]43.190184049079754601226993865031[/color]C = A

Method 2:

Code:

100C = 75B + 24I + A
100C = (105/16)I + 24I + A
100C = (489/16)I + A
100C = (1467/640)A + A
100C = (2107/640)A
[color=Red]30.374940673943996203132415757[/color]C = A

As you can see, the results are radically different, and it demonstrates that a single percent in being able to gain an advanced crystal/gem directly from the initial appraisal affects the averages greatly.

Is the logic sound?