Mathematicians guide to alchemy.

(disclaimer : if you're a masochist, or a farmville junkie , please consult your doctor before reading this.On second thought , fuck you!)

"Heed this , Alchemists , crafter and weapon enchanters , in all the fantasy worlds out there!"

I've seen many games boast about their crafting/alchemy part of the game mechanism , and how much fun it is to explore the limitless potential of creating your own weapons and potions, but let's be frank here , i never , like n.e.v.e.r. had fun exploring that part of the game. And i assure you , i've played my fair share of RPG's.

Let's bring out the calculator for a moment.
Let's say the game has 30 base ingredients . Using them , you can craft 10 more .Let's say that you have to use 3 different components to craft a new one. Combining these 40 , you can produce 10 extra-super-ultra potions. So , mathematically speaking , you'd use 40 base components in crafting the extra-super-ultra potions.

So , we have the base ingredients , we use unique combination of 3 (the order is not important) of them to make a new one.
The first phase ,
30 base components
combinations of 3

30!
----------- = 4060 .
3!(30-3)!

So , you'll have to click/drag and drop 3 items , 4060 times . Oh , the sheer joy! (I saw that , Farmville junkies.)

But that's not all . With all the new ingredients (10 new ones) You'll have to get back to more of it. Let's say that in order to not repeat youreself , you'll combine 2 of the base ingredients , with each one of the 10 new ones.
So the formula is now

30!
------------ x 10 = 1450.
2!(30-2)!


There we have it. 5510 experiments of joy. Hmm , speaking of joy , you'll fail during crafting , which is roughly about 95% of the time. Your fun sense is (still) tingling?

And that's just this simple scenario , real life examples offer more of the fun .. khm ... I mean more base/cross ingredients , and a combination of potion making AND weapon-gem enchanting AND ingredients for weapon-making. My statistical analysis point out that Japanese RPG's have more of this , than other games , but there are exceptions.

I can honestly say for myself that i ALWAYS look for crafting guides on the net, and sincerely advise you to do the same, and skip all the "fun".