Calculating Shards

[Lore]

Hey

 

I've been trying to figure out how to work out how many shards you need, when you know the total amount you need, and are swapping your pouches for shards.

My math has gotten a little fuzzy since I finished high school, so this is stumping me >.<

 

To find how many shards from a total amount, first we find the equation for the total shards from a base amount, and then take the inverse of that.

 

We know you get 70% of your shards back

Lets assume you start with 100k shards, which we'll call 'a'

 

so for the amount of shards you have at any time, the equation is

y = a * 0.7 ^ x

 

to find the total amount of shards, at first I tried integrating this: Wolfram Alpha Calculation

That gives 280k shards.

From using excel, I know that the answer is 333,333 shards.

 

The difference between the two is that using excel calculates how many shards you have at each exchange and then adds them up, rather than doing it for every point on the line.. it's like taking the area under a bar graph, vs. under a curved line.

The error margin is the area of the (roughly) triangular shapes between the bars and the curve.

 

So I came up with this:

http://www.wolframalpha.com/input/?i=sum+100000+*+0.7+^+x+x%3D0+to+infinity

 

So to find the inverse of this

 

log10(y) = log10(a) + log10(0.7^x)

log10(a) = log10(y) - x*log10(0.7)

 

 

At this point it might be useful to clarify:

a = starting number of shards

x = number of times you have exchanged the shards (Assuming you used them all before exchanging)

y = the number of shards you were given back after the exchange

 

 

Aand that's as far as I can get on my own.

I can't wrap my head around what method you would need to do this in reverse..

We know how many effective shards we need, but not how many to get there.

[Lore]

Oh. I'm an idiot.

 

I don't need a function at all to go backwards.. if you know the exchange rate, you can use any base number of shards to find out what that shard is effectively worth..

 

 

So to find how many shards you need, it's simply the needed number divided by the effective value.

99 Summoning from 52 with terrorbirds? 2.2m shards

2.2m / 3 1/3 = 660k

660,000 shards. Done.

 

Thanks for all the help tipit ^.^

[Marco]

Glad we could help!

 

 

 

 

That honestly must be the most intelligent question and answer there has ever been in Help & Advice. 

 

You sure you didn't just set yourself up though?  ;-)

 

 

[JoeDaStudd]

The only trouble is it won't be 100% accurate as you will pretty much never use the whole number of shards up. You normally have a remainder this coupled with rounded make it very very hard to have a single formula for the problem.