Help with some math

[ilovecuttingyews]

I'm planning on using up all of my banked charms during BXPW but I'm uncertain just how many secondaries I'll need to buy because I have a bunch of spirit gems. I've been trying to figure it out, but I just can't get my head around the math of how many of each charm I'll end up using. Is there someone here who can help me out with the math? Below is my inventory of gems / charms. Obviously I'll be using the best gems on blue first, then crimson, etc.

 

Spirit gems:

onyx = 1

dstone = 1

diamond = 4

ruby = 11

emerald = 17

sapphire = 22

 

Charms

blue = 222

crimson = 2258

green = 941

gold = 1322

 

 

[Arceus]

What you can expect based on probabilities:

 

 

Each spirit gem will, on average, last 100 charms.  For example, Onyx has 60 charges, and a .60 chance of working, so 60/.60 = 100.  So, without recycling:

 

100 charms, 60 saved on 1 onyx

100 charms, 50  saved on 1 dstone

400 charms, 160 saved on 4 diamond (this will use up the rest of your blues and put 378 toward crimson)

1100 charms, 330 saved on 11 ruby

1700 charms, 340 saved on 17 emerald (using up the rest of your crimsons and 920 of your greens)

2200 charms left for sapphires for your remaining 21 greens and 1322 golds, saving you ~2 greens and ~132 golds and leaving you with 8 fully charged sapphires and a 9th with some charges.

 

Of course, you probably want to reinvest in charms, which makes it a little more complicated/messy...starting with the blues:

 

After your onyx and dstone used up, 222 - 200 + 110 = 132 blues left.  Using 1 diamond -> 40 saved, 32+40=72 left.  Using another diamond, you will have 40% of 72 left, which is ~29, and still have 28 charges left on the second diamond.  Re-use that, and you have 7 blue charms with two complete diamonds left.  Finish that off and you have 1 fully charged diamond plus one with ~50 charges left on it.

 

The math is going to get to be a mess quite quickly, but hopefully you can see the idea if you wanted to continue calculating.  I'm surprised a spirit gem calculator doesn't exist to take into account re-processing all the leftovers.

[ilovecuttingyews]

Yeah. I know just how messy its getting.

 

I am able to do ot the long way so I won't ask someone to do that for me unless they really love the math. Was just hoping there was a way to avoid brute forcing it.

 

If someone can confirm my math, I'm coming up with 415 blues used.

[Arceus]

Yeah. I know just how messy its getting.

 

I am able to do ot the long way so I won't ask someone to do that for me unless they really love the math. Was just hoping there was a way to avoid brute forcing it.

 

If someone can confirm my math, I'm coming up with 415 blues used.

That sounds about right :).

[ilovecuttingyews]

Thanks!