Which bundles are better in the chase for exclusive artifacts?

I have been hunting down gnomes tiredlessly to grind ancient silver coins to get maximum out of the stellar compass every time it is around. But it is only 50 we can redeem during one round of stellar compass, so often I find myself tempted to head to the shop and purchase a few extra to a few rounds of horoscopes to get a full 60 pieces of schematic fragments.

But with the different bundles available, which is the best? 

It is quickly obvious to the eye that the 1$ bundle in stellar compass is the best value, granting 4 crystal balls per purchase. The next more affordable bundle is 5$ and grants 10, making it twice as costly per crystal ball. 

Now what we are going to investigate is, if these two bundles are the superior, or if perhaps the daily recharge gift, granting a full schematic if purchased 5 times consequently or the Wonderful Treasures. 

To start out by compiling the rewards on stellar compass, we must account for a certain luck rate. We are guaranteed 20 schematic fragment every 100 horoscopes/crystal ball, but often we are lucky to get it sooner. If we estimate a luck rate of say 30%, then we need 210 crystal balls in order to acquire a full schematic. 

Now to establish a baseline reward, then we need 5x 10$ purchases of the Recharge Gifts for a full Schematic. Mind, this one is only available every 14 days, of which 2 rotations potentially aren't of interest to you. So even it being the "most affordble" it may not be the "best". 

For that reason we are going to include Wonderfull Treasurer as our main baseline. This baseline is sorta to actively acquire schematics on a regular basis. This means its for both light spenders as well as more heavy spenders. 

So the wonderfull treasures provides the same cost per schematic at both the 5$ bundle and the 10$. Its not untill the 3rd purchase at 20$ the cost climbs. 

This gives us a full schematic at 75$. 

Now with a baseline we can go ahead and find a breakeven for the luck needed for Stellar Compass to be equally good of a deal compared to just regulary being wonderfull treasures. 

What this gives is for the 1$ dollar stellar compass deal to become "as good" a deal as the wonderfull treasurer the luck rate could be 0%. meaning even if you go 3 whole rounds, spending 300 crystal balls to get 3x20 schematics, it is still as good as buying the wonderfull treasures. 

Then comes the 5$ packages providing 10 crystal balls. Now this is where things get a bit more debateble, but still does provide a clear answer in my opinion. In comparison to the initial stated 30% luckrate, we are sitting at a cost of 105$ for a full schematic. Thats 30$ more than the wonderfull Treasures. So, what you probably should be considering is how quickly do you need more schematics? Cause you are playing a game of dice, since in order for the 5$ to become only AS affordable as wonderfull treasures, you will need to get a whole 50% luckrate. However, I did have that this round of Stellar Compass. I ran through 101 crystal balls and got 2x20 schematics. 

Hope this gave you some clarity to your investments into schematic fragment chests.

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Untill next time!