Alchemy Stone Math
Alchemy Stones are interesting because when you craft them using alchemy fragments, you get a portion back when you synthesize them.
It costs 75 alchemy fragments to make 1 alchemy stone, and when you synthesize 3 of them, you get 1 stone back + 35 fragments. We can use this information to predict approximately how many stones you will be able to craft if you have a certain amount of fragments.
This math is assuming that you don't get any stones that you want to keep, if you do, depending on when you keep it, will change the numbers very slightly. Also, this is an estimate, the actual amounts may be off by about 3-5%, but it should help provide an insight into about how many attempts you get.
It costs 75 alchemy fragments to make 1 alchemy stone, and when you synthesize 3 of them, you get 1 stone back + 35 fragments. We can use this information to predict approximately how many stones you will be able to craft if you have a certain amount of fragments.
This math is assuming that you don't get any stones that you want to keep, if you do, depending on when you keep it, will change the numbers very slightly. Also, this is an estimate, the actual amounts may be off by about 3-5%, but it should help provide an insight into about how many attempts you get.
The percent error when comparing the values obtained by 3n/115 to the actual amounts (tested for every multiple of 1000 up to 176,000), we get the following graph:
So as an overall, it does seem relatively accurate, being less than 1% off once you get above 10k fragments. Feel free to check over my math and let me know if there are any errors. I've tested this with decently large sets of alchemy shards and this seems to be accurate.