I created a spreadsheet to examine the long-term cost of not using the maximum amount of fire when you heat something.
http://imgur.com/c5bvTvJ
- The odds of getting a box are slim to none (probably around 1%) so it's not really worth trying for one. Let's ignore that potential benefit for now.
- At Low and Med you might fail a forge. But it's cheaper to try--so that makes a difference over time.
- For levels 1-3, with the cost difference being only 1.5 to 2 Fire it's worth paying max and trying for a box.
- For levels 4-10 the Medium amount makes the most sense--you will fail occasionally, but will succeed often enough that it will work out in the long run.
- The Low amount is never worth paying. it will cost (on average) 202 more fire per item to reach level 10.
Conclusions:
Paying medium for all nine levels saves an average 33 fire per item.
Paying max for the first three and medium for the rest saves an average 25 fire per item and still gives three chances to win a box.
Side Rant:
Using these numbers and looking at my Forge window, it appears as though I need... 5144 Radiant Fire Crystals to heat all the gear I haven't been able to heat over the past three months. That's a savings of 334 Radiant Fire!
...now all I need is a way to earn 5144 Radiant Fire without paying 72,016 CE. Hmmm... >.>
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NEW UPDATE 2014/03/25
_____OPTIMAL SHINING FIRE CRYSTAL COSTS - 4★ GEAR_____________________________
SkepticRaven has been tracking forge results and has accumulated some useful data on the probability of getting a prize.
The Prize boxes are so rare that it's hard to predict their exact ratio. Radiant Fire is still hard to come by so he needs more 5* forge data. But already he has a usable amount of 4* gear data!
I created another spreadsheet here: http://i.imgur.com/JNAFvCS.png
- At Low and Med you might fail a forge. But it's cheaper to try--so that makes a difference over time.
- Low will fail half of the time. It is still cheaper than Med for most of the 4★ forges--see below.
- You will not earn any prize boxes by heating with the Low or Med amounts.
- SkepticRaven's crafting bonus odds for 4* items are 12.22% +/- 3.45% for a Double Level Up as of 2014/03/25. I factored that in to the end cost of each level.
- The "Lowest" and "Highest" columns reflect the fact that we do not know the exact odds of getting a Double Level Up. Based on current data we are confident it is within this range.
- BE ADVISED: This projected cost assumes that the odds of getting a Double Level Up are the same when using the Medium fire crystal amount and the Max fire crystal amount.
Conclusions:
The medium path costs almost the same amount as the Low path.
Paying the lowest amount for levels 1-7 and the medium amount for levels 7-10 the Medium amount will save an average of 1 to 11 Shining Fire Crystals.
If you do not wish to remember the suggested forge path, it makes sense to take the Medium path the whole way.
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Followup Notes:
Spiral Knights Wiki: If someone wants to put this data into the heat page for the wiki, you have my permission.
Images: I hosted these images on Imgur. Please save copies of the images in case the Imgur service ever disappears.
Thank you SkepticRaven!
72 K CE, if CE price is around 8K Cr, then it would take 5 760 000 cr to get 51K radiants. So that is about 1920 elite RJP runs, or 600 elite FSC runs. of course if you do include the conversion of those tokens into money (40 vana token sells for 30K dark ember), I will still have to do about 400 elite full vana runs to get the money. And I still have about 8 5* items waiting to be heated up. GG, OOO, GG. GG.