Optimal Radiant & Shining Fire Crystal Expense Path --- aka "How to Heat for Less!" 😸 Cheshireccat's Classes

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!

And that is why I love math... and also the reason why I laugh when I say SK is F2P... might be F2P but you will get nowhere (specally now with new forge system)

72k ce its, less tren 200$ XDDD
smart ppl spend that money on NOT F2PLAY games(its 2 years of WoW as variant), where u never saw that P2WIN system

the failure chance is what makes everything crap. if you fail twice in a row, your calculations are already gone. that's why I don't like statistics, because even with those everything can happen.

Time-wise, might it be faster to do arcade on elite than fsc? I mean yeah you might have to run depth 19-22 but you can also just skip almost every monster and go straight to the elevator until d28.
I got 6 radiants from a d28 deconstruction zone last night, just like I have from a creeping colony and vana...

But, Seiran, think of it like this: If you do enough FSC and get enough tokens, you can buy useless 5 star weps and sell them for 30k each....That is enough to get a four star weapon. Or maybe, JK is less time consuming and you can get tokens and sell the items faster.....

Arcade and RJP are less laggy for me, so I usually do those rather than FSC/OCH. Fire animations... I hate them.

OCH sucks for farming radiants. Its like a gremlin Fc.

OCH sucks for farming radiants. Its like a gremlin Fc.

O:CH can be completed roughly as fast as FSC and probably yields a bit more Radiants because the loot is on a lower depth. Do you have nay arguments to back that statement up?

Sorry, perhaps I wasn't clear... you don't save EXACTLY 33 (or 25) Fire per weapon EVERY TIME. These calculations are for a probabilistic average.
Yes, some weapons will fail multiple times and cost more. Some will fail not at all and cost less. But averaged over time... you will save 33 (or 25) Fire (depending on which route you take).
Please take a look at the spreadsheet's image and let me know if I need to clarify my OP.
--Cheshireccat
PS: Hi Krakob! We still need to chat research numbers at some point. :)

So the drop chance for a Forge Box is 1 in 3. I can see where this is going.

The who chance is what?
Are you trolling, or was I really really unclear?
If it's the latter, I sincerely apologize. Also, I direct you to this bit, "The odds of getting a box are slim to none (probably around 1%) so it's not really worth trying for one."
and this bit, "For levels 1-3.... it's worth paying max and trying for a box."
Not that the chance for a forge box is 1 in 3. God that... that would solve all of the fire crystal problems. And all of my Punch problems. It would be like a crafting ouroboros.
--Cheshireccat

@Krakob
I ran a OCH elite run about 10 days ago.
Aside from being more boring than FSC, if had the same exact number of red prize boxes at the end. And the depth was labeled ???, so that didnt help much.
12 red boxes after doing och...rather do FSC. Plus, FSC is easier with optimized set, whereas OCH needs different set.
Only benefit OCH has is more skippable areas (D25 FSC is the death knell for speedrunners). But FSC has nice payout as well.

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
SEE THE OP FOR THE ANALYSIS AND CONCLUSIONS. I EDITED THE OP TO KEEP ALL OF THE USEFUL INFORMATION IN ONE SPOT

Bump.
I feel this should be resurrected given the continuing complaints about radiants.

Thanks, I found this information useful.
Cheers.

I feel like I get burned too often with failed forging, so why would I want to mess with the odds of failure with one of the games rarer natural resources?
Do you know how long it takes to accumulate even the 2nd option of forging? And then fail?
Like all that grinding I just did meant nothing? YOUR TIME MEANS NOTHING.
**** that. Sure it doesn't happen all the time, but are you really telling me you want to gamble those odds because you're impatient enough to use the 100% option? That's exactly what OOO and the game wants you to do. You get burned.

@Paintool
"Sure it doesn't happen all the time, but are you really telling me you want to gamble those odds because you're impatient enough to use the 100% option?"
No. Cheshireccat is stating that on average it will cost less.
With the data in my forge data thread for 5* items heated at 2x crystal multipliers...
2/13 lvl 1, 3/15 lvl 2, 5/14 lvl 3, 1/11 lvl 4, 2/9 lvl 5, 3/9 lvl 6, 2/9 lvl 7, 4/10 lvl 8, 5/12 lvl 9 failed.
...Totaling 970 radiants "wasted" an 1,016 radiants "saved". Net of 46 radiants less using 2x crystals compared to 3x within my dataset. [Large thanks to Cheshireccat for submitting this 2x data, as all mine is 3x].
Does luck play a role in this strategy? Yes. Datapoints 1053-1056 are 4 failed lvl 8 attempts in a row on a single 5* item.
If you have a lot of items to heat, this will on average save you 33 fire per item. Your mileage will vary.

Moral of the story, why take your chances when you can go for an extra mile and have guaranteed chance of success? Haven't castlevania games and all the final fantasies taught you that lesson yet?

Why take your chances? Because on average it saves you fire crystals.
Yes, you have to deal with the disappointment of occasionally failing a forge. You need to suppress this irrational part of your mind with the other part of your mind.
Of course, all of this depends on the rates being what Three Rings says they are. Thus far I have seen no data to the contrary, despite several players (including me) collecting data.
25 radiant over 500, didn't take in double levels...
I upped one item like this... 1>2>4>6>8>10
100% may cost 25 radiant more over time, but it will save it back at some point, it depends when you do your graph and what happened prior to when you did your stats.
They are stats, they are 100% accurate and for a ~5% profit and all stats have a margin of error, that is unknown in this scenario. Odds are you can be the unlucky one and use more fire crystal with stats, or you are the luckiest and it works all the tiime, they are still stats and for that little margin, I think it's insignificant.
At least that's my PoV....
25 radiant is 1 lucky FSC or 2 unlucky one.... and failing a lvl 9 > 10 is 60 radiant down the drain

didn't take in double levels...
Right. To fully understand the optimal heating strategy, we would have to understand how low/medium/high levels of fire crystals affect the chance of double-level-up. Several players are keeping detailed, long-term records, in the hope of figuring out these chances. While we wait to accumulate enough data, this thread assumes that the levels don't affect the double-level-up chance.
They are stats, they are 100% accurate and for a ~5% profit and all stats have a margin of error, that is unknown in this scenario.
Right. That's why several players keep detailed long-term records. More data make that margin of error get smaller and smaller.
25 radiant is 1 lucky FSC or 2 unlucky one.... and failing a lvl 9 > 10 is 60 radiant down the drain
A lot of posters in this thread agree with you. They are willing to throw away a small number of Radiants on every forge, just to avoid throwing away a large number of Radiants occasionally. Even though the latter strategy is more efficient usually.
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.