Thoughts on Crafting 2.0

Thanks... I had arrived at some of these numbers logically, but for the life of me, I couldn't figure out why my approach wasn't working. I knew it was wrong, because my issue was related to n Choose k where k was larger than n which is by definition 0. I can see at a glance that you results match what I was expecting, but I'll read the formulas later to figure out where I went wrong. I spent 5+ hours wringing my brain out over this and it probably didn't help that I was getting more and more tired.

The best way I can describe what I had above was that it set the minimum boundary for the probabilities.

Regarding your highlighted section, that could describe your odds at trying to inject better stats into your already "perfect" items.

 

I cannot argue with your math because you've proven it correct too many times, I'm not really questioning it either, but DSO has a way of creating random that doesn't always add up.

We've had 2 versions of their plan in just the last couple of weeks and who knows what they'll say tomorrow during the twitch, what will happen on the test server and then what we end up with. That's on top of whether it works as intended or not.

The first time discussing "losing" 3 items sounded a lot like what DSO does. Now the we keep all 4 (like) items sounds a little too good to be true.

Maybe it's just me being pessimistic and assuming that they'll figure out some way to make us unhappy with this latest "improvement".

Until it hits the live servers, it's all a guess on what could be good or bad.

 

So, another aspect that has yet to be discussed in this thread is trying to improve the number of slots as you move up as opposed to just passing on good stats. This has the greatest impact on those with less ander, or those who want to be wise in how they spend their ander.

To save a bit on typing, here was my thoughts on this when some of the details of Crafting 2.0 were announced.

We still didn't get an answer about how added slots, particularly 5 slot items, will work with this, but I'm sure that a bit of playing around on test server tomorrow will answer this question. That being said, if the assumption holds true, the math above becomes relevant again. At the high end (crafting exos->legendaries and legendaries->legendaries), this is rather important. Since the purpose of this thread is to outline best practices under the new crafting system, I'd be remiss not to bring this up again. Thoughts anyone? Armando?

Oh, and Armando, I finally understood what you did. You did the successive probabilities of each stat and then multiplied that by the n Chose K of the number of arrangements of a set of stats. My brain had started down that path, but didn't think to use n Chose k to account for all the possible permutations of identical stats. I had been thinking (4/16)*(3/16)*(2/16)*(1/16) sort of formula, but then discarded it because it didn't account for the order of the stats. I tip my hat to your expertise on this one.

 

In today's twitch when Greg was explaining slot averaging he used as an example 4 items. One with 5 slots + 1 slot + 1 slot + 1slot = 2 slot avg (8/4). According to this added slots calculate into the average.

I don't have enough resources on any of my TS toons to test crafting so I will be looking forward to what y'all find out.

Luck be with ye,
Mikey,
Tegan

 

But shouldn't this not affect the calculation, as if you use permutation in both the numerator and denominator the result will the same as using combination in numerator and denominator.

 

Greg specifically used, in yesterday's twitch at 27:43, an example with 5 slots in one input item to explain the slot calculation ((1+1+1+5)/4=2). As 5 slots can't be found but only reached by buying at least one, the message is clear.
I am pretty sure Haruki answered this also explicitly during the session. As it is NOT in the video, I think I had seen it as a chat reply (with the official Drakensang account) to some user question, clearly stating that yes, additional bought slots in the inputs will be taken into account for calculating the average (and thus the number of slots in the output). This is also what a moderator in the German feedback thread provided as the current design already some weeks ago.

What has not been disclosed yet, however, is how the rounding will be done. In the worst case, we might have to face a rounding down to the next lower integer, ALWAYS, even if we reach 19/4= 4.75 slots in average.

On the other hand, as you already deduced, it will ALWAYS make sense to buy at least 1 slot for at least 1 input item first (unless you have at least 3.5 slots in average already):
The fact that you already bought slots for the inputs would not be remembered for the resulting item, and you could profit again from the low price for the first additional slot.
And as we can now keep all inputs after reverting, there is no risk in buying slots before crafting.

Of course you would buy exactly enough slots in the inputs to reach the next rounding threshold for the output.
If the rounding is "round half up" (down from x.25, up from x.5 and x.75), you would want to reach an x.5 average (only multiples of 0.25 are possible anyway, due to the division by 4 input items).
If the rounding is "round half down", you would want to reach an x.75 average.
And in the worst case of rounding down always, you would want to reach the x.0 threshold.

The interesting thing is that we can actually start "collecting" slots at improved (green) level, where the cost per slot is only 80% (20 as opposed to 100/4= 25 for the first slot). PLUS, as you have a 25% chance of getting your one specific desired enchantment inherited, we can actually use the mechanism @_Baragain_ described above to get more slots:
Use 1 green item with a "golden" desired stat. Craft it with any 3 other green items of the same item type with 4 slots each, buying additional slots for 20 Andermant to reach the next rounding threshold. Repeat crafting until you get a magic item with your desired stat line and at least 4 slots, for a maximum of 80 Andermants...
(Assume the item with your golden stat line has acually no slot at all. If you combine it with 3 items that have 4 slots each, you could buy 1 additional slot per input for 4 x 20 Andermants and would get ((0+1)+(4+1)+(4+1)+(4+1))/4= 4 slots on the resulting magic.)
If you do this 16 times (1280 Andermants max.), you have the basis to get a legendary item with 4 slots, where you can buy the 5th for another 1600.

Of course, dropped green and blue input items have a risk of initially having no slots at all.
But the above mechanism makes it easy to mitigate that risk by some more "slot farming".

If you ask me, that is almost too easy to be true. If I were BP, I would probably change the cost of slots from a certain price for the n.th ADDITIONAL slot in an item to a fixed price for the n.th slot, no matter how many slots the item had initially - so that the 5th slot would ALWAYS cost 1620/8100/10800/14400 for an improved/magic/extraordinary/legendary item, even if the item had 4 slots from the beginning...

Yeah. The mean thing about it is that we don't actually need to include n choose k in the formula for items with ONLY desired enchantment lines, because n choose n is 1 and thus doesn't have any effect.
As I said, it also took me a while to take that step for items with mixed enchantments.

N choose k is not used in the denominator.
You have to multiply the odds of getting the respective enchantments, and then multiply that by the permutations.
If we use 4 legendary weapons with 8 times damage and 8 times % weapon damage, the chance of getting a resulting weapon with exactly 2+2 of those enchantments is 8/16 * 7/15 * 8/14 * 7/13 * (4 choose 2).

This is rather straight forward for just 2 enchantment types. Anyone up for a challenge? ... Calculate the probability of getting a 2/1/1 item if we use inputs with 8+4+4 enchantments!
This is where MY brain currently says "no, thanks".

 

One downside of crafting 2.0 is now you can have 1 slot on legendary item.
Or even 0.

 

Ty for the explanation..but i have 2 doubts

1)why is it 4P2 and not 8P2 as there are 8 possible enchantments that i want to end up in those 2 slots.

2) in your example shouldn't the odd be multiplied by two permutations as there are 2 separate arrangements of 2 out of 8 and 2 out of 8 , 1 for each enchantment type?

This discussion and maths is more fun to read and do then the crafting and grinding we have to do after the math is complete

That would require your legendary to be crafted from all magic or improved items only with 0 slots..now who would do that

 

The possible enchantments ("left in the pot") get reflected in the odds for picking an individual enchantment - e.g. 8/16 or 7/13.
7/13 means that for the 4th enchantment, there are 7 enchantments in the remaining 13 that would give me the item I am looking at.

The permutations are NOT for the enchantments in the input, but for the enchantments in the output, because the sequence in these is irrelevant. It doesn't matter whether the first and second or first and fourth enchantment are weapon damage, (and respectively the other 2 absolute damage).
These permutations are what you need to consider.
So we have a multiplier of e.g. (3 choose 1) = (3 choose 2) for 1+2 inherited enchantments of a legendary item resulting from 4 pink ones, or of (4 choose 3) = (4 choose 1) for the 1+3 inherited enchantments when crafting 4 legendaries together.
N in (n choose k) is the number of inherited echantments in the output item, k is the number of output enchantments of one specific type (also e.g. desired/unwanted)!

To explain it in detail: you have 16*15*14*13 possible combinations to draw 4 enchantments from a pool of 16. This DOES account for the order!
Now, if you have only 2 different types of stats (8+8) in that pool of 16, you have following possibilities to draw 2+2:
AABB=8*7*8*7
ABAB=8*8*7*7
ABBA=8*8*7*7
BAAB=8*8*7*7
BABA=8*8*7*7
BBAA=8*7*8*7

So, we have to multiply the initial 8*7*8*7 with 4choose2 = 6 to get the actual number of combinations we are looking for, as a fraction of the total 16*15*14*13.
Et voilà!

 

then why are we not multiplying the denominator (total possible out comes) with the same n choose k as they can also be arranged the same way?

 

Who?
I would. XD Remember the stats are the goal not the slots. If i get uber stats on items without slots I would craft them.
They said "new rules" for crafting ... but never mention old rules are staying in game (exos have at least 1 slot and legs at least 2 slots) ... that means you can get legs with 0 slots.


BTW guys ... I hate always to be "party breaker" ... but I have to XD
Your math is correct only in theory ... but not in practice. Because your combinations and permutations apply ONLY if there is no repetition. In practice there will be frequent repetitions ... meaning the possibilities are infinite.
There will be repetitions more often than you would think ... i know this game ... if you are stuck with "bad luck" you are doomed forever.

 

The only repetition excluded by the math so far is that the same input enchantment cannot be used twice in one output item, during the same crafting attempt (and I am pretty sure that's how it is implemented).
Apart from that, every single crafting attempt has the same chances of getting or not getting the "desired" output.
Of course you can be unlucky and get every non-desired output TWICE or even 10 times before you actually happen to get a desired one.
But this does not change the EXPECTATION VALUE of 1/p attempts, where p is the probability we derived above.
Nobody said that there is a guarantee to have your desired item after (expectation value) attempts the latest.

The math is correct, only its RELEVANCE for practice under the circumstance of bad luck can be doubted. xD

 

Now, if Armando or I were really feeling adventurous, we could look at the expected standard deviation to find how many crafts for a given probability you would have to do to ensure a 99.7% (three standard deviations) chance of getting your desired output, assuming a fair PRNG (we all know better when it comes to DSO though). That being said, I'm not too worried about this so I won't be doing that math... I really hate statistics, if truth be told. Put it this way, for the 1/1820 chance (a 4/4 legendary from 4x 1/4 legendaries), you would need to likely do close to 8,000 crafts to be 99.7% sure that somewhere in those 8,000 crafts you got at least one 4/4 legendary. The 1/1820 chance is just the average probability.

 

Exactly. I love math. It can take a very simple thing and overly complicate it, or it can take an overly complicated thing and simplify it.

The math was driving me nuts last night, then it finally hit me. This is just a complicated coin toss. In a coin toss, the odds are always 50-50. Even if the coin lands on heads one hundred times in a row, the odds on the one hundred and first flip are still 50-50.

Each time you revert a craft the odds become the same again. This is what I had in my head the other day but I didn't think it all the way through until late last night.

Example: I want to craft a nice legendary 2h sword. Since we know that we can influence the first 3 enchantments, what we need to do is limit the possible options. This way, we can up the odds to a 25% chance that we get what we want.

Possible 1 ----------- Possible 2 ---------- Possible 3 ---------- Possible 4
damage ------------- damage ------------ damage ------------ % damage
damage ------------- damage ------------ % damage --------- % damage
damage ------------- % damage --------- % damage --------- % damage

As you can see, there are 4 possibilities. However, like the coin toss, any possibility can repeat infinitely and is never effected by the previous attempt(s).

Now one could make the argument that the odds are better than 25% because either possible 2 or 3 could lead to a great weapon dependent on the 2nd part of the crafting.

Like any good gambling feature, if you add a 2nd independent part, the odds get worse not better.

Up until we get to craft 4 leg's together, the random number generating god gets the opportunity to further complicate things.

The last enchantment also has 4 possibilities.

Possible 1 ---------- Possible 2 ---------- Possible 3 ---------- Possible 4
Damage ----------- % damage ---------- Crit ----------------- Crit %

Again, there is a 25% chance of getting what you want, independent of the influenced lines. Once again, this option can repeat as each craft attempt in independent of the other. There is nothing to stop something like crit showing up 5 times in a row, or 10 or 100, or 100,000.

So the argument that if we (in the first 3 choices) get two chances at getting what we want, that the odds become better. It is still discounted because we cannot influence the second part of the equation (random factor).

No matter what, we always retain a 75% minimum chance of not getting what we want.

Until you get 4 good legendary items to influence all 4 enchantments, we are still relying on nothing but pure luck. It will always be the coin toss.

Now if someone is a gambler, they can talk themselves into believing that the more gold they feed into the machine that their odds improve. However, since each pull on the arm is 100% independent, your odds will always stay the same.

Yes, it is 100% better than what we have now, simply because we don't know what influences anything in the crafting process now.

We also control the gem slots, which is a major development (if it stands as explained).

For those of us with average or lower weapons, most of us will end up with something better, simply because we don't need a perfect set of enchantments to improve.

For those wanting to create that god-like weapon, I wish you the best, I really do. Because each time someone gets one, it makes me believe that I can influence my odds and I feed the machine.

 

That is correct. You just described the "Gambler's Fallacy."

 

Not a Gambler's Fallacy ... it is real
It is not quite like you think ... but it is not like i was thinking too.
It is something in the middle. I have tested almost entire day and I made good use of the 30K gold from BP and the gold from the DtU bugged chests
I spent something like 100K gold to craft one staff, one pair of average gloves and one crappy wand .
There are lot of repetitions of the whole group of stats ... but not that much like i previously thought it would be the case.

Oh yes it can
I have tested it and there are repetitions.

 

What !

Do you mean it is possible to get 1 of the 16 lines of the 4 legendary used to craft 1 legendary to appear on all 4 slots of the crafted item? That would lower our odds even further :\ and make the sample space grow from 43k to 65k ! thats 66% increase in sample space .

Edit:

Just read the announcement , you can never inherit all 4 enchantments of the same item.. now this limits/reduces the total possible combinations

 

I had 190k gold left over from the DtU bug a couple months back. That means that I could use gold to compensate for a lack of items. I farmed a handful of green items and could craft them together and revert until I got a good stat line as the random stat, and then I could pass those on. In the end, I spent 165k (and my free 30k on the jesters), and got some very nice items. My favorites were the nearly perfect 2H axe and the amazing % damage torso:



These two items cost me about 100k of that 165k though and I used methods that I'd never use on live server. In some ways, it will be easier. I'll only use a reasonable amount of stats as an input so that I'm not wasting tens of thousands of gold. On the other hand, finding the ingredient items will be so time consuming that it will take months to make one such legendary.

 

I heard, or I think I heard something about future "recipe book", which might channel all possibilities into more desired outcome...

 

During testing, I found myself mainly looking for 2 specific, exceptionally good stat lines out of those 16 input lines.
So what is the probability of having 2 specific lines within the 4 output lines?
It is 2/16 * 1/15 * (4 choose 2) = 5%.
So, we can expect to need 20 attempts in average (at a cost of 222 gold each, without discount) in order to unite 2 golden enchantments from 2 different legendaries in a new one.

On the live servers, I will also focus on building items from the (green) scratch, but I thought this might be a curiosity fact interesting to some people.

I think the recipe book is more some kind of in-game help/documentation, probably very similar to this information here: