Diablo® III

[Discussion] Crafting Strategies & Odds

Preface
The initial posts have been completely re-done to reflect some of the results of the discussion so far, and more clear ideas around strategies. The purpose here is to put into words a strategy towards upgrades that fully incorporates AH and crafting.

I have updated this page: http://us.battle.net/d3/en/forum/topic/8517952016#3 to include numbers generated for probabilities of crafting upgrades in each slot, and along with that, the expected costs around that for each. More explanations about that will be found in that post.

There is no TLDR, although the closest thing that comes to it will be at the top of page 2 of this thread in which I wrote:

(1) The amount that you craft of each slot is inversely proportional to the odds of crafting an upgrade for that slot
(2) Which slot you choose to upgrade for is determined by which slot has the highest likelihood of upgrade via crafting
(3) Upon determining (1) & (2), the amount that you craft should also be inversely proportional to the availability & affordability of AH upgrades in other slots

Corollary is that I would suggest that the main focus of crafting be DPS since DPS generally costs more than EHP for most monks (especially OWE monks). Focus first on DPS slots (amulets, gloves and bracers) before EHP slots (shoulders and chest).

In that post, case studies were explored to show the complications that one may experience in attempting to apply this strategy.

Introduction
With the introduction of 1.0.7 came crafting, and people have gone crafting crazy. In reading these boards, people have come and shown off their awesome crafts. But more often than that, I’ve also seen people frustrated because they themselves have not been successful with their crafts. I’m not sure if anyone has attempted to put something like this together, so I’m deciding to take a crack at it.

And if you haven’t done so already, I strongly encourage you guys to check out the following posts that deal directly with crafting:
http://us.battle.net/d3/en/forum/topic/7005435884#6 (from Piffle's gearing guide)
http://us.battle.net/d3/en/forum/topic/8505340450?page=2#27 (gotaplanstan's suggestions)
http://us.battle.net/d3/en/forum/topic/8505340450 (Violentine's list of godly crafts)
https://docs.google.com/file/d/0B0gMgiAJ3WsmN3lJWVFfVnJlVTQ/edit?usp=sharing (Chazhang's work on crafting in 1.0.7)

Crafting Approaches / Strategies
Over the course of this thread, there have been two approaches that have been advocated. Discussions around this aspect of crafting began around http://us.battle.net/d3/en/forum/topic/8517952016?page=3#43 in case you are interested in some of the discussion around this. I will describe them as such:

Craft as you go - leave no crafting mats behind
In this approach, the general philosophy is to use up all crafting materials as you find them in the game. The availability / affordability of an AH upgrade for the monk is important, but only with funds left over after crafting is done.

The prime benefit of this approach is that the player maximizes the opportunities that crafting provides - that the sooner you are able to craft an upgrade, the sooner you are able to use it on your toon. The financial cost of crafting is not as noticeable since this is done at the end of each session and the amount of gold spent on crafting is generally absorbed by gold acquired in the run and AH sales from prior runs. This approach also maximizes the possibility of getting an upgrade after each session, and can fuel interest in playing further as more upgrades are upgraded.

The primary drawback is that, while the costs to crafting is hidden, it is still quite present. The average cost to craft BoA averages around 90K per craft. If a player is able to acquire 20-25 DEs in a farming session and associated crafting materials over that timeframe, the player can expect to spend on average 2M after each DE run on crafting alone. Depending on the frequency that a player plays, the costs of crafting do accumulate over time and a player can easily spend at least 10M on crafting in a week without really knowing it. Depending on the player, this could hinder the process of upgrading other items via AH.

In other words, this approach prioritizes opportunity of crafting upgrade > opportunity of AH upgrades (while also being aware that crafting does not come at the exclusion of AH considerations).

Balanced Approach to Crafting
While it is undeniable that crafting is a great source of upgrades and yields the greatest potential of BiS items for each BoA slot, one must consider many different factors when deciding which slots to craft for and how much to craft. For this player, AH upgrades and crafting upgrades are comparable in terms of possibility, and one must make decisions about crafting that will preserve their opportunity to upgrade via AH. Factors to consider include:

(1) Availability of AH upgrades in other slots
(2) Amount of gold in players’ balance
(3) Odds of upgrading BoA slot given already existing gear

Decisions will need to be made about whether to save gold for AH upgrades by choosing to craft less (or maybe even suspending for a period while the player is working on AH upgrades). The decision making process is more complicated in this scenario, as the decision making process is part of the larger strategy of where to find upgrades and how they will find it. There will be periods that crafting is accelerated, and other periods where it will slow down for a variety of factors (as listed above). In this scenario, one must decide on the kind of strategy they want to employ to balance the opportunity costs of crafting vs. opportunity costs of AH upgrades.

Factor (3) is an especially tricky one because, to some degree, I think we all intuitively know that stronger your already-existing gear in each slot is, the less likely it is that you will find an upgrade because what you would quality as an upgrade would become more restrictive the stronger you gear gets. As it becomes more restrictive, the odds of crafting a desired item get exponentially worse and so at some point, one must decide on whether you are throwing good money after bad. While that does not mean you stop crafting, it does mean that one must need to look at crafting as part of a larger upgrade philosophy as it pertains to factors (1) and (2) above.

The law of diminishing returns most certainly applies to crafting and I think we need to take this into account for those players who are dealing with limited resources (gold) and making good decisions on how best to use your gold to maximize your opportunity for gain & upgrade.

The balance of these posts will deal specifically with the dilemmas that people face if they choose to adopt the balanced approach towards crafting since the decisions are more complicated than the craft-as-you-go approach.

The Numbers Behind Crafting
I have finally gotten around to calculating some numbers around crafting, and have compiled them all in this post: http://us.battle.net/d3/en/forum/topic/8517952016#3

From this, I'd like to draw some attention to crafting odds, and by virtue of that, expected costs around crafting upgrades. As I have mentioned earlier, the likelihood of crafting an upgrade in your initial attempts will be quite high, and it will be higher the worse your original gear was. But with each subsequent upgrade, it will become harder to find an upgrade for that slot. And in the numbers I have produced, it will be important to note that the jump from probability & expected cost of an item with 3 desired affixes to 4 desired affixes has a pretty steep jump.

To draw one example to observe: in the case of an amulet (where you don't even worry about the quality of rolls), it goes from 1 chance in 12 to 1 chance in 107. That translates to expected crafting costs from 1.6M to 14M. When you are concerned about quality, top half rolls probability goes form 1 in 96 to t in 1,716. This translates to expected costs from 12.5M to 223M. You will see similar jumps in other items in crafting as well.

Now, I realize that these numbers are not 100% accurate because of some assumptions that I made (about what a desireable combination looks like and that I am assuming that there is no affix weighting). The point of those numbers is to see the kind of jump that it takes the better your quality of gear is, and how much you can expect to have to craft in order to see an upgrade.

Does this mean you it will take that many crafts? Not at all. It could take the amount that I am projecting, it could take much less, or it could take much longer. RNG being the beast that it is, we cannot predict it.

But how we can use the numbers that I have produced is to decide which item produces the most likely odds of crafting an upgrade. As long as we are spending our resources on the item that yields the highest likelihood of an upgrade, this will mean that the projected costs of upgrading that item should cost you the least. And if we have limited amounts of gold on hand, we want to make sure use our gold smartly as it pertains to crafting.
Edited by Nameless#1537 on 5/5/2013 7:10 AM PDT
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Nameless’ Philosophy Towards a Balanced Approach to Crafting:
(1) The amount that you craft of each slot is inversely proportional to the odds of crafting an upgrade for that slot
(2) Which slot you choose to upgrade for is determined by which slot has the highest likelihood of upgrade via crafting (ie, which slot has the lowest expected cost of an upgrade, according to numbers like what you see in this post: http://us.battle.net/d3/en/forum/topic/8517952016#3
(3) Upon determining (1) & (2), the amount that you craft should also be inversely proportional to the availability & affordability of AH upgrades in other slots

Corollary is that I would suggest that the main focus of crafting be DPS since DPS generally costs more than EHP for most monks (especially OWE monks). Focus first on DPS slots (amulets, gloves and bracers) before EHP slots (shoulders and chest).

This may seem extremely simple and intuitive, but I think the considerations get more complicated as soon as you begin to encounter actual situations. For the purposes of clarity, I have considered 4 different simplified scenarios that many may be able to relate to, and how this thought process can apply to different situations.

Case Studies to Illustrate Philosophy in Action
(A) John currently has 40M in his account and he has taken a thorough look at his monk and after evaluating all of his options, determines that he has multiple upgrades that are still affordable in other slots. He budgets those upgrades to be approximately 20M per slot. This leaves him with just enough gold to go after those upgrades. However, the upgrades are not currently available (to be purchased on the bid) in the AH and he refuses to buyout what’s there (which will cost more than 20M per slot). He has also done some crafting on his toon and has yielded some good initial upgrades, but also determined that the likelihood of upgrading those slots has become increasingly unlikely. But the slot that yields the greatest potential for upgrade are gloves, with fewer requirements for most potential. Using the approach, he would determine that:

(1) Odds of crafting upgrades are not likely, so craft a little less than full-bore
(2) Decide to work primarily on gloves to the exclusion of others (for now)
(3) Since his upgrades are very likely, he may need every bit of gold to purchase his upgrades. Saving what he has would be prudent, and he would likely want to continue crafting but ensure that his gold balance stays above 40M to give him every opportunity to purchase those upgrades

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(B) Jane is in a similar bind to John, but in her case, she has 20M in her account, does not have great quality of gear so far, and AH upgrades are very much affordable to the point that she has determined that upgrades can cost 5M per slot over 4 slots. She has not yet begun crafting, so her present items on her toon are mediochre at best, and has determined that all slots need upgrades. Considering the factors above:

(1) Odds of crafting upgrades in BoA slots are highly likely, therefore craft more
(2) If she finds that all slots are equally upgradeable, she can spread her efforts amongst many focusing on DPS upgrades in amulets & gloves first
(3) Her upgrades in AH are also very likely, but they each cost less. In this case, crafting more may not necessarily inhibit her upgrade options via AH, and so on balance, she may be better off crafting more until she finds adequate upgrades in her BoA slots at which point, she may want to revisit the factors to determine her next steps.

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(C) Joe is in a particular bind. He has 100M in his account, but has determined that his next upgrade will actually cost him upwards of 140M. He estimates that he would probably be able to save enough gold on AH sales and suspension of crafting that the upgrade will be affordable in 2-3 weeks of play. He has been crafting all along, and has crafted some very nice upgrades in his BoA slots, but finding that more crafting has not been leading to increasing frequency of upgrades. Based on factors above:

(1) Odds of crafting upgrades in BoA slots are highly unlikely for him at this point, therefore craft less
(2) Joe can likely choose slots according to bang-for-buck in terms of upgrade potential. It’s likely a tossup at this point - no wrong item to work on
(3) The upgrades in AH are there, and not yet affordable (although he could be very lucky and snipe something for less than his budget). In this case, crafting less and saving gold to bid for that upgrade may be prudent.

In this scenario, temporary suspension of crafting for the purposes of saving for that upgrade may be a better strategy and then resume crafting after upgrade is complete.

-----

(D) Josie has an amazing toon. Upper echelon monk, and has nearly BiS items all over her monk. She has very few options when it comes to AH upgrades, and she has determined that the only way for her to upgrade at this point is via crafting. So taking a look at the three factors

(1) Odds of crafting upgrades in BoA slots are minimal at best therefore craft less
(2) It’s a tossup about which items to upgrade. They are all just as likely.
(3) Upgrades in AH are virtually non-existent. And if they do exist, it would require billions of gold to do so. Therefore craft more.

In her scenario, there is also precious little to play for as far as upgrades go. Crafting is the only way, so she can dedicate all of her resources to crafting. In fact, consideration (1) is now moot because of consideration (3).

Other Thoughts
At this point in time, the discussion has been largely qualitative. Numbers have been used minimally and we haven't started using actual crafting odds (for consideration #1 & #2 in my philosophy) in the discussion yet. This technical piece is something I endeavour to work on. I have a methodology in place, but I just need time to put it together. The next page is reserved for conclusions around that, and that may also factor into the discussion from above.

Thanks for reading up to this point. Feel free to leave some feedback at the end of this thread to tell me what you think. I hope that people find this helpful.
Edited by Nameless#1537 on 5/4/2013 7:56 PM PDT
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Appendix: Supporting Mathematics / Numbers
It has taken me a while to put something together that is meaningful, and I think I have finally done it. Not that this was terribly time consuming, but I just needed an hour or two to put this together and I needed to muster up enough motivation to do this.

What I have done is go through item by item, and listed out lists of desired affixes for each and then the number of ways that this can be crafted, and then generate probability numbers off of that. Some things to note in how these numbers were generated:

(1) I have assumed equal affix weighting. I realize that people have strong opinions otherwise, but I don't have any access to information on actual weighting numbers for any of the affixes (the closest thing I have is for amulets, and even then, I am not sure how to apply those numbers to what I have generated.

(2) What is considered a desireable affix, or even desireable combinations -- these are subjective, I realize. But even if you were to substitute or add lines based on what you would put in, I don't think the numbers would shift that much. I picked combinations that made sense to me. I tried to be more inclusive than the average to generate more useful numbers.

(3) The costs that I used to calculate expected costs all assume that you already have the crafting materials, so this is just the fee you pay to the blacksmith or jeweller for crafting. Also, please note that the cost of crafting an amulet also includes the cost of combining gems for the purposes of crafting an amulet.

(4) The numbers do take into account the mutual exclusive nature of the single elemental resists as well as the double-stat rolls. In the case of the double stat rolls, it is assumed that the user would want anything but str/int roll (which accounts for 5 out of 6 desirable double stat rolls).

(5) The ways in which each line was generated was in determining a list of desired affixes, and then determining which kinds of combinations would be considered desirable. I would then plug in some of the numbers into a permutations & combinations calculator found here: http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html and from within that, ensure the when I choose one combination, it also excludes the other desired affixes from counting. This is to ensure that there is no double-counting when I add up the numbers for final numbers.

The purpose in putting these numbers together is to get some kind of an idea of probabilities, so that it can impact our decisions around what to craft and when to craft it. The idea here is not to give a predictor of how many crafts it will take to upgrade (since we cannot really predict RNG), but we can certainly make decisions that will help us craft with the odds, and not against it. So it is primarily used in a comparative basis (between different slots according to your requirements).

So without further ado, here is a link to the spreadsheet that I have put together so far:
https://docs.google.com/spreadsheet/ccc?key=0Aie1WlDfyFCYdEtFRTRpZm9YUjZWc3dnLVhjR3JRanc&usp=drive_web

Just wanted to note that parts of this spreadsheet was modelled after Mandlebarb's spreadsheet that he generated as part of his work on BoA crafting. His spreadsheet can be found here:

https://docs.google.com/spreadsheet/pub?key=0ArooAQ_ASbpjdHRpWnowSTNNcm41ZFVsS09ZUkpwc2c&output=html

And from that, I will go through slot by slot and pull out some key numbers to consider:

Amulet
Prob (At least 2 Desired Affixes) = 1 in 5
Prob (At least 3 Desired Affixes) = 1 in 12
Prob (At least 4 Desired Affixes) = 1 in 107
Prob (At least 5 Desired Affixes) = 1 in 2,290

Expected Cost (At least 2 Desired Affixes) = ~610K
Expected Cost (At least 3 Desired Affixes) = ~1.6M
Expected Cost (At least 4 Desired Affixes) = ~14M
Expected Cost (At least 5 Desired Affixes) = ~298M

Top Half Rolls
Prob (At least 2 Desired Affixes) = 1 in 19
Prob (At least 3 Desired Affixes) = 1 in 96
Prob (At least 4 Desired Affixes) = 1 in 1,716
Prob (At least 5 Desired Affixes) = 1 in 73,277

Expected Cost (At least 2 Desired Affixes) = ~2.4M
Expected Cost (At least 3 Desired Affixes) = ~12.5M
Expected Cost (At least 4 Desired Affixes) = ~223M
Expected Cost (At least 5 Desired Affixes) = ~9.526B

Gloves
Prob (At least 2 Desired Affixes) = 1 in 5
Prob (At least 3 Desired Affixes) = 1 in 12
Prob (At least 4 Desired Affixes) = 1 in 90
Prob (At least 5 Desired Affixes) = 1 in 5,436

Expected Cost (At least 2 Desired Affixes) = ~250K
Expected Cost (At least 3 Desired Affixes) = ~600K
Expected Cost (At least 4 Desired Affixes) = ~4.5M
Expected Cost (At least 5 Desired Affixes) = ~271.8M

Top Half Rolls
Prob (At least 2 Desired Affixes) = 1 in 20
Prob (At least 3 Desired Affixes) = 1 in 96
Prob (At least 4 Desired Affixes) = 1 in 1,444
Prob (At least 5 Desired Affixes) = 1 in 173,967

Expected Cost (At least 2 Desired Affixes) = ~1M
Expected Cost (At least 3 Desired Affixes) = ~4.8M
Expected Cost (At least 4 Desired Affixes) = ~72M
Expected Cost (At least 5 Desired Affixes) = ~8.7B

Bracers
Prob (At least 2 Desired Affixes) = 1 in 3
Prob (At least 3 Desired Affixes) = 1 in 14
Prob (At least 4 Desired Affixes) = 1 in 174
Prob (At least 5 Desired Affixes) = 1 in 24,624

Expected Cost (At least 2 Desired Affixes) = ~165K
Expected Cost (At least 3 Desired Affixes) = ~724K
Expected Cost (At least 4 Desired Affixes) = ~8.7M
Expected Cost (At least 5 Desired Affixes) = ~1.2B

Top Half Rolls
Prob (At least 2 Desired Affixes) = 1 in 13
Prob (At least 3 Desired Affixes) = 1 in 116
Prob (At least 4 Desired Affixes) = 1 in 2,788
Prob (At least 5 Desired Affixes) = 1 in 787,968

Expected Cost (At least 2 Desired Affixes) = ~660K
Expected Cost (At least 3 Desired Affixes) = ~5.8M
Expected Cost (At least 4 Desired Affixes) = ~139M
Expected Cost (At least 5 Desired Affixes) = ~39.4B

Shoulders
Prob (At least 2 Desired Affixes) = 1 in 2
Prob (At least 3 Desired Affixes) = 1 in 5
Prob (At least 4 Desired Affixes) = 1 in 102
Prob (At least 5 Desired Affixes) = 1 in 4,843

Expected Cost (At least 2 Desired Affixes) = ~114K
Expected Cost (At least 3 Desired Affixes) = ~367K
Expected Cost (At least 4 Desired Affixes) = ~7.6M
Expected Cost (At least 5 Desired Affixes) = ~363M

Top Half Rolls
Prob (At least 2 Desired Affixes) = 1 in 6
Prob (At least 3 Desired Affixes) = 1 in 39
Prob (At least 4 Desired Affixes) = 1 in 1,627
Prob (At least 5 Desired Affixes) = 1 in 154,969

Expected Cost (At least 2 Desired Affixes) = ~457K
Expected Cost (At least 3 Desired Affixes) = ~2.9M
Expected Cost (At least 4 Desired Affixes) = ~122M
Expected Cost (At least 5 Desired Affixes) = ~11.6B

Chest
Prob (At least 2 Desired Affixes) = 1 in 6
Prob (At least 3 Desired Affixes) = 1 in 12
Prob (At least 4 Desired Affixes) = 1 in 151
Prob (At least 5 Desired Affixes) = 1 in 3,510

Expected Cost (At least 2 Desired Affixes) = ~829K
Expected Cost (At least 3 Desired Affixes) = ~1.8M
Expected Cost (At least 4 Desired Affixes) = ~22.6M
Expected Cost (At least 5 Desired Affixes) = ~526M

Top Half Rolls
Prob (At least 2 Desired Affixes) = 1 in 22
Prob (At least 3 Desired Affixes) = 1 in 95
Prob (At least 4 Desired Affixes) = 1 in 2,417
Prob (At least 5 Desired Affixes) = 1 in 112,331

Expected Cost (At least 2 Desired Affixes) = ~3.3M
Expected Cost (At least 3 Desired Affixes) = ~14.2M
Expected Cost (At least 4 Desired Affixes) = ~362.5M
Expected Cost (At least 5 Desired Affixes) = ~16.85B
Edited by Nameless#1537 on 5/6/2013 4:32 AM PDT
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FIRST
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oooooooowwwwww my braaaaaain huuuuuurts
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LOL. I know. It's a lot of numbers. But that's why I put in a TLDR section (to be expanded over time). Conclusions will come first, mathematics to "explain" the conclusion comes after.
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kamel get on it and put it in sticky :)
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Nameless, your probability calculations appear to be off.

Mathematics to consider:
Then the probability of rolling one desired affix (say, ChC) is
P(DA) = 1/20 = 0.05 (5%).

Now let’s say you are looking for 2 desired stats (say a duofecta combination ChC & ChD). That would look like this:
P(2DA) = (1/20) * (1/19) = 0.0026315 (0.26%)

[This is operating on the principle that if you need X and Y, then the mathematics around that is P(X) * P(Y), but if you need X or Y, then the mathematics of that is P(X) + P(Y)]

The probability of rolling one desired affix out of five rolls, with twenty mutually exclusive affixes available, is not 1/20. Instead, it's this:

The probability of getting the affix on the first roll
PLUS
The probability of getting it on the second roll
PLUS
The probability of getting it on the third roll
PLUS
The probability of getting it on the fourth roll
PLUS
The probability of getting it on the fifth roll

Or it's this:

1
MINUS
The probability of not getting it on ANY roll

What is that number?

1 - (19/20 x 18/19 x 17/18 x 16/17 x 15/16)
= 1 - 15/20
= 1 - 0.75
= 0.25
= 25%

This is five times more likely than the number you posted.

If your post were a D2 character, you'd have hit level 85 or so, only to find out that you need to reroll. Sorry.
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I think you made a huge mistake where you started the math part by saying if you need 1 affix, then the chance is 1/20th. The chance is actually 1/20th * 5 = 25%, because you have 5 chances to roll it.
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Also, here's the math for getting exactly two of twenty affixes, although I'm confident there's a shortcut somewhere.

2/20 x 1/19 x 18/18 x 17/17 x 16/16 x 5C2 ("5 combination 2," or the number of ways you can combine those 2 rolls, given 5 attempts

= 1/10 x 1/19 x 5 x 4 ÷ 2

= 1/190 x 10

= 1/19

= 5.26%

This is twenty times more likely than the number you calculated.

Anyway, that's enough from me :)
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Vrkhyz just mathed your ar$e!! hahahahaha

tl:dr: luck is everything!

my second pair of gloves i ever rolled are the ones my WD is wearing. trifecta with like over 70 AR. lucky lucky!!!
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bah Blizz RNG is not properly random. Done hundreds of crafts, my 2 best gloves were sequential!

And don't forget about the magic and mystery. It's more fun when you craft and don't know the odds :)
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This is good (embarrassing, but good). I knew I made some mistakes along the way... needed someone like Vrkhyz to correct me. Care to give me the number for "5 combination 3"? I want to try to figure out the numbers, but this is an area of math that has always tripped me up back when I was in university. I'll make the adjustments to my OP. I thought my conclusions were off -- it didn't seem exactly reasonable... so thanks Vrk for the correction. Probability was never my strongest suit when I was in university. :P

But Vrkhyz, that huge initial blunder aside, is the rest of my logic making sense?
Edited by Nameless#1537 on 3/29/2013 7:10 PM PDT
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Vrkhyz I think you have over complicated the situation a bit. We don't need to worry about the chance of getting an affix on a single roll (especially since we will only be able to infer that) what we can find out though is the chance of getting the affix in six rolls or one craft. Then you can use those chances just like listed above to find the odds of getting a particular set of affixes.

To refine this if you track individual crafts with all of the stats, you can enter in not only an affix you want but also a stat range you want to get to a better sense of what it takes to get a perfect craft. Based on the data I collected for vit bracers, I'd say you have a fairly good sense of the odds within 100 crafts for any scenario you want. The only think you need to make sure is that you understand what cannot roll on the same item. e.g. you can't get two elemental resists on the same item, while you can get one resist and one all resist. You can also infer that the chance of getting any one elemental resist is the same as any other elemental resist (This looks to be true) which allows some extra data to be collected. Also it appears atleast on vit bracers that int/str/dex all occur at the same chance so you can effectively triple the information collected here.

I was typically finding that my acceptable results for vit bracers were about 1 in 400 and that my ideal results were 1 in 4000. Given that a 1 in 4000 result is probably around 400 million in expected expense (and I'm not even sure what the volatility of this is...you might craft 8000 or 1200 before you get close). This suggests that top tier found items and even 2nd tier items (the 1 in 1000 craft rate type items) should have more value than they currently do.
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I are not good with math or reading, but I suppose the way things roll is not in any kind of order, and that in the 5 rolls we got on each item, it will try to roll any of the ~20 mods for each of the 5 rolls and that they don't have to be rolled in any particular order. What I mean is that if you don't get average damage on your amulet on the first roll you could still get it on any of the other rolls, and that your chances of getting it on each consecutive roll gets better because there are fewer things to roll against since something else just got taken out of the pool of things to roll against? Maybe that is exactly what you guys have worked into your formulas though, and that you conclude that any mod can roll in any order.
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03/29/2013 06:59 PMPosted by Nameless
But Vrkhyz, that huge initial blunder aside, is the rest of my logic making sense?

Sorry, got distracted by the math and didn't read any further. And I'm going to sleep now because poker drains my brain. But, at nearly $28 per hour during the course of nearly 18 hours with the players in this particular cash game, it's worth the drive. (Won $56 in 2 hours last night. Almost exactly my average to date!)

I like Xoran's point:

03/29/2013 07:03 PMPosted by Xoran
I was typically finding that my acceptable results for vit bracers were about 1 in 400 and that my ideal results were 1 in 4000. Given that a 1 in 4000 result is probably around 400 million in expected expense (and I'm not even sure what the volatility of this is...you might craft 8000 or 1200 before you get close). This suggests that top tier found items and even 2nd tier items (the 1 in 1000 craft rate type items) should have more value than they currently do.

Xoran, are you the one who sent me that Excel spreadsheet for tracking this stuff? If so, you should share it with the group.

BTW, if your ideal roll is a 1-in-4,000 chance, it's 50/50 that you'll get it within 2,700 rolls or thereabouts. There's always a chance to nail something early.

Anyway, I'm too tired to think, so I'm going to bed. Catch up with this thread tomorrow.
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03/29/2013 06:27 PMPosted by Nameless
# of Duofecta = [P(ChC + ChD) or P(ChC + IAS)] * 100 = (0.0026*2)*100 = .52

Should be :
# of Duofecta = [P(ChC + ChD) or P(ChC + IAS) or P(ChD + IAS)] * 100 = (0.0026*3)*100 = .78
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03/29/2013 07:43 PMPosted by yuhhaur
# of Duofecta = [P(ChC + ChD) or P(ChC + IAS)] * 100 = (0.0026*2)*100 = .52

Should be :
# of Duofecta = [P(ChC + ChD) or P(ChC + IAS) or P(ChD + IAS)] * 100 = (0.0026*3)*100 = .78

Is this to account for the ChD & IAS conbination? I did discount that, didn't I? I guess I never valued duofectas that didn't include ChC.

But beyond that, Vrkhyz is saying that my formulation is wrong. Which I freely admit to erring on... I just want to make sure I get this right.

It appears that I may have been mixing up combinatorics with probability theory. :/. Ugh. I may need help getting the first part of my premise right.
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I also did some work on that, which is included in my thread here:

http://us.battle.net/d3/en/forum/topic/7592800637?page=7#130
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My internet sucks and I just lost a post so I'll keep it short. Won't get the spreadsheet up until later. Anyway here are the numbers just cross multiply the probabilities to get the chance. Don't worry about this argument over combinations versus probability since we are looking on a single item basis not a single roll basis.

For vit bracers (we will need to do a similar exercise for other items but some stats such as CC should be the same)
45% single stat rolling (int/dex/str)
10% chance of a double stat roll
15% per elemental resist (only one per item)
11% for all resist
33% for CC
22% for armor
20% for pickup radius

The second thing to consider is if the rolls are linear (i.e. ever value along the range happens equally or not) I don't have enough data for this but it appears that CC is not linear. The range of values for a bracer is 3 to 6. If we look at the 32 I have collected data on we get the following chances

3 crit: 4 times
3.5 crit: 5 times
4 crit: 12 times
4.5 crit: 5 times
5 crit: 1 time
5.5 crit: 2 times
6 crit: 3 times

This distribution appears more like a normal distribution with a long tail to the right as opposed to a linear distribution. I admit that the data is sparse but if 4 of the values 3-4.5 have roughly 80% of the results and 3 of the values 5-6 have about 20% those seem vastly different than the expected 4/7ths 3/7th split that a linear distribution would give you. This could have implications for say a trifecta where if you want good rolls you might be looking at a 1 in 150 to 200 (somewhere betwen 1/5^3 and 1/6^3) chance of a trifecta being a good one with most trifectas falling into a more average range. This would be much different if the distributions were linear as you would probably get a good roll more like 1 out of 30 times (roughly 1/3^3). Anyway we need more data on this.
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