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    To Bag or not to Bag: how do I craft a lvl77 item?

    Due to very popular demand, I'll try to compile an overview of everything we know about crafting high-level items and trying to get those elusive lvl77's.

    This post is mainly based on research done by LodWig , Icedin and myself.


    Short summary:

    Crafting with Mastery Level 50 has a 50% chance per item to get an extra item level, up to 6 times. Therefore, you have 1/64 chance of getting a lvl77 item when clicking the button on a lvl71 craft.
    The game also uses a mechanism to ensure you never get too unlucky (or lucky!), known among veterans as the "Gambler's Fallacy Enforcement Mechanism" (GFEM), the "Bag" and the "There is no Bag™". Due to this mechanism, if you have not crafted a 77 for a long time, the odds that your next one is one rise exponentially. However, after just having crafted a 77, the chance of a second one drops to almost zero and starts to slowly rise again the more crafts you do.

    Important note #1
    All of this post only applies to crafting of lvl70 and lvl71 legendary set or unique items, as well as Mastery Level 50.
    If you do a normal legendary, a lower lvl or an uncommon/rare/epic item, it's still 1/64 chance but with fair random dice rolls, you could have 5 in a row or you could have none for 300 crafts.
    Side note: the GFEM applies to both lvl 70 and lvl71 items, but if you select 70 you would be getting a lvl76 at most, not a 77.
    So it's definitely not worth it to try to cheap out, just always go for 71!


    Important note #2
    If you are not yet Mastery Level 50, don't craft any set/unique 70+ legendaries with the hero(es) you plan to use for lvl77 item crafting.
    There is a bug in the game that will lower your odds afterwards once you have finally reached ML50.
    If you did craft set/unique 70+ legendaries with a hero, do not continue to craft with this hero, use a new one after becoming ML50.

    Update 2021-06-08: New experimentation refutes this. It is possible this was simply caused by wrong assumptions in past experiments.
    So in all likelihood, you can safely continue crafting on a hero you crafted on before reaching ML50



    Important note #3
    Do all important crafting on a mobile device. The Random Number Generator of the PC version is known to have some issues with loops etc, so you will risk getting unexpected results.
    More details can be found here: https://forum.makingfun.com/forum/et...players-1-5-34



    The nitty gritty details (for those interested):

    It all started with the observation that crafts of lvl71 legendary set/unique items don't follow the same behaviour as all other "normal" crafts in the game.
    For the "normal" ones, 50% of the outcomes is lvl71, 25% is lvl72, and so on, until 1/64 is 77 on average.

    However for "special" (set/unique legendary lvl71) crafts, the distribution looks very differently. It's 50% lvl72, 25% lvl73, and so on, but still ending at 1/64 for lvl77.
    Interestingly, lvl71 also only has a 1/64 chance.
    After that, players also started noticing that the levels seem to have a sort of "spread" to them.
    You almost never get 4 lvl72s in a row, but similarly you also almost never get 2 lvl75+s in a row.

    These observations mean that "special" crafts are not really random, but there is some mechanism behind them to guide the numbers.
    Think of it like rolling some dice, where the dice have weights inside them that move around to avoid you rolling a number too often in a row.


    A first attempt to explain this was "The Bag".

    "The Bag" is a theory that crafts are not really random, but instead every player is handed a bag of levels, and the game randomly picks on of those levels (without putting it back in). This means you can actually count how many items are left in the bag, and predict the remaining draws.

    2 versions existed: 32 items, and 64 items.
    In the 32 items theory, the idea was that each bag contains 16 lvl72, 8 lvl 73, 4 lvl74, 2 lvl75, 1 lvl76 and 1 "wildcard" item. The "wildcard" is randomly chosen as either a lvl71 or a lvl77.
    The 64 items version was similar, but just a bag of 64 with in there 32 lvl72, 16 lvl73, 8 lvl 74, 4 lvl75, 2 lvl76, 1 lvl71 and 1 lvl77.

    This theory proved to be quite accurate.

    It meant that if you are crafting, and your current "counts" in the 64 item bag model are e.g. 29, 15, 6, 4, 2, 1 and 1, that you can expect the next 6 crafts to still contain 3 lvl72, 1 lvl 73 and 2 lvl74 items.
    You could then choose to "empty the bag" by doing Water Essence crafts instead, or crafting cheaper items...

    Sadly, it turns out "There is no Bag™".

    Too many players were using this, emptying their bags, counting on a high lvl items to come very soon, etc, and sometimes getting burned because the outcome was not correct.
    Many screenshots exist of people with e.g. lvl77 pants with Dodge Rating, Life Regen, Life on Hit and Deflect, because they were certain their next craft would be a lvl72 and it was disposable.



    A shiny new and perfected theory has now appeared, explaining everything nicely and tying it together.
    This mainly thanks to LodWig's tremendous efforts to collect crafting statistics from dozens of players.


    Consider e.g. the crafting data from these 4 unnamed heroes, each with their first 96 crafts plotted:



    We see that there is a sort of "spacing" between the levels. The higher the crafted level, the "longer" it takes for a new one to appear right after a craft with the level.

    We actually observe the game keeping track of how many crafts you do of each level, and increasing/decreasing the odds exponentially to ensure you on average have a nice flat spread.

    So the game uses what we call, the "Gambler's Fallacy Enforcement Mechanism" (GFEM), to ensure you don't get all crafts of the same level at once, but you get them nicely spread with an average of:
    • 1 every 2 items for a lvl72
    • 1 every 4 items for a lvl73
    • 1 every 8 items for a lvl 74
    • 1 every 16 items for a lvl 75
    • 1 every 32 items for a lvl 76
    • 1 every 64 items for a lvl 77
    • 1 every 64 items for a lvl 71


    And the longer it has been since a particular level showed up, the higher the chance will be that the next craft has that level.


    How do we use this information now?

    By using the spacing, we can make some useful statements about your crafts. These are things like:
    • If you just start a new character, you can expect the first craft to have 1/64 chance for a lvl77
    • If you just start a new character, you can expect on average the first lvl77 to come after only 28 crafts (calculated by mass simulation)
    • If you have been doing a lot of crafting, and you have not received any lvl77 in the last 50+ crafts, there is a decent chance you will get a lvl77 soon.
    • If you have been doing a lot of crafting, and you have not received any lvl77 in the last 80+ crafts, there is a very very high chance you will get a lvl77 soon.
    • If you start a new character you manage to craft a lvl77 on there, your next one will likely still take so long it's worth it to just delete the character and create a new one from scratch, that way you'll have a much higher chance of a lvl77 item.
    • If you just crafted a lvl71, don't despair! It's independent of a lvl77, so the odds of your next one being 77 will still increase each craft!
    • If you have created a new character in ANB and it has not crafted any lvl77 in recent history, keep it after the event is over! Transfer it to main account, craft until you get the 77, and then delete it, don't just end the event and let it expire. A lvl77 being coming soon stays part of the hero history when transferred from ANB to main.
    A trick you can also use:
    • Keep track of your crafts.
      • If you have been getting too many 72s/73s, your next couple of items are very likely high(er) level. Adapt accordingly!
      • If you have been getting less 72s/73s than expected, you can count on it you'll get a bunch of them in your next items, so maybe consider not picking the really expensive items...
    And finally a friendly reminder: Craft on Mobile, not on PC.
    Last edited by UmbraDei; 06-08-2021, 08:23 AM. Reason: Important Note #2 seems to be refuted by new experiments

    #2
    * Reserving this post for future use if needed *

    Comment


      #3
      Due to how the game enforces the GFEM, the first 77 is actually expected at around craft 32, but the next 77 is expected at around craft 96 (32+72). This is why you should make fresh crafting characters each time you want to craft a level 77 outside of ANB. The time it takes to level to 70 is much shorter than the time it takes to farm 32 sets of materials.

      Comment


        #4
        Level 70 legendary set/unique items are also part of a “bag” of +item levels, so perhaps you should add something about not crafting level 70s as a way to avoid consuming “bag” contents.

        Comment


        • UmbraDei
          UmbraDei commented
          Editing a comment
          Changed that now, thanks!

        #5
        Wow this is alot of deliciously palatable information,like steak and shrimp with red wine. Only problem is I now have to really consider my toon stable and creating new toons to roll those 77s of which I have had 3-4 in two years. And yes I fall flat into the Important Note#2 as I was newbie happily crafting away at random set items oblivious of all the real math involved. So,can I reset my roll chances with water essence craft and or with new toons?
        ​​​

        Comment


        • UmbraDei
          UmbraDei commented
          Editing a comment
          New toons works: the crafting counts per toon, any "past" crafts when you weren't ML50 are only bound to the toons you crafted them on.

        #6
        Found a new tidbit of info in there, for this venerable Bag Scholar.... regarding the PC RNG inconsistency. I had no idea and have crafted 95% of all my items, ANB or otherwise on PC lol. I do much of my jewelry crafting on Tablet for the speed of use increase. This is interesting for me as I appear to have escaped this fate, at least in my ANB attempts since I started recording my Bag results in Bronze 6. My first ANB period was Gold 5, the month I started playing Eternium, and I had no clue what an ANB was, let alone the crafting bag or methodology lol. Since B-6, I have full records of all 8 ANB's and of each item crafted, in which order, and even the date crafted for notable Items or discrepancies, given Screenshot history. The bulk of the info is catalogued on good old fashioned tree corpses,

        The last 4 ANB's have double records, as I've adopted my roommate's account as well. Out of 12 Toon's run, most of them had completed the full 1st & 2nd "Reliable Bag". Some of these ANB legends would craft on further into the 3rd & 4th bags, where data begins to undulate uncertainly, as if it were imitating me at age 10, attempting to dance with a girl at school, for the first time. Dissimilar to me though, the data didn't puke on the Gym floor, after said accomplishment.

        In fact it's been remarkably accurate, including right down to the even 32-32 mirrored level distribution for 72's - 76's, in 10 of the 12 Toon's records. User error is certainly possible for the 2 inconsistencies, as many of these notes were taken by a somewhat mentally disabled person, me, (according to modern science, it's sad but true lol) after hours of playing late into the night or morning. I've discussed all this on the Forums ad-nauseum, but I actually find the following section of your post to be the most prone for elaboration, if I may be so bold:
        • If you have been doing a lot of crafting, and you have not received any lvl77 in the last 50+ crafts, there is a decent chance you will get a lvl77 soon.
        • If you have been doing a lot of crafting, and you have not received any lvl77 in the last 80+ crafts, there is a very very high chance you will get a lvl77 soon.

        I'm not sure where in my jumbled mess of papers, the actual numbers are, and I know it's somewhere in my forum post history.... but for brevity's sake I calculated the actual constantly growing % likelihood of those lingering 77's appearing, which obviously was bucking the traditional or "normal spacing" of high/low level items. I believe the rate of increased appearance chance started at around 20%, immediately at craft 33, and continuing into the bag, increasing to above 45% by craft 48-50. These numbers were of course based upon my own human compiled notes, but I have since used that data trend to accurately predict the crafting of over 10 level 77 items (mostly weapons, as I believe getting a weapon as your first 77 greatly increases your ranking potential), to within a window of 7-10 crafts. Again I've made a crap ton of forum posts during these ANBs, talking about spamming a specific item 5-10 times in a row, because I knew the probability of a 77 appearing, was near certainly at hand. So far so good, and it's all fascinating stuff that I love to go deeper into every ANB.

        Thank you for the awesome guide to help our fellow gamers, and I'll say the only line I no longer feel is necessarily applicable to crafting logic is this one:
        • If you just start a new character, you can expect on average the first lvl77 to come after only 28 crafts (calculated by mass simulation)
        This was indeed my original belief, based upon early personal statistical analysis. However following an abrupt about face, and now, near constant change in odds, I've found the first 77 to be over 70% likely to appear in the second half of the bag. I however don't have the mass results you likely had access to (jealous btw), as I've only catalogued 12 characters (and 37 bags in total, I think?) worth of ANB crafting sessions, and so my opinion on this could shift back again over time I have however cross referenced my info with many others over the months.

        Regardless, unlike many players, I GREATLY prefer the 77 to appear in the second bag. This is given that, the moment I get past 32 crafted items, I have a binder full of data, showing an increasing and highly accurate window during which the 77 will appear, becoming more clear with each resultant craft. I know the usage of the weighted assertion "highly accurate" is radioactively relative to interpretation lol! However as it is my own assertion, I'll say that it is much, much more accurate than any predictions you can make within the first 32 crafts.

        As the final tangential strand... this actually and very interestingly changes the second half (crafts 33-64) odds-making into utter entropic chaos, when a 77 is actually crafted early in the first 32. MY wildest ANB results happened following a level 77 Malice craft with the 6th or 7th craft. The % chances and pattern theory pretty much can be tossed out the window in these occasions, the unravelling revealing itself in an accelerating fashion, until the pattern resets, upon beginning bag 2.

        I will still do it anyway, of course, because I have both O.C.D. and A.D.D. Thus I will find it intrinsically difficult in each of life's situations, to focus on any specific "Goal", or event... while becoming absolutely unable to ignore any hint of conundrum or hidden pattern in the quilt, so to speak, until its resolution has devoured my every available moment... amused and annoyed with myself I always am

        If you'd like me to delete or move this mass of word soup, that I've strewn on the doorstep of your pretty new post, I'd be happy to. I just wanted to convey my relevant thoughts to the author on this studied subject, that I'm quite interested in. Good luck in Gold friend!
        Last edited by DethStrike; 02-18-2021, 07:47 PM.

        Comment


        • UmbraDei
          UmbraDei commented
          Editing a comment
          Gold is also kept. You should really compare an ANB hero with a "new account with 1 hero slot". If you delete the hero and create a new one, all things in stash, crafting materials, gold etc are kept, as well as Champion Levels. Everything in the hero inventory or equipped gear disappears.

        • Bali_Lenni
          Bali_Lenni commented
          Editing a comment
          In ANB, does the second toon lose all the ability levels (frostbeam/lightning level 1-10,the ones with the Books of learning)...?

          Need to make a decision as I have my first 77 and still 7:45h left in this Bronze.
          A) Is it better to stash and delete know or is it
          B) better to continue normally....get as high as possible with 35 minutes left, then.delete and use the last half hour simply to get comfortably to Lvl70 and craft the 2nd 77 ?

          If all abilities are lost, then B seems to be the better option, if not, A might be the go...?

          Have never made a second toon in ANB and a bit awed and confused on how to do it without any major catastrophes.

        • Bali_Lenni
          Bali_Lenni commented
          Editing a comment
          .....I think.I found the answer in another thread... the abilities are set back to Lvl.1 and ability upgrade slot #2 would also.have to be opened again...seems.logical...

        #7
        Here is a graph done by simulating the results obtained by a cohort of 65536 "krafters". (I call "kraft" a special craft that is submitted to the GFEM.)

        It shows for each kraft rank (x-axis) the number of krafters that got their first 77 on this rank. Each krafter was dismissed exactly after this.

        You can see that a great number got their 77 on kraft #33, and also that at least one krafter got the first 77 on kraft #72...



        Click image for larger version

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        Mobile Only (iPhone 5 / iPad Air 1st gen / iPad Pro 11" 2nd gen)
        Eternium Files

        Comment


          #8
          That's an impressive and super awesome, wealth of knowledge, but with each individual self recording and then reporting I assume, the odds of it being innacurate increase wildly. However the sheer quantity of such aggregate result data being overall representational, increase the odds of accuracy simultaneously. Just the kind of data to drive me completely insane.
          Last edited by DethStrike; 02-18-2021, 07:56 PM.

          Comment


          • UmbraDei
            UmbraDei commented
            Editing a comment
            LodWig indeed showed the data I was talking about, indicating that it's definitely worth it to start new characters for dedicated lvl77 crafting, much better than continuing on existing ones.

          • DethStrike
            DethStrike commented
            Editing a comment
            I couldn't agree more. No level 77 will be as predictable as the one in your first bag, even though it can still be a crapshoot Looking at all those 1st overall crafts cracks me up. 11 of 12 times, I've been able to craft at least one of each of the requisite items, before having to focus on identifying the 77. These results just show how influenced my actions are by confirmation bias, and how risky my "reliable method" is, given a protracted quantity of results over time. In all fairness I admitted as much, given my limited data pool. However I'm not going to start ignoring the train that brought me to predicting and choosing 10 of the last 12 level 77's I've made. If it's ALL luck, then I'm all in, lol.
            Last edited by DethStrike; 02-18-2021, 08:48 PM.

          #9
          +1 on making this thread a sticky guide. This is really useful information. Thanks to UmbraDei, LodWig, and Icedin for your work on this topic!!!

          Comment


          • kurtcabage
            kurtcabage commented
            Editing a comment
            +1

          • DethStrike
            DethStrike commented
            Editing a comment
            Word, +1 more

          #10
          thank u for the effort making guide, will translate skme hard english because i cant understand it.

          乁[ ◕ ᴥ ◕ ]ㄏ

          Comment


          • Travis | Support Mgr.
            Travis | Support Mgr. commented
            Editing a comment
            Please don't quote an entire post when leaving a reply.

          #11
          Those who complain that having a hard time crafting a level 77 gear or two in ANBs can confirm this by just making a list of their crafting activities during the event. You'll be able to learn to adapt, predict and utilize your crafting materials, gold and even gems by doing so.

          Comment


            #12
            what is the point max to 50 if results not always 77!

            Comment


            • UmbraDei
              UmbraDei commented
              Editing a comment
              Because you absolutely need the 50% Master Craft perk. It gives a 1/64 chance of a lvl77.

              Consider if you would only have 40% chance because you've not yet maxed the Mastery Level, then the chance of a lvl77 would be 1/244! And at lower percentages the chance is even a lot worse.

            • Benedicto
              Benedicto commented
              Editing a comment
              If you do not have patience, then RPG games is not fit for you..

            • kurtcabage
              kurtcabage commented
              Editing a comment
              you need to re-read the guide if you don't get it

            #13
            This post is to provide some bit of context and history for the There Is No BagTM idea, which is that the GFEM is not simply picking from a bag. I wrote it in the discord server, circa mid-2020. Then Icedin published a proposal for what could be the algorithm of the GFEM, we discussed its merits and flaws, then UmbraDei joined us with two key ideas, from which we devised an algorithm that we think is very close to the one used (based on simulations and comparison to actual outputs). This algorithm is the one I used for the chart published above.

            The bag model is a model of the behaviour of the "randomness" of the item level you get when crafting a level 71 legendary set item, when your Mastery Level is 50.
            When this is, the Master Crafter perk gives you a 50% chance to gain an extra item level, applying multiple time.
            So, when trying to craft an item level 71, you have 50% chance to get a 71 item, and 50% chance to get a higher item.
            In turn, this item may be a 72 (with 50% chance) or a higher item, etc.
            All in all, according to the theory, you will have 1/2 chance to get a 71, 1/4 chance to get a 72, 1/8 for a 73, 1/16 for a 74, 1/32 for a 75, 1/64 for a 76 and 1/64 for a 77.
            It turns out that for level 71 set (or unique) items, the distribution is skewed in favor of higher levels.
            This, at least, for heroes that have never crafted before, up to a certain unknown limit. A particular case in point: ANB heroes.
            Numerous experiments have shown that for these heroes, the distribution of item levels is very close to: 1/64 71, 1/2 72, 1/4 73, 1/8 74, 1/16 75, 1/32 76, 1/64 77
            Furthermore, it seems the game tries really hard to stick to this distribution, and often, each group of 64 crafts done by a hero contains exactly 1 71, 32 72s, 16 73s, ... , 2 76s, 1 77
            (By "group of 64" here we mean the first 64 crafts, then the next 64 crafts (i.e. crafts 65 to 128), etc.)
            Moreover, more often than not, grouping by packs of 32 shows also an "ideal" distribution: 16 72s, 8 73s, ..., 1 76 and either one 71 or one 77
            Hence, the bag theory was (long (?) ago) that the game (sort of) used a bag of 32 tokens, with levels written on it, showing the ideal distribution, and randomly picked a token in this bag each time you crafted a level 71 legendary set item, to get the final level of the item, throwing the token afterwards. (One of the token was either presenting a level 71 or a level 77)
            When the bag was empty, the game used a new one (with maybe a new choice of 71 or 77)
            Because several experiments were not following this theory, it is now considered only a "model" of how the game choose the levels (akin to a weather model, which forecast the weather, with no certainty but enough accuracy to help you decide to go to the beach or stay at home)
            One big blow to the theory is that if you effectively try to use a bag and pick randomly from it (throwing what you picked), you will not see close to ideal distribution for even smaller bags (16, or 8, even 4)
            It is unknown, to me at least, what is the algorithm used by the game to choose item levels, with a certain randomness in results, but somehow managing to stay so close to the ideal distribution at all time
            But
            When crafting, you can think about the model, when choosing the items and the stats on it.
            For example, if you got a 77 at craft #9, it is unlikely you will have another one before craft #33 (you have "pulled the 77 out of the bag of 32, there are no more left")
            But beware, this is a model, some are well known to have been bitten by it.
            Mobile Only (iPhone 5 / iPad Air 1st gen / iPad Pro 11" 2nd gen)
            Eternium Files

            Comment


              #14
              After we had discovered what could be the GFEM algorithm, I also wrote this, trying to get rid of the ill-conceived Bag Theory. (Which, in my defence, was born after I had observed that my first seven "bag-of-32" were perfect, with one 77 in each.)

              There Is No Bag

              Assuming max Mastery Level, the ideal frequency for level gains from 0 to 6 is
              1/64 | 1/2 | 1/4 | 1/8 | 1/16 | 1/32 | 1/64

              So after 64 krafts (that is, "special" or "in the bag" crafts), the ideal distribution is of course
              1 | 32 | 16 | 8 | 4 | 2 | 1

              and this may be an actual distribution, because all numbers are whole numbers.


              After 32 krafts only, the ideal distribution is
              1/2 | 16 | 8 | 4 | 2 | 1 | 1/2

              and this of course cannot be an actual distribution. In this sense, there cannot be a perfect bag of 32, but we use to call perfect this actual distribution:
              1 | 16 | 8 | 4 | 2 | 1 | 0

              and this one:
              0 | 16 | 8 | 4 | 2 | 1 | 1

              And indeed these two form of so-called perfect distributions do happen a lot.


              You can also consider bags of 16, with ideal distribution
              1/4 | 8 | 4 | 2 | 1 | 1/2 | 1/4

              and call perfect any actual distribution of the form
              ? | 8 | 4 | 2 | 1 | ? | ?


              Again, this so-called perfect distributions happens a lot, but maybe less frequently than perfects 32.

              Whatever the ideal distribution is according to the number of krafts, the Gambler's Fallacy mechanism will try to make so the actual distribution is very close. There is no "grouping" done, *there is no bag*, it's just that by observing the krafts by group of 32 or 64 we see patterns more easily.
              (Edit: The ideal frequency given on top is for "krafts".)
              Last edited by LodWig; 02-20-2021, 12:48 PM.
              Mobile Only (iPhone 5 / iPad Air 1st gen / iPad Pro 11" 2nd gen)
              Eternium Files

              Comment


                #15
                This is my first time posting in the forums. It says at the top of forums that everyone's very first post must first be approved... but I can't find the tab to create a post, and the "Guides and Walkthroughs - PLEASE READ BEFORE POSTING" thread doesn't seem contain any threads that indicate where to start... just a bunch of random topics (it seemed to be designed for people who already know what they're doing). So I randomly picked this threat to make my first post. I don't know what I need to do to get approved to start making posts. I've been playing RP games most of my life (I'm an ancient 52... but SOMEONE has to be the old wizard, right?), and I'm enjoying this game on my smartphone. I just downloaded it onto my PC because the smartphone screen is just to small. However I can't figure out how to link the account. Any advice? I'll just sit here in this dark corner hoping someone will find me and tell me what to go do with myself.

                Comment


                • Nhat
                  Nhat commented
                  Editing a comment
                  No one can make new topics in the Guides sub-forum, admin (Travis) moves topics here after they have been posted elsewhere...

                  Either start in Tavern, for general discussions, or the specific classes sub-forums for class specific questions...

                • Turgeon
                  Turgeon commented
                  Editing a comment
                  The old wizard title is already being hold by Tin Man

                • Turgeon
                  Turgeon commented
                  Editing a comment
                  But welc9me to the game dont be shy to ask question. There is already plenty of answer in the forum but some are outdated.
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