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

[UmbraDei]

Changed that now, thanks!

[CREMATED]

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?

[Oshisin]

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.

[Icedin]

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.

[UmbraDei]

* Reserving this post for future use if needed *

[UmbraDei]

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.