LK vs Travincal vs Cows - runefinding guide

@T72on1 So what that means is you decide "what chance do I want to find this item?" (I like to use 75%), and then you pull the total runs needed off of his graph. Usually (but not necessarily in this case) the average is 63.2% chance, and that's why drmalawi includes that number in his video, to compare with the old, supposed, average. Another way you can use the graphs is if you say "I've done 8000 runs and still dont have infinity", you can see how unlucky you are.

The point I wanted to make, was to compare how a Binomial/Poisson distribution would look like using the "naive average" given in the guide in the OP compared to the "real deal".

In other words, can we treat 1 Sur as 0.5 Ber? (which is implied in the OP guide)

Answer is: no.

@art_vandelay I could be wrong, but I'm pretty sure the resulting probability distribution from including cubing is no longer a plain binomial distribution (OR a high number/low probability poisson distribution that is essentially the same thing). Been discussing this with malawi on discord a while now. If it's indeed a different shape, it's not a given that 63.2% CL is the average. Would have to derive and find the centroid like i mentioned.

Exactly, the resulting distribution of including cubing is not a Binomial/Poisson.
 
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@drmalawi That sounds good, and your point was made convincingly IMO. I was simply providing more instruction on how to read the graphs. What numbers do you think would be best presented in a summary/guide? I think if you could post your graphs, as well as a table of your runs at the 3 CL benchmarks you listed in your video, it could be helpful as a reference in addition to demonstrating the inaccuracies of previous methods.
 
@drmalawi That sounds good, and your point was made convincingly IMO. I was simply providing more instruction on how to read the graphs. What numbers do you think would be best presented in a summary/guide? I think if you could post your graphs, as well as a table of your runs at the 3 CL benchmarks you listed in your video, it could be helpful as a reference in addition to demonstrating the inaccuracies of previous methods.

A graph say more than 1000 words, and since the difference is biggest at low and high CL, a table should include those cases as well.

25, 50, 65, 75, 85, 90 and 95% could be worth it I guess.

(and have graphs as pictures in spoiler boxes)
 
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@drmalawi @Luhkoh Sorry, I meant the distribution for a series of drops, not for cubing. The underlying probability space is still the same, we're just looking at different variables and their (different) distributions. My background in this stuff is purely theoretical, I never actually used it before I started playing Diablo, so forgive me when I confuse things like this ;)

I don't know which patterns fruit gave you already (I assume all?) but I think RoF could be much more interesting than LK in terms of 'upsets' to runefinding. A while back people seemed to really be interested in finding Cham and Jah in RoF. And after Griffon brought up the idea of RoF running in a tournament setting recently I think this is the best set of chests to analyze.
 
I gave a little explanation of what expected value means in the same post where I put the video. Have fun with that
 
@art_vandelay yes @Fruit quantified the number of gul+ patterns for all the superchests in the game. I don't want to steal his thunder posting it, and it probably doesn't belong in this thread, but I'd be happy to post a summary of the findings if he wants me to, but I figured he'd like to at some point.
 
@drmalawi Great, now I understand it better. Note that I definitely didn't say 'completely' there, as that still is a long way off. Awesome work, thanks a lot !!!

From a perspective of people like me (noobs at statistics), I think we are mainly interested in 'what player setting should I run to get item X from scratch'. With item X mainly being Infinity and Enigma I guess, and to a lesser extent CtA, HotO and maybe Grief.

As someone else noted though, runes aren't the entire story for LK runs, certainly not when doing them with an untwinked character. In that case charms, jewelry, jewels, gems, rares, ... all matter too, and I think you get more of those on /p7 compared to /p5. That needs verification too though.
 
@ffs @art_vandelay
Perhaps this isn't the place, but since it was brought up here:

P5:
Code:
NONLOCKED:

Patterns containing Jewels: 1373
         Total Jewel count: 1388

Patterns containing Charms: 4175
         Total Charm count: 4299


LOCKED:

Patterns containing Jewels: 1474
         Total Jewel count: 1489

Patterns containing Charms: 4512
         Total Charm count: 4658

P7:
Code:
NONLOCKED:

Patterns containing Jewels: 1625
         Total Jewel count: 1649

Patterns containing Charms: 4696
         Total Charm count: 4853


LOCKED:

Patterns containing Jewels: 1760
         Total Jewel count: 1785

Patterns containing Charms: 5050
         Total Charm count: 5226


Note that the fact that "total" is more is because a bunch of patterns have multiple Jewels or Charms. (The counters for Charms include all 3 kinds.)
Definitely not an insignificant difference, I'd say!
 
To be precise for Lower Kurast there's a 19% chance to be locked.

Here's a full list for anyone interested (just ignore the areas that can't spawn chests):
Code:
  8% Rogue Encampment
  8% Blood Moor
  9% Cold Plains
 10% Stony Field
 10% Dark Wood
 11% Black Marsh
 12% Tamoe Highland
  8% Den of Evil
  9% Cave Level 1
 10% Underground Passage Level 1
 10% Hole Level 1
 11% Pit Level 1
  9% Cave Level 2
 10% Underground Passage Level 2
 10% Hole Level 2
 11% Pit Level 2
  9% Burial Grounds
  9% Crypt
  9% Mausoleum
 11% Forgotten Tower
 11% Tower Cellar Level 1
 11% Tower Cellar Level 2
 11% Tower Cellar Level 3
 11% Tower Cellar Level 4
 11% Tower Cellar Level 5
 12% Monastery Gate
 12% Outer Cloister
 12% Barracks
 13% Jail Level 1
 13% Jail Level 2
 13% Jail Level 3
 13% Inner Cloister
 13% Cathedral
 13% Catacombs Level 1
 13% Catacombs Level 2
 14% Catacombs Level 3
 14% Catacombs Level 4
 11% Tristram
 22% The Secret Cow Level
  8% Lut Gholein
 15% Rocky Waste
 15% Dry Hills
 16% Far Oasis
 16% Lost City
 17% Valley of Snakes
 16% Canyon of the Magi
 14% Sewers Level 1
 14% Sewers Level 2
 15% Sewers Level 3
  8% Harem Level 1
 14% Harem Level 2
 14% Palace Cellar Level 1
 14% Palace Cellar Level 2
 14% Palace Cellar Level 3
 14% Stony Tomb Level 1
 14% Halls of the Dead Level 1
 14% Halls of the Dead Level 2
 15% Claw Viper Temple Level 1
 14% Stony Tomb Level 2
 14% Halls of the Dead Level 3
 15% Claw Viper Temple Level 2
 16% Maggot Lair Level 1
 16% Maggot Lair Level 2
 16% Maggot Lair Level 3
 16% Ancient Tunnels
 16% Tal Rasha's Tomb
 16% Tal Rasha's Tomb
 16% Tal Rasha's Tomb
 16% Tal Rasha's Tomb
 16% Tal Rasha's Tomb
 16% Tal Rasha's Tomb
 16% Tal Rasha's Tomb
 16% Tal Rasha's Chamber
 15% Arcane Sanctuary
  8% Kurast Docks
 18% Spider Forest
 18% Great Marsh
 19% Flayer Jungle
 19% Lower Kurast
 19% Kurast Bazaar
 19% Upper Kurast
 20% Kurast Causeway
 20% Travincal
 18% Arachnid Lair
 18% Spider Cavern
 18% Swampy Pit Level 1
 18% Swampy Pit Level 2
 19% Flayer Dungeon Level 1
 19% Flayer Dungeon Level 2
 18% Swampy Pit Level 3
 19% Flayer Dungeon Level 3
 19% Sewers Level 1
 20% Sewers Level 2
 19% Ruined Temple
 19% Disused Fane
 19% Forgotten Reliquary
 20% Forgotten Temple
 20% Ruined Fane
 20% Disused Reliquary
 20% Durance of Hate Level 1
 20% Durance of Hate Level 2
 20% Durance of Hate Level 3
  8% The Pandemonium Fortress
 21% Outer Steppes
 21% Plains of Despair
 21% City of the Damned
 21% River of Flame
 22% The Chaos Sanctuary
  8% Harrogath
 20% Bloody Foothills
 20% Frigid Highlands
 21% Arreat Plateau
 22% Crystalline Passage
 22% Frozen River
 22% Glacial Trail
 22% Drifter Cavern
 21% Frozen Tundra
 22% The Ancients' Way
 22% Icy Cellar
 21% Arreat Summit
 24% Nihlathak's Temple
 24% Halls of Anguish
 25% Halls of Pain
 26% Halls of Vaught
 27% Abaddon
 27% Pit of Acheron
 27% Infernal Pit
 27% Worldstone Keep Level 1
 28% Worldstone Keep Level 2
 29% Worldstone Keep Level 3
 29% Throne of Destruction
  8% The Worldstone Chamber
 33% Matron's Den
 33% Forgotten Sands
 33% Furnace of Pain
 33% Tristram

Note that the chances are the same across difficulties.
 
Using the table of #Jewels & #Charms by Fruit, and the ratio of locked vs nonlocked chests (19% vs 81%)

#Jewels p7: 1675
#Jewels p5: 1407
19% more on p7

#Charms p7 : 4924
#Charms p5 : 4367
12.7% more on p7
 
@Fruit great work. I couldn't find the Ber pattern you mentioned in my screenshots either. The patterns I personally saw were ID 150 and 151 – does this check out with your data?

@drmalawi nice job providing more accurate numbers, certainly interesting how the confidence levels change over the course of many runs. I mean it doesn't change anything in terms of which targets to run for which goal, and the ballbark remains similar... but something to keep in mind for complaining rights. :p
 
@drmalawi nice job providing more accurate numbers, certainly interesting how the confidence levels change over the course of many runs. I mean it doesn't change anything in terms of which targets to run for which goal, and the ballbark remains similar... but something to keep in mind for complaining rights. :p

The ballpark is not similar for low and high CL's. Especially for more than 1 effective Ber.

It is also quite nice to know different CL's in case one get's discouraged after say 2k runs.
"Why haven't I got xyz yet?"
Well, then you check what CL you have so far.
So yeah, complaining rights - and we all know that "complaining helps" ;)

The "you can get it in less or fewer runs" hand-waving about probability in the guide is what my results are supposed to improve.

When I get the correct data for LK chest patterns, I will do CL graphs for basically everything in the guide, like Jah from LK vs. Trav (from my earlier simulations, there is a break-even CL at around 45% and 2k runs of each (under the assumption that one p3 Trav run is more or less identical time as one full LK run).
 
Yeah I understand that, what I'm saying is that if I want to farm Enigma in LK (e.g. untwinked), I will just run it until I have it. Whether I have a X% CL after Y or Z runs will merely dictate the point in time when I'll drop by to complain, if I'm on the wrong side of that number. :D But from what I understand it doesn't have an impact on the decision whether to run LK or another target.

Not to take anything away from your thorough work though. Always cool to see improvements on such theoretical aspects of the game.
 
Yeah I understand that, what I'm saying is that if I want to farm Enigma in LK (e.g. untwinked), I will just run it until I have it. Whether I have a X% CL after Y or Z runs will merely dictate the point in time when I'll drop by to complain, if I'm on the wrong side of that number. :D But from what I understand it doesn't have an impact on the decision whether to run LK or another target.

Not to take anything away from your thorough work though. Always cool to see improvements on such theoretical aspects of the game.

There are more applications than untwinked 99ers etc, people play and farm for different reasons and use this guide as a primarily resource.

It's like saying that the actual drop chance for item X does not matter at all (the only thing that matters is what source have the best chance/time to drop it), since someone who really really wants that item will farm it until they have it anyway.

Well, in the case of Jah - if you can run p3 trav just as fast as an LK run, I would do around 2k trav runs first (or at least prepare doing so) until I switch for LK since the travCL(Jah) > LKCL(Jah) for runs < 2k. But more precise numbers will come when I have the correct LK patterns (and one should study this in two-dimensions, where the max CL contour lines are in the Trav-run, Lk-run space)
 
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@Fruit great work. I couldn't find the Ber pattern you mentioned in my screenshots either. The patterns I personally saw were ID 150 and 151 – does this check out with your data?
Danke, danke. :D

And si, this the the only output when searching for Ber patterns for P7 (not printing junk):
Code:
----------start_seed:  4468
Ber Rune
Wrist Spike
Crossbow
Chain Gloves
Blade Bow
Heavy Crossbow
Antlers
Small Shield
Stygian Pike


----------start_seed: 47052
War Sword
Ber Rune
Ring
Wyrmhide Boots

When I get the correct data for LK chest patterns
Is something like this what you meant?
Code:
Lower Kurast
Kurast Bazaar
Upper Kurast
Sewers Level 1
Sewers Level 2
Durance of Hate Level 3


---------------------------------------------

                              /players 1 & 2

 non-locked chests:

   18 hi patterns

 Patterns with   Ber:   1
                 Sur:   2
                  Lo:   3
                 Ohm:   4
                 Vex:   2
                 Gul:   6


 locked chests:

   19 hi patterns

 Patterns with   Ber:   1
                 Sur:   3
                  Lo:   3
                 Ohm:   4
                 Vex:   2
                 Gul:   6


---------------------------------------------

                              /players 3 & 4

 non-locked chests:

   19 hi patterns

 Patterns with   Ber:   2
                 Sur:   4
                  Lo:   4
                 Ohm:   2
                 Vex:   3
                 Gul:   4


 locked chests:

   22 hi patterns

 Patterns with   Ber:   2
                 Sur:   5
                  Lo:   4
                 Ohm:   2
                 Vex:   3
                 Gul:   6


---------------------------------------------

                              /players 5 & 6

 non-locked chests:

   26 hi patterns

 Patterns with   Ber:   4
                 Sur:   5
                  Lo:   4
                 Ohm:   2
                 Vex:   6
                 Gul:   5


 locked chests:

   28 hi patterns

 Patterns with   Ber:   4
                 Sur:   7
                  Lo:   4
                 Ohm:   2
                 Vex:   6
                 Gul:   5


---------------------------------------------

                              /players 7 & 8

 non-locked chests:

   35 hi patterns

 Patterns with   Ber:   2
                 Sur:   9
                  Lo:   2
                 Ohm:   5
                 Vex:   6
                 Gul:  11


 locked chests:

   35 hi patterns

 Patterns with   Ber:   2
                 Sur:   9
                  Lo:   2
                 Ohm:   5
                 Vex:   6
                 Gul:  11
 
@Fruit exactly, I will start calculating stuff tomorrow or something. Will definitely have some results to publish next week!
 
Good job everyone. I'll include all the improved calculations into the guide and graphs and whatever else is presented once it comes. Goal is to compare LK with Travincal and cows.
 
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